A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 194
... lemmas constitutes no difficulty , because ( 1 ) Archimedes himself uses the Euclidean lemma in one proof of his proposition about the area of a parabolic segment , and ( 2 ) Archimedes ' lemma in the form of Eucl . V , Def . 4 , is in ...
... lemmas constitutes no difficulty , because ( 1 ) Archimedes himself uses the Euclidean lemma in one proof of his proposition about the area of a parabolic segment , and ( 2 ) Archimedes ' lemma in the form of Eucl . V , Def . 4 , is in ...
Pagina 458
... Lemmas to the Porisms of Euclid form an im- portant collection , of which full use is made in the ' restora- tions ' by Chasles and others of the original treatise . Six of them ( Lemmas 1 , 2 , 4 , 5 , 6 , 7 ) deal with a quadrilateral ...
... Lemmas to the Porisms of Euclid form an im- portant collection , of which full use is made in the ' restora- tions ' by Chasles and others of the original treatise . Six of them ( Lemmas 1 , 2 , 4 , 5 , 6 , 7 ) deal with a quadrilateral ...
Pagina 459
... lemmas to the Conics of Apollonius there are a large number containing geometrical algebra of the usual kind . There are also propositions about the construction of the hyperbola , and another proving that two hyperbolas having the same ...
... lemmas to the Conics of Apollonius there are a large number containing geometrical algebra of the usual kind . There are also propositions about the construction of the hyperbola , and another proving that two hyperbolas having the same ...
Inhoudsopgave
INTRODUCTORY 1 157 | 1 |
NUMERICAL NOTATION AND PRACTICAL CAL | 11 |
PYTHAGOREAN ARITHMETIC | 36 |
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according added algebra Apollonius appears Archimedes assumes base begins Book called centre circle cone conics construction contained corresponding cube curve cylinder definition described diameter Diophantus divided draw drawn earth edition Elements equal equation equivalent Euclid expression fact figure five follows four geometry given gives greater Greek height Heron included inscribed Join known latter lemmas length less mathematics means measure meet mentioned method moon multiplied namely observations obtained original Pappus parallel particular perpendicular plane polygon position problem produced proof Prop proportion propositions proved Ptolemy pyramid Pythagoreans radius ratio rectangle reference regarded regular relation represented respectively result right angles segment shows sides similar solid solution solved sphere square straight line Suppose surface theorem theory tion translation treatise triangle volume whole