A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 122
... latter being held to have infringed one or other of the admitted principles of geometry ) . It is clear that by the quadrature ' by means of segments ' in this passage Aristotle means the same thing as what he elsewhere ( Soph . El ...
... latter being held to have infringed one or other of the admitted principles of geometry ) . It is clear that by the quadrature ' by means of segments ' in this passage Aristotle means the same thing as what he elsewhere ( Soph . El ...
Pagina 294
... latter was discovered first , and the fact stated in the former was originally inferred from the latter . ' From the theorem ' , says Archimedes , ' that a sphere is four times as great as the cone with a great circle of the sphere as ...
... latter was discovered first , and the fact stated in the former was originally inferred from the latter . ' From the theorem ' , says Archimedes , ' that a sphere is four times as great as the cone with a great circle of the sphere as ...
Pagina 296
... latter a ratio less than B : S. Inscribe in A a similar regular polygon and set up on it a pyramid inscribed in the cone . Then ( polygon in A ) : ( polygon in B ) = C2 : E2 = C : D > ( polygon in A ) : surface of pyramid . [ The latter ...
... latter a ratio less than B : S. Inscribe in A a similar regular polygon and set up on it a pyramid inscribed in the cone . Then ( polygon in A ) : ( polygon in B ) = C2 : E2 = C : D > ( polygon in A ) : surface of pyramid . [ The latter ...
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