The History of Mathematics: A Brief Course

322 11. POST-EUCLIDEAN GEOMETRY proportion (see Problem 11.3). Working with the sides of the squares, it would then be legitimat ...

HELLENISTIC GEOMETRY 323 prism required the least material to enclose a given volume, out of all the possible prisms whose bas ...

324 11. POST-EUCLIDEAN GEOMETRY Third, in connection with the extension of these locus problems, Pappus con- siders the locus to ...

ROMAN GEOMETRY 325 the area rotated and the distance traversed by its center of gravity (which is 2ð times the length of the l ...

326 11 POST-EUCLIDEAN GEOMETRY FIGURE 4. Ptolemy's first method of mapping. the Equator. The extreme southern limit of his map w ...

ROMAN GEOMETRY 327 of longitude as straight lines emanating from the common center, representing the north pole. Thus, his pla ...

328 11. POST-EUCLIDEAN GEOMETRY FIGURE 5. Nipsus' method of computing the width of a river. (on the left decumanus) and how many ...

MEDIEVAL GEOMETRY 329 early books of Euclid, often drastically edited. The tradition of attributing these works to Boethius co ...

330 11. POST-EUCLIDEAN GEOMETRY navigators and explorers for many centuries)^11 and a discussion of different ways of using simi ...

MEDIEVAL GEOMETRY^331 Uniformly uniform Uniformly difform Difformly difform FIGURE 6. Nicole Oresme's classification of motion ...

332 11. POST-EUCLIDEAN GEOMETRY FIGURE 7. Pitiscus' derivation of the proportions in which an al- titude divides a side of a tri ...

GEOMETRY IN THE MUSLIM WORLD 333 distinction between magnitude and number, they actually operated with quadratic and quartic i ...

334 11. POST-EUCLIDEAN GEOMETRY Í t X / w A Ê A U Æ ç Ε Ç FIGURE 8. Thabit ibn-Qurra's attempted proof of the parallel postulate ...

GEOMETRY IN THE MUSLIM WORLD 335 FIGURE 9. Thabit ibn-Qurra's Pythagorean theorem. 4.3. Al-Kuhi. A mathematician who devoted h ...

336 11. POST-EUCLIDEAN GEOMETRY FIGURE 10. Al-Kuhi's angle trisection. Al-Haytham also attempted to prove the parallel postulate ...

GEOMETRY IN THE MUSLIM WORLD 337 converging lines must intersect. Although none of the writings now attributed to Aristotle co ...

338 11. POST-EUCLIDEAN GEOMETRY of the Mongol expansion, which brought the conquest of China in the early part of the century, t ...

NON-EUCLIDEAN GEOMETRY 339 in attitude took place, as a few mathematicians began to explore non-Euclidean geometries as if the ...

340 11. POST-EUCLIDEAN GEOMETRY FIGURE 11. (a) Lines through A that intersect BE and those that share a common perpendicular wit ...

NON-EUCLIDEAN GEOMETRY 341 clockwise about A to make angles that decreased to <9 0. He then—too hastily, as we now know—dre ...