a scratch pad for half-formed thoughts by a liberal political junkie who's nobody special. ''Hard Heads, Soft Hearts'' is the title of a book by Princeton economist Alan Blinder, and tends to be a favorite motto of neoliberals, especially liberal economists.
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Arthur Silber - Once Upon A Time. . .

R.K. Narayan - A Writer's Nightmare

Curiosity

If I had the time and resources I should soon be starting an organization called S.P.C. - Society for the Promotion of Curiosity. . .

. . .The old type of question that an aged lady puts a stranger, "How many children have you? What is your husband's salary? How much has he saved?" is one of the most spontaneous acts on earth. The modern tendency is to shudder at such `personal' questions. What question is worth asking unless it be personal? When it is discredited, naturally, a lot of coldness creeps in, and all intimacy and warmth goes out of human relationship. When two persons meet, they are obliged to talk of the weather, test-scores, ministerial crises and such other impersonal matters, and waste precious hours of existence. . .One may outwardly be engaged in discussing political questions with a friend, while really wanting to know what are the latest antics of that pugnacious brother demanding a share of the ancestral estate. . .one might discourse on comparative religion while one would rather ask of one's hearer if so and so and his wife are still quarreling like wild cats and if not, why not? All this is tabooed in polite company. This is one of the reasons why club-life has become somewhat dull nowadays. Members disappear into the cards room or billiard room or sit morosely reading weekly papers in a corner. . .nothing in their talk which is not found in the day's paper and known to one lakh of persons already.

It seems to me that the old town planning was based on the principle that curiosity must be kept alive. Rows and rows of houses stuck side by side, thin partition walls through which you could follow all the conversation in the next house. . .No one could flaunt suddenly his prosperity or suffer adversity without everyone being aware of all the reasons for it. . .

It is only through curiosity that children learn to understand the world around them, it is only through curiosity that artists and writers gather material for their work, it is only through curiosity that science has progressed. If Newton had ignored the fall of the apple as an unwanted personal question pertaining to the tree and the apple, mankind would probably never have known of gravitation.

C.S. Lewis - Present Concerns

My First School

. . .Whether the hirsute old humbug who owned it would have run the place by espionage if the boys had given him the chance, I do not know. The treacle-like sycophancy of his letters to my father, which shocked me when they came into my hands years afterwards, does not make it improbable. But he was given no chance. We had no sneaks among us. The Head had, indeed, a grown-up son, a smooth-faced carpet-slipper sort of creature apt for the sport; a privileged demi-god who ate the same food as his father though his sisters shared the food of the boys. But we ourselves were (as the Trades Unions say) "solid". Beaten, cheated, scared, ill-fed, we did not sneak. And I cannot help feeling that it was in that school I imbibed a certain indispensable attitude towards mere power on the one hand and towards every variety of Quisling on the other. So much so that I find it hard to see what can replace the bad schoolmaster if he has indeed become extinct. He was, sore against will, a teacher of honour and a bulwark of freedom. . .Of course one must wish for good schoolmasters. But if they breed up a generation of the "Yes, Sir, and Oh, Sir, and Please, Sir brigade", Squeers himself will have been less of a national calamity. . .

. . .What is the moral of this? Not, assuredly, that we should not try to make boys happy at school. The good results which I think I can trace to my first school would not have come about if its vile procedure have been intended to produce them. They were all by-products thrown off of a wicked old man's desire to make as much as he could out of deluded parents and to give as little as could in return. That is the point. While we are planning the education of the future we can be rid of the illusion that we shall ever replace destiny. Make the plans as good as you can, of course. But be sure that the deep and final effect on every single boy will be something you never envisaged and will spring from little free movements in your machine which neither your blueprint nor your working model gave any hint of.

J.R.R. Tolkien - Tree and Leaf

. . .It is easy for the student to feel that with all his labour he is collecting only a few leaves, many of them now torn or decayed, from the countless foliage of the Tree of Tales, with which the Forest of Days is carpeted. It seems vain to add to the litter. Who can design a new leaf? The patterns from bud to unfolding, and the colours from spring to autumn were all discovered by men long ago. But that is not true. The seed of the tree can be replanted in almost any soil, even in one so smoke-ridden (as Lang said) as that of England. Spring is, of course, not really less beautiful because we have seen or heard of other like events: like events, never from world's beginning to world's end the same event. Each leaf, of oak and ash and thorn, is a unique embodiment of the pattern, and for some this very year may be the embodiment, the first ever seen and recognized, though oaks have put forth leaves for countless generations of men.

We do not, or need not, despair of drawing because all lines must be either curved or straight, nor of painting because there are only three “primary” colours. We may indeed be older now, in so far as we are heirs in enjoyment or in practice of many generations of ancestors in the arts. In this inheritance of wealth there may be a danger of boredom or of anxiety to be original, and that may lead to a distaste for fine drawing, delicate pattern, and “pretty” colours, or else to mere manipulation and over-elaboration of old material, clever and heartless. But the true road of escape from such weariness is not to be found in the wilfully awkward, clumsy, or misshapen, not in making all things dark or unremittingly violent; nor in the mixing of colours on through subtlety to drabness, and the fantastical complication of shapes to the point of silliness and on towards delirium. Before we reach such states we need recovery. We should look at green again, and be startled anew (but not blinded) by blue and yellow and red. We should meet the centaur and the dragon, and then perhaps suddenly behold, like the ancient shepherds, sheep, and dogs, and horses— and wolves. This recovery fairy-stories help us to make. In that sense only a taste for them may make us, or keep us, childish.

Recovery (which includes return and renewal of health) is a re-gaining — regaining of a clear view. I do not say “seeing things as they are” and involve myself with the philosophers, though I might venture to say “seeing things as we are (or were)meant to see them” — as things apart from ourselves. We need, in any case, to clean our windows; so that the things seen clearly may be freed from the drab blur of triteness or familiarity—from possessiveness. Of all faces those of our familiares are the ones both most difficult to play fantastic tricks with, and most difficult really to see with fresh attention, perceiving their likeness and unlikeness: that they are faces, and yet unique faces. This triteness is really the penalty of “appropriation”: the things that are trite, or (in a bad sense) familiar, are the things that we have appropriated, legally or mentally. We say we know them. They have become like the things which once attracted us by their glitter, or their colour, or their shape, and we laid hands on them, and then locked them in our hoard, acquired them, and acquiring ceased to look at them.

Of course, fairy-stories are not the only means of recovery, or prophylactic against loss. Humility is enough. . .

. . .Fantasy is made out of the Primary World, but a good craftsman loves his material, and has a knowledge and feeling for clay, stone and wood which only the art of making can give. By the forging of Gram cold iron was revealed; by the making of Pegasus horses were ennobled . . .It was in fairy-stories that I first divined the potency of the words, and the wonder of the things, such as stone, and wood, and iron; tree and grass; house and fire; bread and wine. . .

‘I Can’t Believe What I’m Confessing to You’: The Wikileaks Chats

. . .(02:31:02 PM) Manning: i think the thing that got me the most… that made me rethink the world more than anything
(02:35:46 PM) Manning: was watching 15 detainees taken by the Iraqi Federal Police… for printing “anti-Iraqi literature”… the iraqi federal police wouldn’t cooperate with US forces, so i was instructed to investigate the matter, find out who the “bad guys” were, and how significant this was for the FPs… it turned out, they had printed a scholarly critique against PM Maliki… i had an interpreter read it for me… and when i found out that it was a benign political critique titled “Where did the money go?” and following the corruption trail within the PM’s cabinet… i immediately took that information and *ran* to the officer to explain what was going on… he didn’t want to hear any of it… he told me to shut up and explain how we could assist the FPs in finding *MORE* detainees…
(02:35:46 PM) Lamo : I’m not here right now
(02:36:27 PM) Manning: everything started slipping after that… i saw things differently. . .

posted by Anonymous at 11:55 AM

 
in my inbox today & worth reading:

National Down Syndrome Congress:

Medicaid - States Considering Opting Out

In several states, officials have floated the idea of opting out of the federal Medicaid program. These states include Washington, Texas and South Carolina, Wyoming and Nevada. Medicaid is a jointly funded federal and state program (the federal government matching rates vary from50-60%). Those who qualify can get health insurance, nursing home or other institutional services. States must keep Medicaid open to all who qualify. Most individuals with Down syndrome qualify for Medicaid funding.


Medicaid is the only public funding program currently available for long-term support services for adults with disabilities to live in the community. While Individuals may qualify for these community services, the services are only provided under a Medicaid waiver or “optional services” program. Many individuals with Down syndrome and other disabilities are served under this program, however the state is not required to provide these services and long waiting lists exist.


The types of support services provided under optional services or the Medicaid waiver can help one manage in his or her own home or a living situation with one or two roommates. They include assistance with all the activities of daily living such as shopping, paying bills, decision making assistance, transportation, support to go to work, setting up medical appointments, etc.


The states mentioned above are floating the idea of giving up the federal funding and replacing Medicaid with a narrower program of their own. Gov. Rick Perry (R-TX) has proposed that his state get out of Medicaid in favor of a state-run system. However, it is not clear how a state would provide the community based services needed by adults with disabilities with no federal government assistance. . ."

