By American Mathematical Society, János Kollár, Robert Lazarsfeld

ISBN-10: 0821808958

ISBN-13: 9780821808955

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Extra info for Algebraic Geometry Santa Cruz 1995, Part 2: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz

Example text

This whole book is about mathematics, but here we are looking only at the etymological side of the question. UX) originally means "that which is learned, learning, science" and was first used in this sense by Plato and, probably, the Pythagoreans. The associated verb is the Greek manthanein, to learn. " Here are some related words from other languages: English: mind German: munter (awake, lively, merry, vigorous) Middle High German: Minne (love) Gothic: munda (to aim) Old Slavic: modru (wise, sage) Sanskrit: man (to think) Latin: mens (mind) Greek: mantis (a seer), and possibly even the Greek muse and Prometheus.

4. 12 if produced indefinitely, meet on that side on which are the angles less than the two right angles. [Fig. 12] Prop. 29. A straight line falling on parallel straight lines makes the altemate 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. We will abbreviate the proof by using the notation from Fig. 13(b) and dealing with the main case of alternating angles a , p only. 27. then a=p.

6. Book I, Part D: The Theorem of Pythagoras 45 Proof Let 6ABC be the given triangle. We take the notation from Fig. 21 and abbreviate. 47 we have [2 = d 2 + b2 = c2 + b2 , which by assumption is equal to a2 . Hence [ is equal to a. (Here is a little gap. ) Now, by the congruence theorem SSS the two triangles 6ABC and 6ADC are congruent, and hence a = fP is a right angle. 47 and 48 combined are the full theorem of Pythagoras. We conclude this chapter by quoting a fine sonnet by the German poet Adelbert von Chamisso, translated by Max Delbriick, together with a nice remark by C.

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Algebraic Geometry Santa Cruz 1995, Part 2: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz by American Mathematical Society, János Kollár, Robert Lazarsfeld


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