A History of Greek Mathematics, Том 1Cambridge University Press, 21 нояб. 2013 г. - Всего страниц: 468 'If one would understand the Greek genius fully, it would be a good plan to begin with their geometry.' As early as the sixth century BCE, Thales of Miletus used geometrical principles to calculate distance and height. Within a few hundred years, Euclid had produced his seminal Elements, which was still used as a textbook when this two-volume work was first published in 1921. A distinguished civil servant as well as an expert on ancient Greek mathematics, Sir Thomas Little Heath (1861-1940) includes here sufficient detail for a modern mathematician to grasp ancient methodology, alongside explanatory sections aimed at classicists. This remains a rigorous and essential exposition of a vast topic. Volume 1 includes an introduction that touches on the conditions which made possible the rapid development of philosophy and science in ancient Greece. The coverage begins with Thales and ends with Euclid. |
Содержание
INTRODUCTORY PAGES 125 | 1 |
GREEK NUMERICAL NOTATION AND ARITHMETICAL | 26 |
Fractions | 41 |
a Rightangled triangles with sides in | 79 |
two cubes | 89 |
THE EARLIEST GREEK GEOMETRY THALES | 118 |
PYlHAGOREAN GEOMETRY | 139 |
t10n of quadratic equations | 151 |
Recapitulation | 165 |
PROGRESS IN THE ELEMENTS DOWN TO PLATOS | 170 |
SPECIAL PROBLEMS 218270 | 218 |
A Approximation to a solution by plane methods only 268270 | 268 |
PLATO 284315 | 284 |
K FROM PLATO TO EUCLID 316353 | 316 |
A lost textbook on Sphaeric l 349350 | 349 |
7879 | 408 |
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alphabet Apollonius Archimedes Archytas argument Arist Aristotle arithmetic astronomy attributed axis base Book centre circle circumference commensurable cone construction cube curve defined definition Democritus diameter difficulty discovered discovery Elements equal equation Eratosthenes Euclid Eudemus Eudoxus Eutocius figure find finding first five fixed follows geometry given straight line gives gnomon Greek Hippias Hippocrates Hippocrates’s Iamblichus incommensurable indivisible indivisible lines infinite inscribed irrationals isosceles lemma length letters lune magnitudes mathematician mathematics mean proportionals measure Menaechmus method method of exhaustion motion multiple namely Nicom Nicomachus odd numbers Oenopides Pappus parallel parallelogram passage plane Plato Plutarch polygon problem Proclus Proclus on Eucl proof propositions proved pyramid Pythagoras Pythagoreans quadrature radius ratio rectangle right angles right-angled triangle says scientific semicircle side similar segments Simplicius solid solution sphere square number square root suppose Thales Theaetetus Theon of Smyrna theory of proportion things tion trisection Zeno