R.K. Narayan - A Writer's Nightmare (1988)

India and America

. . .On the whole my memories of America are happy ones. I enjoy them in retrospect. If I were to maintain a single outstanding experience, it would be my visit to the Grand Canyon. To call it a visit is not right; a better word is "pilgrimage" - I understood why certain areas of the canyon's outcrops have been named after the temples of Brahma, Shiva and Zoroaster. I spent a day at the canyon. At dawn or a little before, I left my room at El Tovaro before other guests woke up, then took myself to a seat on the brink of the canyon. It was still dark under a starry sky. At that hour the whole scene acquired a different dimension and a strange, indescribable quality. Far down below, the Colorado River wound its course, muffled and softened. The wind roared in the valley; as the stars gradually vanished a faint light appeared on the horizon. At first there was absolute, enveloping darkness. But if you kept looking on, contours gently emerged, little by little, as if at the beginning of creation itself. The Grand Canyon seemed to me not a geological object, but some cosmic creature spanning the horizons. I felt a thrill more mystic than physical, and that sensation has unfadingly remained with me all through the years. At any moment I can relive that ecstasy. For me the word "immortal" has a meaning now. . .

Dorothy L Sayers - Begin Here (1941)

. . .I confess that I view with some uneasiness the attempt to draw up detailed schemes for a "new society"; I am afraid we may fall back into the delusion that so long as we make the schemes the society will make itself. I am particularly distrustful of slogans about "peace, prosperity, and security," because I fear we may again forget the paradoxical nature of these things. . .society is not a kind of detective problem, for which a single, final and complete solution can be found. It is a work, like a work of art, which has to be imagined with vision, and made with intelligence and unremitting labor. This book does not pretend to offer any formula for constructing an Earthly Paradise: no such formula is possible. . .

Arthur Silber on H.L. Mencken & Bradley Manning

posted by Anonymous at 10:07 AM

 
Arthur Silber - An Extraordinary Man

Arthur Silber - Flecks of Light, Points of Understanding, and the Gift of Sight: All Things Are Connected

Gary Farber's post about the Iraq War

"The American national security establishment is hooked on Afghanistan. They won’t walk away. Not in response to Karzai stealing an election, not in response to their own 2011 deadline, and most likely not in 2014 either. . ."

Matthew Yglesias - Walking Away

". . .wake up. We turned the night sky over the Sinai just a few years ago into flame with a gasoline air mixture which incinerated 100,000 retreating Iraqis in a matter of seconds. Only one out of six of those people even had a weapon. . ."

John Taylor Gatto - The Neglected Genius of America: The Congregational Principle and Original Sin

". . .And she musn't be stupid about it! Good will wasn't enough. One had to manage not to be stupid, too."

Agatha Christie Mallowan - The Water Bus

posted by Anonymous at 12:47 PM

 
Paul Krugman - The Age of Diminished Expectations (1989)

The well-being of the economy is a lot like the well-being of an individual. My happiness depends almost entirely on a few important things, like work, love and health, and everything else is not really worth worrying about - except that I usually can't or won't do anything to change the basic structure of my life, and so I worry about small things, like the state of my basement. For the economy, the important things - the things that affect the standard of living of large numbers of people - are productivity, income distribution and unemployment. If these things are satisfactory, not much else can go wrong, while if they are not, nothing can go right. Yet very little of the business of economic policy is concerned with these big trends.

To many readers this list may seem too short. What about inflation or international competitiveness? What about the state of the financial markets or the budget deficit? The answer is that these problems are in a different class, mainly because they have only an indirect bearing on the nation's well-being. For example, inflation (at least at rates the United States has experienced) does little direct harm. The only reason to be concerned about it is the possibility - which is surprisingly uncertain - that it indirectly compromises productivity growth. Similarly, the budget deficit is not a problem in and of itself; we care about it because we suspect that it leads to low national saving, which ultimately leads to low productivity growth. . .

Paul Krugman - Peddling Prosperity (1993)

. . .And yet, however ridiculous the professors may sometimes appear, their work isn't all academic games. After all, everything I just wrote about academic economists could be said equally well about university physicists or medical researchers - but physics and medicine have made startling progress over time. Close up, it's all ego, pettiness and careerism; back up, and you see an enterprise that adds steadily to our knowledge. . .

. . .Other things being equal, it would be better to seek fundamental solutions than to look for a number of ways to make things somewhat better. But it's no use insisting that economic policy face the big issues when you have no good idea about what to do about them. As Raymond Chandler once pointed out, there have been some very bad books written about God, and some very good ones about trying to make a living while staying fairly honest. . .

Paul Krugman - The Return of Depression Economics (1998)

. . .Well, as Robert Solow - the same economist who described total factor productivity as the "measure of our ignorance" - once pointed out, efforts to explain differences in economic growth rates typically end in a "blaze of amateur sociology." Which is not to say that such sociological speculations may not be right. . .

Paul Krugman's article endorsing Kathleen Brown for California Governor (1994)

. . .The larger point is that taxes and regulations are only part of what makes for a good business climate, and Wilson doesn't seem to understand this point.

After all, what was the basis of California's past prosperity? Was it a government that did nothing but build prisons? Of course not. California's prosperity was built on the foundation of superb public services--on the nation's best school system, from kindergarten through to its great public universities; a system of roads, ports, water supplies, that was the wonder of the world. . .

Paul Krugman - Baby-Sitting the Economy (1998)

. . .Above all, the story of the baby-sitting co-op tells you that economic slumps are not punishments for our sins, pains that we are fated to suffer. The Capitol Hill co-op did not get into trouble because its members were bad, inefficient baby sitters; its troubles did not reveal the fundamental flaws of "Capitol Hill values" or "crony baby-sittingism." It had a technical problem--too many people chasing too little scrip--which could be, and was, solved with a little clear thinking. . .

. . .But what about Japan--where the economy slumps despite interest rates having fallen almost to zero? Has the baby-sitting metaphor finally found a situation it cannot handle?

Well, imagine there is a seasonality in the demand and supply for baby-sitting. During the winter, when it's cold and dark, couples don't want to go out much but are quite willing to stay home and look after other people's children--thereby accumulating points they can use on balmy summer evenings. If this seasonality isn't too pronounced, the co-op could still keep the supply and demand for baby-sitting in balance by charging low interest rates in the winter months, higher rates in the summer. But suppose that the seasonality is very strong indeed. Then in the winter, even at a zero interest rate, there will be more couples seeking opportunities to baby-sit than there are couples going out, which will mean that baby-sitting opportunities will be hard to find, which means that couples seeking to build up reserves for summer fun will be even less willing to use those points in the winter, meaning even fewer opportunities to baby-sit ... and the co-op will slide into a recession even at a zero interest rate.

And now is the winter of Japan's discontent. Perhaps because of its aging population, perhaps also because of a general nervousness about the future, the Japanese public does not appear willing to spend enough to use the economy's capacity, even at a zero interest rate. Japan, say the economists, has fallen into the dread "liquidity trap." Well, what you have just read is an infantile explanation of what a liquidity trap is and how it can happen. And once you understand that this is what has gone wrong, the answer to Japan's problems is, of course, quite obvious.

Well, maybe not so obvious. The basic problem with the winter co-op is that people want to save the credit they earn from baby-sitting in the winter to use in the summer, even at a zero interest rate. But in the aggregate, the co-op's members can't save up winter baby-sitting for summer use. So individual efforts to do so end up producing nothing but a winter slump.

The answer is to make it clear that points earned in the winter will be devalued if held until the summer--say, to make five hours of baby-sitting credit earned in the winter melt into only four hours by summer. This will encourage people to use their baby-sitting hours sooner and hence create more baby-sitting opportunities. You might be tempted to think there is something unfair about this--that it means expropriating people's savings. But the reality is that the co-op as a whole cannot bank winter baby-sitting for summer use, so it is actually distorting members' incentives to allow them to trade winter hours for summer hours on a one-for-one basis.

But what in the nonbaby-sitting economy corresponds to our coupons that melt in the summer? The answer is that an economy that is in a liquidity trap needs expected inflation--that is, it needs to convince people that the yen they are tempted to hoard will buy less a month or a year from now than they do today.

The diagnosis that Japan is in a liquidity trap--and proposals for inflation as a way out of this trap--has been widely publicized in the last few months. But they have had to contend with a deep-seated prejudice that stable prices are always desirable, that to promote inflation is to cheat the public out of its just reward for saving to create perverse and dangerous incentives. Indeed, some economists and commentators have tried to claim that despite all appearances, Japan is not in a liquidity trap, perhaps even that such a thing can't really happen. But the extended baby-sitting story tells us it can--and that inflation is actually the economically correct way out.

It's worth noting that inflation, while probably the best way, is not the *only* way out of the slump. Anything that encourages people to invest now instead of hoarding for later will work. More "Cash for Clunkers"-style programs, while clunky, would work. When saving and investment cannot be coordinated, either elegantly by the interest rate or through some clunkier mechanism, saving isn't saving - it's hoarding. And while saving is virtuous behavior that will be rewarded in this world and the next, hoarding is not and will not.

John Maynard Keynes excerpt via Brad Delong

There is a respectable and influential body of opinion which… fulminates alike against devaluations and levies, on the ground that they infringe the untouchable sacredness of contract.... Yet such persons, by overlooking one of the greatest of all social principles, namely the fundamental distinction between the right of the individual to repudiate contract and the right of the State to control vested interest, are the worst enemies of what they seek to preserve. For nothing can preserve the integrity of contract between individuals except a discretionary authority in the State to revise what has become intolerable. The powers of uninterrupted usury are great. If the accreations of vested interest were to grow without mitigation for many generations, half the population would be no better than slaves to the other half.... The absolutists of contract... are the real parents of revolution...

Avinash Dixit's article on Krugman (1992).

Deirdre McCloskey - Economical Writing

You will have done some research (this is known as "thinking" and "reading" and "calculating") and are sitting down to write. . .the ancient recipe for success in intellectual pursuits: locate chair; apply rear-end to it. locate writing implement; use it. You may wish to increase the element of surprise by writing standing at a tall desk, as my colleague Gary Fethke does. . .Irrational cheerfulness is hard to teach but good to have for any work. . .

. . .Impenetrable theoretical utterances have prestige in economics. That's sad, because no scientific advance can be expected from such games on a blackboard. . .the result is filigreed boilerplate. The economist will write about the completeness of arbitrage in this way: "Consider two cities, A and B, trading an asset, X. If the prices of X are the same in market A and market B, then arbitrage may be said to be complete." The clear way does not draw attention to its "theoretical" character at all: "New York and London in 1870 both had markets for Union Pacific bonds. The question is, did the bonds sell for the same in both places?"

Paul Krugman - Two Cheers For Formalism

Attacks on the excessive formalism of economics - on its reliance on abstract models, on its use of too much mathematics - have been a constant for the past 150 years. Some of those attacks have come from knowledgeable insiders - from the likes of McCloskey (1997) or even Marshall. . .

. . .Here, then, is a revised version of Marshall's rules:

(1) Figure out what you think about an issue, working back and forth among verbal intuition, evidence, and as much math as you need. (2) Stay with it till you are done. (3) Publish the intuition, the math, and the evidence - all three - in an economics journal. (4) But also try to find a way of expressing the idea without the formal apparatus. (5) If you can, publish that where it can do the world some good.

In short, two cheers for formalism - but reserve the third for sophisticated informality.

I sort of think McCloskey is an economist David Brooks could love.

David Brooks - The Two Cultures

It’s become harder to have confidence that legislators can successfully enact the brilliant policies that liberal technicians come up with. . .It all makes one doubt the wizardry of the economic surgeons and appreciate the old wisdom of common sense: simple regulations, low debt, high savings, hard work, few distortions. You don’t have to be a genius to come up with an economic policy like that.

I guess my response to this, is that the conservative story seems to be we have a fundamental problems in the engine, attempts to go faster will make things worse, and there's no quick fix. The liberal story is that the car is fundamentally fine, it just needs more gas. The liberal story is certainly more easy and, if you like, self-indulgent. But that doesn't mean it isn't true.

The problem with attributing current economic problems with fundamentals is that we are no worse, and probably better, in fundamental terms than we were in 2007. We are more eager to work, more prudent about not squandering our paychecks, than we were in 2007. Yet despite the fundamentals, in that sense, being much better, the outcome is much worse. Why? Because this is not a problem of fundamentals.

In terms of fundamentals, saving is not as fundamental a fundamental as work. Only when saving is channelled into investment is it productive - otherwise it's not really saving, it's just hoarding. Normally we don't have to worry about channelling savings into investment, the interest-rate and other easy mechanisms take care of it, but these are not normal times.

The other problem I have with Brooks's column, is what's so difficult/genius-y about cutting interest-rates and other expansionary moves? It doesn't take a genius to put gas in the car. What does take genius is to build the car, but the US has already done that over 400+ years. What also perhaps takes genius, what indeed seems imposssible for a man of even Obama's ability, is running the car properly without enough gas.

But the main problem I have with Brooks's column is there's something missing from his list of fundamentals: high employment/low unemployment. I have no idea why.

The other thought I have on uncertainty is based on Paul Krugman's old Foreign Affairs piece on Global Glut. What we have is not so much regulatory uncertainty as a failure of imagination in the face of being twice-bitten, thrice-shy. Bitten by the stock bubble and the real estate bubble, and therefore sticking on to whatever we have left like glue. We can't imagine an exciting investment opportunity that doesn't end in tears. An understandable problem, and not one that repealing healthcare is going to fix.

But there are plenty of worthy things to invest in, and, without deifying him, Charlie Munger is a man who knows something about investing, and he recently suggested that now is the right time to fund large-scale government infrastructure projects, with "with special emphasis on becoming energy independent via the sun". Munger is a Republican, and doesn't have a very high opinion of Al Gore, so I would hope Republicans listen to him.

Ben Carson - interviewed by Robert H. Schuller for the "Hour of Power"

. . .interestingly enough you know I wanted to be a psychiatrist for the wrong reasons. Because you know growing up in poverty initially I wanted to be a missionary doctor and I said, "I'm not going to do well as a missionary doctor," because I didn't want to be poor for the rest of my life. So I said I wanted to be a psychiatrist because at least on television they all drove Jaguars, had big plush offices. And fancy houses, and all they did is talk to crazy people all day. And I said ... I said well, you know, I'm doing that anyway. So ... so why not make some money.

But you know I majored in psychology and advanced psyche, but then I started meeting a bunch of psychiatrists. But I discovered very quickly that they don't actually do in reality, what they do on television. Actually the things they do are much more interesting. But it wasn't what I wanted to do.

So I stopped and I assessed my gifts and talents and discovered that what I was really good at was things that involve tremendous eye-hand coordination. The ability to think in three dimensions. You know I was a very careful person. Never knocked things over and said, "Oops" and I loved to dissect things. When I was a child if there was a [already dead!] little animal or bug or something around, I always knew what was inside.

So, you know, I put all that together and I said, "You know you would be a terrific neurosurgeon." And that's how I actually made that choice. . .

RD India interview with Devi Prasad Shetty (2010)

. . .Dr Shetty’s group now does 12 percent of all heart surgeries in India, and he’s known for smartly using these numbers to haggle down the cost of medical equipment—so that patients pay less. . .

. . .Q. Were you a brilliant student?
DS. I was not very studious and had great difficulty with mathematics—still a mystery to me. I was educated in a small-town school. But my drawing teacher was so dedicated, he used to teach me maths too at his home. . .

. . .Q. What is the one medical reform you are rooting for?
DS. Medical education should be made inclusive. Any young doctor who wants to become a heart surgeon or neurosurgeon should be able to become one. What he makes of it is left to him. If we create the infrastructure, we can train ten thousand heart surgeons a year. Why put an artificial barrier? It is exactly like a licence raj, when we only had Ambassador cars. Once we liberalized, we got the world’s best cars. Why not do the same with medical education?. . .

It seems to me that all the "problems", which we as human beings have the ability to do anything about, can be thought of as due to a want of competence, a want of compassion, or a want of good cheer. And competence, it seems to me, can be thought of as having at least six dimensions: emotional, physical, mental, technical, social & spiritual.

Personally leery of saying anything more about competence, except that in my opinion, mental competence includes not only language & math, but some degree of "art" as well, at least the kind of art required for some degree of 1D/2D/3D visualization/imagination/representation.

Update: And, since a pseudonymous blog probably is the one place to speak without knowledge, some speculations on emotional/spiritual competence:

Emotional competence would mean your actions are in some accord with your hierarchy of desires. Spiritual competence would mean your hierarchy of desires is in some accord with the universe.

Emotional competence, stage I: the intention to try to do your best (worth a little)

Emotional competence, stage II: some reasonable confidence in your ability to do some reasonable approximation of your best over some reasonably sustained period of time. (worth a lot)

What proportion of the population is in emotional competence, stage II? Does it vary among times & places?

In ordinary times we get along surprisingly well, on the whole, without ever discovering what our faith really is. If, now and again, this remote and academic problem is so unmannerly as to thrust its way into our minds, there are plenty of things we can do to drive the intruder away. We can get the car out, or go to a party or the cinema, or read a detective story, or have a row with the district council, or write a letter to the papers about the habits of the night-jar or Shakespeare's use of nautical metaphor. Thus we build up a defence mechanism against self-questioning, because, to tell the truth, we are very much afraid of ourselves.

Dorothy L Sayers - What Do We Believe

". . .we must deeply acknowledge certain things to be serious yet retain the power and will to treat them often as lightly as a game. But there will be a time for saying more about this in the next chapter. For the moment I will only quote Dunbar's beautifully balanced advice:

Man, Please thy Maker, and be merry,
And give not for this world a cherry."

C.S. Lewis - The Four Loves

The Mysticism of the East

"Many people in the west think that in my country (India), because of our religions, because of our history, because of I don't know what, somehow we are more in tune with our spirituality, more at one with the forces of Nature. Well. . .we are! So well done, all those people who said that! . . .Now one of the ways in which we Gurus like to express our spirituality is in the form of ancient Sanskrit ragas. Now these are very similar to your Christian hymns, but they're more catchy tunes, with more chippanh. . ."

Guru Maharishi Yogi Goodness - "Goodness Gracious Me"

Reluctant Guru

When I accepted an invitation to become a Visiting Professor at a certain mid-western University, I had no clear notion as to what it meant. I asked myself again and again what does a Visiting Professor do. I also asked several of my friends in the academic world the same question. No one could give me a concrete or a convincing answer and so I contented myself with the thought that a Visiting Professor just visits and professes and if he happens to be in the special category of `DVP' (Distinguished Visiting Professor) he also tries to maintain and flourish his distinguishing qualities. Well, all that seemed to suit me excellently. . .

. . .When the interview appeared in the paper I found it charmingly written but over-emphasizing my mystic aspect!. . .At first it was amusing but day after day I found people on the campus looking at me with awe and wonder, perhaps saying to themselves, "There goes the man who holds the key to mystic life!" . . .A senior professor of the English Department approached me. . ."My student's want to hear you on Indian mysticism."

I told her point blank, "I know nothing about it."

"That shouldn't matter at all," she said. . .

I give here a composite report of my talk to various persons at different times.

Young friend (I said), perhaps you think that all Indians are spiritually preoccupied. We aren't. . .normally we also have to be performing ordinary tasks, such as working, earning, living and breeding. . .

. . .Of course, you are fed up with affluence, gadgets, mobility and organization, and he is fed up with poverty, manual labour, stagnation and disorganization. Your search is for a "guru" who can promise you instant mystic elation; whereas your counterpart looks for a Foundation Grant. The young person in my country would sooner learn how to organize a business or manufacture an atom bomb or an automobile than how to stand on one's head.

As a matter of fact, if you question him, you will find that our young man has not given any serious thought to Yoga and such subjects. . .At the moment the trend appears to be that he is coming in your direction, and you are going in his. So, logically speaking, in course of time, you may have to come to India for technology and the Indian will have to come to your country for spiritual research. . ."

When India Was a Colony

. . .How did a little island so far away maintain its authority over another country many times its size? It used to be said by political orators of those days that the British Isles could be drowned out of sight if every Indian spat simultaneously in that direction. It was a David-Goliath ratio, and Britain maintained its authority for nearly two centuries. How was the feat achieved? Through a masterly organization, which utilized Indians themselves to run the bureaucratic and military machinery. Very much like the Kheddah operations in Mysore forests, where wild elephants are hemmed in and driven into stockades by trained ones, and then pushed and pummelled until they realize the advantages of remaining loyal and useful, in order to earn their ration of sugarcane and rice. Take this as a symbol of the British rule in India.

The Indian branch of the army was well-trained and disciplined, and could be trusted to carry out imperial orders. So was the civil service. . .They turned out to be excellent administrators. They were also educated to carry about them an air of superiority at all times and were expected to keep other Indians at a distance.

I had a close relative in the ICS who could not be seen or spoken to even by members of his family living under the same roof, except by appointment. He had organized his life in a perfect colonial pattern, with a turbaned butler knocking on his door with tea in the morning, black tie and dinner jacket while dining with other ICS men. . .

The ICS was made up of well-paid men, above corruption, efficient and proud to maintain the traditions of the service, but it dehumanized the man, especially during the national struggle for independence. These men proved ruthless in dealing with agitators, and may well be said to have out-Heroded Herod. Under such circumstances, they were viewed as a monstrous creation of the British. An elder statesman once defined the ICS as being neither Indian nor civil nor of service. When Nehru became the Prime Minister, he weeded out many of them. . .

. . .Poverty however, was in the province of the missionary who lived among the lowliest and the lost. Although conversion was his main aim, he established hospitals and schools. . .The street corner assembly was a routine entertainment for us in our boyhood at Madras. A preacher would arrive with harmonium and drum and, facing heavy odds and violent opposition, begin a tirade against Indian gods. . .he could have saved his skin and got a hearing but for a naive notion that he should denigrate our gods as a preparation for proposing the glory of Jesus. . .

Our Scripture master, though a native, was so devout a convert that he would spend the first ten minutes calling Krishna a lecher and thief full of devilry. . .Once, incensed by his remarks, I put the question `If Jesus were a real God, why did he not kill the bad men?' which made the teacher so angry that he screamed, `Stand up on the bench, you idiot.'. . .

The hardiest among the British settlers was the planter who, born and bred in his little village in England, was somehow attracted to India, not to a city and its comforts but to a deserted virgin soil on a remote mountain tract where he struggled and built up, little by little, a plantation and raised coffee, tea and cardamom, which remain our national assets even today. He was firmly settled on his land, loved his work, now and then visiting a neighbour fifty miles away or a country club a hundred miles off. He loved his isolation, he loved the hill folk working on his plantation, learned their language and their habits and became a native in all but name.

R.K. Narayan - "The Writerly Life"

Deep Thought: College-6, a clean comfortable place to get some work done.

Deeper Thought: with towels, soap, and free wake-up calls, but no TV.

The lowest university president salaries of any national chain.

To explain an earlier Deep Thought, "You can't mix sambar with ketchup", like George Costanza, I yearned to combine the two great pleasures of life: the South Indian breakfast & the English breakfast. Alas, it can't be done, and the reason is that you can't mix sambar with ketchup, the combination is just too horrible. The three restaurant-genres which come closest are The South Indian "Military Hotels", the Mumbai Irani Cafes (which I've never been to), and my personal favorite, the Indian Coffee House worker-cooperatives. The Indian Coffee Houses, are, as far as I know, the only restaurants in the world where you can get bread, jam & an egg with South Indian coffee, and for that they have my undying loyalty. Significantly, though they serve South Indian dishes like idly and dosa, they serve them without sambar, only chutney.

To my surprise, I've gotten a few emails in response to this blog, one a very thoughtful, circa-2008 email on Kashmir, which in particular wondered why Kashmiri Muslims had been radicalized since the late 80's, whether that radicalization was due to foreign infilitrators, and what was the situation with the many minority groups in Kashmir: Hindus, Christians, Sikhs, Secular, Bhuddist, etc. FWIW, my reply. In hindsight, I seem to have been just basically borrowing the opinion and analysis of Stephen P. Cohen:

Hi EA,

Thanks for the query, I have to think and research a bit about your questions, and I should emphasize I'm not especially well-informed about what Kashmiris are thinking, even for a lay citizen, because I don't speak or read the relevant languages, except English. To your last question on radicalization, I would say that the deliberate fomenting of terrorism and extremism is responsible for the increase in violence, but not in the alienation and bitterness of the Kashmiri majority. My guess at the right policy, for an Indian, is to lay down these guidelines:

1. No change in international borders, because stability is important in these matters.
2. flexibility on autonomy/other issues
3. laying down the principle that terrorism and killing is not the solution
4. commitment from police/military to hold themselves accountable to minimize killing in dealing with militants, and to have the discipline not to seek revenge on the local population for terrorist attacks.
5. long-term endgame to play for is deligitimization of terrorism and violence, and eventually, turning Kashmir into a demilitarized zone with some autonomous privileges.

But this is just off the top of my head, and I would emphasize I don't have a current read on what all the relevant parties are thinking.

If you want some good background on the issue from an Indian perspective, Rediff produced a series of articles and interviews on Kashmir, in 1999. It's not updated for current events, but it's still useful for background, and as an introduction:

Blood in the snow: Ten years of conflict in Kashmir (1999)

posted by Anonymous at 9:11 AM

 
A thanks to all who have served and sacrificed.

posted by Anonymous at 10:27 PM

 
1 more thought on money vs. time & energy. An individual can increase their economic security by accumulating cash. But a country as a whole cannot increase it's security by merely accumulating cash, it can only do so by producing real output.

As an individual, you can increase your ability to obtain medical care in 2020 by accumulating cash. But you can't increase a society's ability to provide medical care in 2020 by accumulating cash, you can only do so by training researchers, doctors and nurses. No amount of budget-cutting austerity will compensate for a policy that wastes the talents of its citizens, and right now we're wasting, big-time.

Or just read d-squared

. . .5. Households which successfully get out of debt, in general, do it by increasing their household income - either by having a non-working partner take on a job, or by doing overtime, or by changing career to something better paid. That's what Alan Johnson did, when he was on his uppers.

Unlike the rather sickening lectures Margaret Thatcher used to give about housewives and their clever domestic scrimping and saving, this is an analogy between the finances of a single household and those of a country which actually works. When you have a debt/GDP ratio which is too high, this is nearly always because the GDP is too low and needs to be increased, not because the debt has got too high and needs to be decreased. If you have a debt/GDP problem that can't be made better by investment and growth, then it's likely that you have a debt/GDP problem that can't be made better at all - ie, you need to default, a situation which the UK is not even nearly in. [or the US]

A few months in, I'd start showing my man a few straightforward back of the envelope calculations, and maybe even chucking a few debt dynamics finger exercises into his speeches, because I have a canny idea that the man in number 11 is not necessarily in command of his numbers and might be shown up if put in a position of having to do sums in his head (I am guessing that former postmen who have worked with the Byzantine schedule of overtime rates might be quite good at this, plus I seem to remember that Johnson as Work & Pensions Minister did a pretty good number on David Willetts over "the pension crisis", which was a similar combat of neoliberal platitudes versus arithmetic). But the key priority would be to a) get the central intuition lodged into his backbone, and b) set up a sensible and comprehensible counter-narrative to all this dreadful New Austerian nonsense about "money in the kitty" and so on. . .

posted by Anonymous at 9:35 PM

 
A Depressing mone-fairy tale

Princess Investment and Prince Saving need to meet up in order to fully employ their true love, but their only means of connection, Mr. Interest Rate, is in a weakened state and unable to carry out his customary duties. Will Uncle Bernanke, a kindly, avuncular philosopher-wizard (or so we thought) use his special magic to give Mr. Interest Rate the help he so desperately needs? Or, as some have said, is he being prevented from acting by the likes of Gríma "Wormtongue" Hoenig?

Update: This is a pretty rotten story, it must be said. Unfortunately, it has the virtue of being true.

posted by Anonymous at 3:53 PM

 
An 11/10 addition to my post-election post:

The other thing I think about the last two years, is that clearly the dominant idea in American politics at the moment is "Times are tough. Households & businesses are tightening their belts. Governments should too." I think this idea is wrong, and the reason it's wrong is because we don't, in everyday life, ask questions about what money is, namely an intrinsically valueless thing that we, for many good reasons, agree to make a proxy for intrinsically valuable things, like time, space & energy, life, love & joy. To allow the the time and energy of Americans to go to waste, in order to serve the goal of saving money, is confused thinking.

The sentiment "Americans, including government, need to save more and spend less", on reflection, doesn't really make sense. What does make sense is that Americans, and everyone else, should make better use of their limited amounts of time and space and energy, to say nothing of their life, love and joy.

It's worth noting that, according to certain odd people who have cropped up from time to time, money can't buy life, or love, or joy. But at the very least it can buy very tolerably serviceable substitutes, and if those oddballs were so smart, why weren't they rich?

posted by Anonymous at 5:50 PM

 
Euclid for the Impractical Blogger

The Elements. Interactive
Euclid

Book 1

Book 1 Definitions

1. A point is that which has no part.
2. A line is breadthless length
3. The extremities of a line are points
4. A straight line is a line which lies evenly with the points on itself
5. A surface is that which has length and breadth only.
6. The extremities of a surface are lines.
7. A plane surface is a surface which lies evenly with the straight lines on itself
8. A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
9. And when the lines containing the angle are straight, the angle is called rectilineal.
10. When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
11. An obtuse angle is an angle greater than a right angle.
12. An acute angle is an angle less than a right angle.
13. A boundary is that which is an extremity of anything.
14. A figure is that which is contained by any boundary or boundaries.
15. A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another;
16. And the point is called the centre of the circle.
17. A diameter of the circle is any straight line drawn through the center and terminated in both directions by the circle and such a straight line also bisects the circle
18. A semicircle is the figure contained by the diameter and the circumference cut off by it. And the centre of the semicircle is the same as that of the circle.
19. Rectilineal figures are those which are contained by straight lines, trilateral figures being those contained by three, quadrilateral those contained by four, and multilateral those contained by more than four straight lines.
20. Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.
21. Further, of trilateral figures, a right-angled triangle is that which has a right angle, an obtuse-angled triangle that which has an obtuse angle, and an acute angle triangle that which has its three angles acute
22. Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.
23. Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.

Book 1 Postulates

Let the following be postulated:
1. To draw a straight line from any point to any point
2. To produce a finite straight line continuously in a straight line.
3. To describe a circle with any centre and distance.
4. That all right angles are equal to one another.
5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Book 1 Common Notions.

1. Things which are equal to the same thing are also equal to one another.
2. If equals be added to equals, the wholes are equal.
3. If equals be subtracted from equals, the remainders are equal.
[7] 4. Things which coincide with one another are equal to one another.
[8] 5. The whole is greater than the part.

Book 1 Propositions

1. On a given straight line to construct an equilateral triangle. (1.Po1, 1.D15, 1.CN1)
2. To place at a given point (as an extremity) a straight line equal to a given straight line. (1.Po1, 1.1, 1.Po2, 1.Po3, 1.CN3, 1.CN1)
3. Given two unequal straight lines, to cut off from the greater a straight line equal to the less. (1.2, 1.Po3, 1.D15, 1.CN1)
4. If two triangles have the two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be equal to the triangle, and the remaining angles will be equal to the remaining angles respectively, namely those which the equal sides subtend. (1.CN 4)
5. In isosceles triangles the angles at the base are equal to one another, and, if the equal straight lines be produced further, the angles under the base will be equal to one another. (1.Po2, 1.3, 1.Po1, 1.4)
6. If in a triangle two angles be equal to one another, the sides which subtend the equal angles will also be equal to one another.
7. Given two straight lines constructed on a straight line (from its extremities) and meeting in a point, there cannot be constructed on the same straight line (from its extremities) and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively, namely each to that which has the same extremity with it. (1.5)
8. If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they will also have the angles equal which are contained by the equal straight lines.(1.7)
9. To bisect a given rectilineal angle. (1.3, 1.8)
10. To bisect a given finite straight line. (1.1, 1.9, 1.4)
11. To draw a straight line at right angles to a given straight line from a given point on it. (1.3, 1.1, 1.8, 1.D10)
12. To a given infinite straight line, from a given point which is not on it, to draw a perpendicular straight line. (1.Po3, 1.Po1, 1.8, 1.D10)
13. If a straight line set up on a straight line make angles, it will make either two right angles or angles equal to two right angles (1.D10, 1.11, 1.CN2, 1.CN2, 1.CN1)
14. If with any straight line, and at a point on it, two straight lines not lying on the same side make the adjacent angles equal to two right angles, the two straight lines will be in a straight line with one another. (1.13, 1.Po4 & 1.CN1, 1.CN3)
15. If two straight lines cut one another, they make the vertical angles equal to one another. (1.13, 1.13, 1.Po4 & 1.CN1, 1.CN3) Porism: From this it is manifest that, if two straight lines cut one another, they will make the angles at the point of section equal to four right angles.
16. In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. (1.10, 1.3, 1.Po1, 1.Po2, 1.15, 1.4, CN5, 1.15)
17. In any triangle, two angles, taken together in any manner are less than two right angles (1.Po2, 1.16, 1.13)
18. In any triangle the greater side subtends the greater angle. (1.3, 1.16)
19. In any triangle the greater angle is subtended by the greater side. (1.5, 1.18)
20. In any triangle two sides taken together in any manner are greater than the remaining one. (1.5, CN5, 1.19)
21. If on one of the sides of a triangle, from its extremities, there be constructed two straight lines meeting within the triangle, the straight lines so constructed will be less than the remaining two sides of the triangle, but will contain a greater angle. (1.20, 1.16)
22. Out of three straight lines, which are equal to three given straight lines, to construct a triangle: thus it is necessary that two of the straight lines taken together in any manner should be greater than the remaining one. (1.20, 1.3)
23. On a given straight line and a point on it to construct a rectilineal angle equal to a given rectilineal angle. (1.22, 1.8)
24. If two triangles have the two sides equal to two sides respectively, but have one of the angles contained by the equal straight lines greater than the other, they will also have the base greater than the base. (1.23, 1.4, 1.5, 1.19)
25. If two triangles have the two sides equal to two sides respectively, but have the base greater than the base, they will also have the one of the angles contained by the equal straight lines greater than the other. (1.4, 1.24)
26. If two triangles have the two angles equal to two angles respectively, and one side equal to one side, namely, either the side adjoining the equal angles, or that subtending one of the equal angles, they will also have the remaining sides equal to the remaining sides and the remaining angle to the remaining angle. (1.4, 1.4, 1.4, 1.16, 1.4)
27. If a straight line falling on two straight lines make the alternate angles equal to one another, the straight lines will be parallel to one another. (1.16, 1.D23)
28. If a straight line falling on two straight lines make the exterior angle equal to the interior and opposite angle on the same side, or the interior angles on the same side equal to two right angles, the straight lines will be parallel to one another (1.15, 1.27, 1.13, 1.27)
29. A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles. ((1.13, 1.Po5, 1.15, 1.CN1, 1.CN2, 1.13)
30. Straight lines parallel to the same straight line are also parallel to one another (1.29, 1.29, 1.CN1)
31. Through a given point to draw a straight line parallel to a given straight line. (1.23, 1.27)
32.In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. (1.31, 1.29, 1.29, 1.13)
33. The straight lines joining equal and parallel straight (at the extremities which are) in the same directions (respectively) are themselves also equal and parallel. (1.29, 1.4, 1.27)
34. In parallelogrammic areas, the opposite sides and angles are equal to one another, and the diameter bisects the areas. (1.29, 1.29, 1.26, CN2, 1.4)
35. Parallelograms which are on the same base and in the same parallels are equal to one another. (1.34, 1.CN1, 1.CN2, 1.34, 1.29, 1.4, 1.CN3, 1.CN2)
36. Parallelograms which are on equal bases and in the same parallels are equal to one another (1.CN1, 1.33, 1.34, 1.35, 1.35, 1.CN1)
37. Triangles which are on the same base and in the same parallels are equal to one another. (1.31, 1.31, 1.35, 1.34, 1.34)
38. Triangles which are on equal bases and in the same parallels are equal to one another. (1.31, 1.36, 1.34, 1.34)
39. Equal triangles which are on the same base and on the same side are also in the same parallels (1.31, 1.37, 1.CN1)
40. Equal triangles which are on equal bases and on the same side are also in the same parallels (1.31, 1.38, 1.CN1)
41. If a parallelogram have the same base with a triangle and be in the same parallels, the parallelogram is double of the triangle (1.37, 1.34)
42. To construct, in a given rectilineal angle, a parallelogram equal to a given triangle (1.23, 1.31, 1.38, 1.41)
43. In any parallelogram the complements of the parallelograms about the diameter are equal to one another. (1.34, 1.CN2, 1.CN3)
44. To a given straight line to apply, in a given rectilineal angle, a parallelogram equal to a given triangle (1.42, 1.31, 1.29, 1.Po5, 1.31, 1.43, 1.CN1, 1.15)
45. To construct, in a given rectilineal angle, a parallelogram equal to a given rectilineal figure. (1.42, 1.44, 1.CN1, 1.29, 1.14, 1.29, 1.CN2, 1.29, 1.CN1, 1.14, 1.34, 1.CN1, 1.30, 1.33)
46. On a given straight line to describe a square (1.11, 1.31, 1.34, 1.29, 1.34)
47. In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. (1.46, 1.14, 1.CN2, 1.4, 1.41, 1.41, 1.CN2)
48. If in a triangle the square on one of the sides be equal to the squares on the remaining two sides of the triangle the angle contained by the remaining two sides of the triangle is right. (1.47, 1.8)

Book 2

Book 2 Definitions.

1. Any rectangular parallelogram is said to be contained by the two straight lines containing the right angle.
2. And in any parallelogrammic area let any one whatever of the parallelograms about its diameter with two complements be called a gnomon.

Book 2 Propositions

1. If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments. (1.11, 1.3, 1.31, 1.34)
2. If a straight line be cut at random, the rectangle contained by the whole and both of the segments is equal to the square on the whole. (1.46, 1.31)
3. If a straight line be cut at random, the rectangle contained by the whole and one of the segments is equal to the rectangle contained by the segments and the square on the aforesaid segment. (1.46, 1.31)
4. If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the rectangle contained by the segments. (1.46, 1.31, 1.29, 1.5, 1.6, 1.34, 1.29, 1.34, 1.34)
5. If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square one the straight line between the points of section is equal to the square on the half. (1.46, 1.31, 1.43, 1.36)
6. If a straight line be bisected and a straight line be added to it in a straight line, the rectangle contained by the whole with the added straight line and the added straight line together with the square on the half is equal to the square on the straight line made up of half and the added straight line. (1.46, 1.31, 1.36, 1.43)
7. If a straight line be cut at random, the square on the whole and that on one of the segments both together are equal to twice the rectangle contained by the whole and the said segment and the square on the remaining segment. (1.46, 1.43)
8. If a straight line be cut at random, four times the rectangle contained by the whole and one of the segments together with the square on the remaining segment is equal to the square described on the whole and the aforesaid segment as on one straight line. (1.36, 1.43, 1.36, 1.43)
9. If a straight line be cut into equal and unequal segments, the squares on the unequal segments of the whole are double of the square on the half and of the square on the straight line between the points of section. (1.32, 1.29, 1.32, 1.6, 1.29, 1.32, 1.6, 1.47, 1.34, 1.47, 1.47)
10. If a straight line be bisected, and a straight line be added to it in a straight line, the square on the whole with the added straight line and the square on the added straight line both together are double of the square on the half and of the square described on the straight line made up of half and the added straight line as on one straight line. (1.11, 1.3, 1.31, 1.29, 1.Po 5, 1.5, 1.32, 1.15, 1.29, 1.32, 1.6, 1.34, 1.32, 1.6, 1.47, 1.CN1, 1.47, 1.34, 1.47, 1.47)
11. To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment. (1.46, 2.6, 1.47)
12. In obtuse-angled triangles the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle by twice the rectangle contained by one of the sides above the obtuse angle, namely that on which the perpendicular falls, and the straight line cut off outside by the perpendicular towards the obtuse angle. (2.4, 1.47, 1.47)
13. In acute-angled triangles the square on the side subtending the acute angle is less than the squares on the sides containing the acute angle by twice the rectangle contained by one of the sides about the acute angle, namely that on which the perpendicular falls, and the straight line cut off within by the perpendicular towards the acute angle. (2.7, 1.47)
14. To construct a square equal to a given rectilineal figure. (1.45, 2.5, 1.47)

Book 3

Book 3 Definitions.

1. Equal circles are those the diameters of which are equal, or the radii of which are equal.
2. A straight line is said to touch a circle which, meeting the circle and being produced, does not cut the circle.
3. Circles are said to touch one another which, meeting one another, do not cut one another.
4. In a circle straight lines are said to equally distant from the centre when the perpendiculars drawn to them from the centre are equal.
5. And the straight line is said to be at a greater distance on which the greater perpendicular falls.
6. A segment of a circle is the figure contained by a straight line and a circumference of a circle.
7. An angle of a segment is that contained by a straight line and circumference of a circle.
8. An angle in a segment is the angle which, when a point is taken on the circumference of the segment and straight lines are joined from it to the extremities of the straight line which is the base of the segment, is contained by the straight lines so joined.
9. And when the straight lines containing the angle cut off a circumference, the angle is said to stand upon that circumference.
10. A sector of a circle is the figure which, when an angle is constructed at the centre of the circle, is contained by the straight lines containing the angle and the circumference cut off by them.
11. Similar segments of circles are those which admit equal angles, or in which the angles are equal to one another.

Book 3 Propositions.

1. To find the center of a given circle. (1.8, 1.Def 10) Porism: From this it is manifest that, if in a circle a straight line cut a straight line into two equal parts and at right angles, the centre of the circle is on the cutting straight line.
2. If on the circumference of a circle two points be taken at random, the straight line joining the points will fall within the circle. (3.1, 1.5, 1.16, 1.19)
3. If in a circle a straight line through the centre bisect a straight line not through the centre, it also cuts it at right angles; and if it cut it at right angles, it also bisects it. (1.8, 1.Def 10, 1.5, 1.26)
4. If in a circle two straight lines cut one another which are not through the centre, they do not bisect one another. (3.1, 3.3, 3.3)
5. If two circles cut one another, they will not have the same centre. (1.Def 15)
6. If two circles touch one another, they will not have the same centre.
7. If on a diameter of a circle a point be taken which is not the centre of the circle, and from the point straight lines fall upon the circle, that will be greatest on which the centre is, the remainder of the same diameter will be least, and of the rest the nearer to the straight line through the centre is always greater than the more remote, and the only two equal straight lines will fall from the point on the circle, one on each side of the least straight line. (1.20, 1.24, 1.23, 1.4)
8. If a point be taken outside a circle and from the point straight lines be drawn through to the circle, one of which is through the centre and the others are drawn at random, then, of the straight lines which fall on the concave circumference, that through the centre is greatest, while of the rest the nearer to that through the centre is always greater than the more remote, but, of the straight lines falling on the convex circumference, that between the point and the diameter is least, while of the rest the nearer to the least, is always less than the more remote, and the only two equal straight lines will fall on the circle from the point, one on each side of the least. (3.1, 1.20, 1.24, 1.20, 1.21, 1.4)
9. If a point be taken within a circle, and more than two equal straight lines fall from the point on the circle, the point taken is the centre of the circle. (1.8, 1.Def 10, 3.1 Por)
10. A circle does not cut a circle at more points than two. (3.1 Por, 3.5)
11. If two circles touch one another internally, and their centres be taken, the straight line joining their centres, if it be also produced, will fall on the point of contact of the circles.
12. If two circles touch one another externally, the straight line joining their centres will pass through the point of contact. (1.20)
13. A circle does not touch a circle at more points than one, whether it touch it internally or externally. (3.11, 3.2)
14. In a circle equal straight lines are equally distant from the centre, and those which are equally distant from the centre are equal to one another. (3.1, 3.3, 1.47, 3.Def 4, 1.47)
15. Of straight lines in a circle the diameter is greatest, and of the rest the nearer to the centre is always greater than the more remote. (3.Def 5, 3.14, 1.20, 1.24)
16. The straight line drawn at right angles to the diameter of a circle from its extremity will fall outside the circle, and into the space between the straight line and the circumference another straight line cannot be interposed; further the angle of the semicircle is greater, and the remaining angle less, than any acute rectilineal angle (1.5, 1.17, 1.19) Porism: From this it is manifest that the straight line drawn at right angles to the diameter of a circle from its extremity touches the circle.
17. From a given point to draw a straight line touching a given circle. (3.1, 1.4, 3.16 Por)
18. If a straight line touch a circle, and a straight line be joined from the centre to the point of contact, the straight line so joined will be perpendicular to the tangent. (1.17, 1.19)
19. If a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the tangent, the centre of the circle will be on the straight line so drawn. (3.18)
20. In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same circumference as base. (1.5, 1.32)
21. In a circle the angles in the same segment are equal to one another. (3.20)
22. The opposite angles of quadrilaterals in circles are equal to two right angles. (1.32, 3.21)
23. On the same straight line there cannot be constructed two similar and unequal segments of circles on the same side. (3.Def 11, 1.16)
24. Similar segments of circles on equal straight lines are equal to one another. (3.10)
25. Given a segment of a circle, to describe the complete circle of which it is a segment. (1.6, 3.9)
26. In equal circles equal angles stand on equal circumferences, whether they stand at the centres or at the circumferences. (1.4, 3.Def 11, 3.24)
27. In equal circles angles standing on equal circumferences are equal to one another, whether they stand at the centres or at the circumferences. (1.23, 3.26, 3.20)
28. In equal circles equal straight lines cut off equal circumferences, the greater equal to the greater and the less to the less. (1.8, 3.26)
29. In equal circles equal circumferences are subtended by equal straight lines. (3.27, 1.4)
30. To bisect a given circumference (1.4, 3.28)
31. In a circle the angle in the semicircle is right, that in a greater segment less than a right angle, and that in a less segment greater than a right angle, and further the angle of the greater segment is greater than a right angle, and the angle of the less segment less than a right angle. (1.5, 1.5, 1.32, 1.Def 10, 1.17, 3.22)
32. If a straight line touch a circle, and from the point of contact there be drawn across, in the circle, a straight line cutting the circle, the angles which it makes with the tangent will be equal to the angles in the alternate segments of the circle. (3.19, 3.31, 1.32, 3.22)
33. On a given straight line to describe a segment of a circle admitting an angle equal to a given rectilineal angle. (1.4, 3.16 Por, 3.32, 3.16 Por, 3.31, 1.4, 3.16 Por, 3.32)
34. From a given circle to cut off a segment admitting an angle equal to a given rectilineal angle. (1.23, 3.32)
35. If in a circle two straight lines cut one another, the rectangle contained by the segments of the one is equal to the rectangle contained by the segments of the other. (3.3, 2.5, 1.47)
36. If a point be taken outside a circle and from it there fall on the circle two straight lines, and if one of them cut the circle and the other touch it, the rectangle contained by the whole of the straight line which cuts the circle and the straight line intercepted on it outside between the point and the convex circumference will be equal to the square on the tangent. (3.18, 2.6, 1.47, 3.18, 3.3, 2.6, 1.47, 1.47)
37. If a point be taken outside a circle and from the point there fall on the circle two straight lines, if one of them cut the circle, and the other fall on it, and if further the rectangle contained by the whole of the straight line which cuts the circle and the straight line intercepted on it outside between the point and the convex circumference be equal to the square on the straight line which falls on the circle, the straight line which falls on it will touch the circle. (3.18, 3.36, 1.8, 3.16 Por)

Book 4

Book 4 Definitions

1. A rectilineal figure is said to be inscribed in a rectilineal figure when the respective angles of the inscribed figure lie on the respective sides of that in which it is inscribed.
2. Similarly a figure is said to be circumscribed about a figure when the respective sides of the circumscribed figure pass through the respective angles of that about which it is circumscribed.
3. A rectilineal figure is said to be inscribed in a circle when each angle of the inscribed figure lies on the circumference of the circle.
4. A rectilineal figure is said to be circumscribed about a circle, when each side of the circumscribed figure touches the circumference of the circle.
5. Similarly a circle is said to be inscribed in a figure when the circumference of the circle touches each side of the figure in which it is inscribed.
6. A circle is said to be circumscribed about a figure when the circumference of the circle passes through each angle of the figure about which it is circumscribed.
7. A straight line is said to be fitted into a circle when its extremities are on the circumference of the circle.

Book 4 Propositions

1. Into a given circle to fit a straight line equal to a given straight line which is not greater than the diameter of the circle.
2. In a given circle to inscribe a triangle equiangular with a given triangle. (3.16 Por, 1.23, 3.32, 1.32)
3. About a given circle to circumscribe a triangle equiangular with a given triangle. (3.1, 1.23, 3.16 Por, 3.18, 1.13, 1.32)
4. In a given triangle to inscribe a circle. (1.9, 1.26, 3.16, 4.Def 5)
5. About a given triangle to circumscribe a circle. (1.10, 1.4, 1.4, 3.31)
6. In a given circle to inscribe a square. (1.4, 3.31, 1.Def 22)
7. About a given circle to circumscribe a square. (3.16 Por, 3.18, 1.28, 1.30, 1.34, 1.34, 1.34)
8. In a given square to inscribe a circle. (1.10, 1.31, 1.34, 3.16)
9. About a given square to circumscribe a circle. (1.8, 1.6)
10. To construct an isosceles triangle having each of the angles at the base double of the remaining one. (2.11, 4.1, 4.5, 3.37, 3.32, 1.32, 1.5, 1.6, 1.5)
11. In a given circle to inscribe an equilateral and equiangular pentagon. (4.10, 4.2, 1.9, 3.26, 3.29, 3.27)
12. About a given circle to circumscribe an equilateral and equiangular pentagon. (4.11, 3.16 Por, 3.1, 3.18, 1.47, 1.8, 3.27, 1.26)
13. In a given pentagon, which is equilateral and equiangular, to inscribe a circle. (1.4, 1.26, 3.16)
14. About a given pentagon, which is equilateral and equiangular, to circumscribe a circle. (1.6)
15. In a given circle to inscribe an equilateral and equiangular hexagon. (1.5, 1.32, 1.15, 3.26, 3.29, 3.27) Porism: From this it is manifest that the side of the hexagon is equal to the radius of the circle. And, in like manner as in the case of the pentagon if through the points of division on the circle we draw tangents to the circle, there will be circumscribed about the circle an equilateral and equiangular hexagon in conformity with what was explained in the case of the pentagon. And further by means similar to those explained in the case of the pentagon we can both inscrible a circle in a given hexagon and circumscribe one about it.
16. In a given circle to inscribe a fifteen-angled figure which shall be both equilateral and equiangular. (3.30) And, in like manner as in the case of the pentagon, if through the points of division on the circle we draw tangents to the circle, there will be circumscribed about the circle a fifteen-angles figure which is equilateral and equiangular. And further, by proofs similar to those in the case of the pentagon, we can both inscribe a circle in the given fifteen-angled figure and circumscribe one about it.

Book 5

Book 5 Definitions

1. A magnitude is a part of a magnitude, the less of the greater, when it measures the greater.
2. The greater is a multiple of the less when it is measured by the less.
3. A ratio is a sort of relation in respect of size between two magnitudes of the same kind.
4. Magnitudes are said to have a ratio to one another which are capable, when multiplied, of exceeding one another.
5. Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, is any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
6. Let magnitudes which have the same ratio be called proportional.
7. When, of the equimultiples, the multiple of the first magnitude exceeds the multiple of the second, but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second than the third has to the fourth.
8. A proportion in three terms is the least possible
9. When three magnitudes are proportional, the first is said to have to the third the duplicate ratio of that which it has to the second.
10. When four magnitudes are proportional, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on continually, whatever be the proportion.
11. The term corresponding magnitudes is used of antecedents in relation to antecedents, and of consequents in relation to consequents.
12. Alternate ratio means taking the antecedent in relation the the antecedent and the consequent in relation to the consequent.
13. Inverse ratio means taking the consequent as antecedent in relation to the antecedent as consequent.
14. Composition of a ratio means taking the antecedent together with the consequent as one in relation to the consequent by itself.
15. Separation of a ratio means taking the excess by which the antecedent exceeds the consequent in relation to the consequent by itself.
16. Conversion of a ratio means taking the antecedent in relation to the excess by which the antecedent exceeds the consequent.
17. A ratio ex aequali arises when, there being several magnitudes and another set equal to them in multitude which taken two and two are in the same proportion, as the first is to the last among the first magnitudes, so is the first to the last among the second magnitudes; Or, in other words, it means taking the extreme terms by virtue of the removal of the intermediate terms.
18. A perturbed proportion arises when, there being three magnitudes and another set equal to them in multitude, as antecedent is to consequent among the first magnitudes, so is antecedent to consequent among the second magnitudes, while, as the consequent is to a third among the first magnitudes, so is a third to the antecedent among the second magnitudes.

Book 5 Propositions.

1. If there be any number of magnitudes whatever which are, respectively, equimultiples of any magnitudes equal in multitude , then, whatever multiple one of the magnitudes is of one, that multiple also will all be of all.
2. If a first magnitude be the same multiple of a second that a third is of a fourth, and a fifth also be the same multiple of the second that a sixth is of the fourth, the sum of the first and fifth will also be the same multiple of the second that the sum of the third and sixth is of the fourth.
3. If a first magnitude be the same multiple of a second that a third is of a fourth, and if equimultiples be taken of the first and third, then also ex aequali the magnitudes taken will be equimultiples respectively, the one of the second and the other of the fourth. (5.2)
4. If a first magnitude have to a second the same ratio as a third to a fourth, any equimultiples whatever of the first and third will also have the same ratio to any equimultiples whatever of the second and fourth respectively, taken in corresponding order. (5.3, 5.Def 5, 5.Def 5)
5. If a magnitude be the same multiple of a magnitude that a part subtracted is of a part subtracted, the remainder will also be the same multiple of the remainder that the whole is of the whole. (5.1)
6. If two magnitudes be equimultiples of two magnitudes, and any magnitudes subtracted from them be equimultiples of the same, the remainders also are either equal to the same or equimultiples of them. (5.2)
7. Equal magnitudes have to the same the same ratio, as also has the same to equal magnitudes. (5.Def 5, 5.Def 5) Porism: From this it is manifest that, if any magnitudes are proportional, they will also be proportional inversely.
8. Of unequal magnitudes, the greater has to the same, a greater ratio than the less has, and the same has to the less a greater ratio than it has to the greater. (5.Def 4, 5.1, 5.Def 7, 5.Def 7, 5.Def 4)
9. Magnitudes which have the same ratio to the same are equal to one another; and magnitudes to which the same has the same ratio are equal. (5.8, 5.8)
10. Of magnitudes which have a ratio to the same, that which has a greater ratio is greater, and that to which the same has a greater ratio is greater; and that to which the same has a greater ratio is less. (5.7, 5.8, 5.7, 5.8)
11. Ratios which are the same with the same ratio are also the same with one another.
12. If any number of magnitudes be proportional, as one of the antecedents is to one of the consequents, so will all the antecedents be to all the consequents. (5.1, 5.Def 5)
13. If a first magnitude have to a second the same ratio as a third to a fourth, and the third have to the fourth a greater ratio than a fifth has to a sixth, the first will also have to the second a greater ratio than the fifth to the sixth. (5.Def 7, 5.Def 5, 5.Def 7)
14. If a first magnitude have to a second the same ratio as a third has to a fourth, and the first be greater than the third, the second will also be greater than the fourth ; if equal, equal; and if less, less. (5.8, 5.13, 5.10)
15. Parts have the same ratio as the same multiples of them taken in corresponding order. (5.7, 5.12)
16. If four magnitudes be proportional, they will also be proportional alternately. (5.15, 5.11, 5.15, 5.11, 5.14, 5.Def 5)
17. If magnitudes be proportional componendo, they will also be proportional separando. (5.1, 5.1, 5.2)
18. If magnitudes be proportional separando, they will also be proportional componendo. (5.17, 5.11, 5.14)
19. If, as a whole is to a whole, so is a part subtracted to a part subtracted, the remainder will also be to the remainder as whole to whole. (5.16, 5.17, 5.16, 5.11) Porism: From this it is manifest that, if magnitudes be proportional componendo, they will also be proportional convertendo.
20. If there be three magnitudes, and others equal to them in multitude, which taken two and two are in the same ratio, and if ex aequali the first be greater than the third, the fourth will also be greater than the sixth; if equal, equal; and, if less, less. (5.8, 5.13, 5.10)
21. If there be three magnitudes, and others equal to them in multitude, which taken two and two together are in the same ratio, and the proprtion of them be perturbed, then, if ex aequali the first magnitude is greater than the third, the fourth will also be greater than the sixth; if equal, equal; and if less, less. (5.8, 5.13, 5.10)
22. If there be any number of magnitudes whatever, and others equal to them in multitude, which taken two and two together are in the same ratio, they will also be in the same ratio ex aequali. (5.4, 5.20, 5.Def 5)
23. If there be three magnitudes, and others equal to them in multitude, which taken two and two together are in the same ratio, and the proportion of them be perturbed, they will also be in the same ratio ex aequali. (5.15, 5.11, 5.16, 5.15, 5.11, 5.15, 5.11, 5.16, 5.21)
24. If a first magnitude have to a second the same ratio as a third has to a fourth , and also a fifth have to the second the same ratio as a sixth to the fourth, the first and fifth added together will have to the second the same ratio as the third and sixth have to the fourth.(5.22, 5.18, 5.22)
25. If four magnitudes be proportional, the greatest and the least are greater than the remaining two. (5.19)

Book 6

Book 6 Definitions

1. Similar rectilinieal figures are such as have their angles severally equal and the sides about the equal angles proportional.
2. Two figures are reciprocally related when there are in each of the two figures antecedent and consequent ratios
3. A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.
4. The height of any figure is the perpendicular drawn from the vertex to the base.

Book 6 Propositions

1. Triangles and parallelograms which are under the same height are to one another as their bases. (1.38, 1.38, 5.Def 5, 1.41, 5.15, 5.11)
2. If a straight line be drawn parallel to one of the sides of the triangle, it will cut the sides of the triangle proportionally; and if the the sides of the triangle be cut proportionally, the line joining the points of section will be parallel to the remaining side of the triangle. (5.7, 6.1, 5.11, 6.1, 5.11, 5.9, 1.39)
3. If an angle of a triangle be bisected and the straight line cutting the angle cut the base also, the segments of the base will have the same ratio as the remaining sides of the triangle; and if the segments of the base have the same ratio as the remaining sides of the triangle, the straight line joined from the vertex to the point of section will bisect the angle of the triangle. (1.29, 1.29, 1.6, 6.2, 6.2, 5.11, 5.9, 1.5, 1.29, [id.]
4. In equiangular triangles the sides about the equal angles are proportional, and those are corresponding sides which subtend the equal angles. (1.17, 1.Post 5, 1.28, 1.28, 1.34, 6.2, 5.16, 6.2, 5.16, 5.22)
5. If two triangles have their sides proportional, the triangles will be equiangular and will have those angles equal which the corresponding sides subtend. (1.23, 1.32, 6.4, 5.11, 5.9, 1.8, 1.4)
6. If two triangles have one angle equal to one angle and the sides about the equal angles proportional, the triangles will be equiangular and will have those angles equal which the corresponding sides subtend. (1.23, 1.32, 6.4, 5.11, 5.9, 1.4, 1.32)
7. If two triangles have one angle equal to one angle, the sides about other angles proportional, and the remaining angles either both less or both not less than a right angle, the triangles will be equiangular and will have those angles equal, the sides about which are proportional. (1.23, 1.32, 6.4, 5.11, 5.9. 1.5, 1.13, 1.32, 1.5, 1.17, 1.32)
8. If in a right-angled triangle a perpendicular be drawn from the right angle to the base, the triangles adjoining the perpendicular are similar both to the whole and to one another (1.32, 6.4, 6.Def 1, 1.32, 6.4, 6.Def 1) Porism: From this it is clear that, if in a right-angled triangle a perpendicular be drawn from the right angle to the base, the straight line so drawn is a mean proportional between the segments of the base.
9. From a given straight line to cut off a prescribed part (1.3, 1.31, 6.2)
10. To cut a given uncut straight line similarly to a given cut straight line. (1.31, 1.34, 6.2, 6.2)
11. To two given straight lines to find a third proportional. (1.3, 1.31, 6.2)
12. To three given straight lines to find a fourth proportional. (1.31, 6.2)
13. To two given straight lines to find a mean proportional. (3.31, 6.8 Por)
14. In equal and equiangular parallelograms the sides about the equal angles are reciprocally proportional; and equiangular parallelograms in which the sides about the equal angles are receprocally proportional are equal. (1.14, 5.7, 6.1, [id.], 5.11, 6.1, 6.1, 5.11, 5.9)
15. In equal triangles which have one angle equal to one angle the sides about the equal angles are reciprocally proportional; and those triangles which have one angle equal to one angle, and in which the sides about the equal angles are reciprocally proportional, are equal. (1.14, 5.7, 6.1, [id.], 5.11, 6.1, 5.11, 5.9)
16. If four straight lines be proportional, the rectangle contained by the extremes is equal to the rectangle contained by the means; and if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines will be proportional. (6.14, 6.14)
17. If three straight lines be proportional the rectangle contained by the extremes is equal to the square on the mean; and if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines will be proportional. (6.16, 6.16)
18. On a given straight line to describe a rectilineal figure similar and similarly situated to a given rectilineal figure. (1.23, 1.32, 1.23, 1.32, 6.4, 6.Def 1)
19. Similar triangles are to one another in the duplicate ratio of the corresponding sides. (5.Def 11, 6.11, 5.16, 5.11, 6.15, 5.Def 9, 6.1) Porism: From this it is manifest that, if three straight lines be proportional, then, as the first is to the the third, so is the figure described on the first to that which is similar and similarly described on the second.
20. Similar polygons are divided into similar triangles, and into triangles equal in multitude and in the same ratio as the wholes, and the polygon has to the polygon a ratio duplicate of that which the corresponding side has to the corresponding side. (6.Def 1, 6.6, 6.4 & 6.Def 1, 5.22, 6.6, 6.4 & 6.Def 1, 6.6, 1.32, 6.1, 5.12, 5.12, 6.19) Porism: Similarly also it can be proved in the case of quadrilaterals that they are in the duplicate ratio of the corresponding sides. And it was also proved in the case of triangles; therefore, also, generally, similar rectilineal figures are to one another in the duplicate ratio of the corresponding sides.
21. Figures which are similar to the same rectilineal figure are also similar to one another. (6.Def 1)
22. If four straight lines be proportional, the rectilineal figures similar and similarly described upon them will also be proportional; and, if the rectilineal figures similar and similarly described upon them be proportional, the straight lines will themselves also be proportional. (6.11 5.22, 5.11, 6.12, 6.18, 5.11, 5.9)
23. Equiangular parallelograms have to one another the ratio compounded of the ratios of their sides. (6.12, 6.1, 5.11, 6.1, 5.11)
24. In any parallelograms the parallelograms about the diameter are similar both to the whole and to one another. (6.2, 6.2, 5.18, 5.16, 5.22, 6.Def 1, 6.21)
25. To construct one and the same figure similar to a given rectilineal figure and equal to another given rectilineal figure. (1.44, 1.45, 6.13, 6.18, 6.19 Por, 6.1, 5.16)
26. If from a parallelogram there be taken away a parallelogram similar and similarly situated to the whole and having a common angle with it, it is about the same diameter with the whole. (1.31, 6.24, 5.11, 5.9)
27. Of all the parallelograms applied to the same straight line and deficient by parallelogrammic figures similar and similarly situated to that described on the half of the straight line, that parallelogram is greatest which is applied to the half of the straight line and is similar to the defect. (6.26, 1.43, 1.36)
28. To a given straight line to apply a parallelogram equal to a given rectilineal figure and deficient by a parallelogrammic figure similar to a given one: thus the given rectilineal figure must not be greater than the parallelogram described on the half of the straight line and similar to the defect. (6.18, 6.25, 6.21, 6.27, 6.26, 1.36)
29. To a given straight line to apply a parallelogram equal to a given rectilineal figure and exceeding by a parallelogrammic figure similar to a given one. (6.25, 6.21, 6.26, 1.36, 1.43, 6.24)
30. To cut a given finite straight line in extreme and mean ratio. (6.29, 6.14)
31. In right-angled triangles the figure on the side subtending the the right angle is equal to the similar and similarly described figures on the sides containing the right angle. (6.8, 6.Def 1, 6.19 Por)
32. If two triangles having two sides proportional to two sides be placed together at one angle so that their corresponding sides are also parallel, the remaining sides of the triangle will be in a straight line. (1.29, 6.6, 1.32, 1.14)
33. In equal circles angles have the same ratio as the circumferences on which they stand, whether they stand at the centres or at the circumferences (3.27, 3.27, 5.Def 5)

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