A History of Greek Mathematics, Volume 2Clarendon Press, 1921 |
Contents
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Common terms and phrases
Apollonius Archimedes Archimedes's axis base bisecting Book centre of gravity chap chord circle circumscribed commentary cone conic Ctesibius cube curve cylinder diameter Diophantus Dioptra divided draw drawn edition ellipse equal equation Eratosthenes Eucl Euclid Eutocius follows formula frustum Geminus geometry given ratio gives greater Greek Heron Hipparchus hyperbola lemmas mathematics means meet method method of exhaustion Metrica moon Pappus Pappus's parabola parallel parallelogram perpendicular plane polygon Porisms Posidonius problem Proclus produced proof Prop propositions proved Ptolemy radius rectangle respectively right angles right-angled triangle says sector segment semicircle sides solid solution solved sphere spherical spiral square straight line Suppose surface Syntaxis tangent Theon Theon of Alexandria Theon of Smyrna theorem treatise vertex weight whence
Popular passages
Page 3 - His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit...
Page 228 - If a straight line is perpendicular to each of two straight lines, at their point of intersection, it is perpendicular to the plane in which the two lines lie.
Page 21 - I am persuaded, no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.
Page 312 - If two triangles have two sides of the one equal to two sides of the other, and also the angles contained by those sides equal, prove that the triangles are congruent.
Page 95 - BOOK II. Proposition 1. If a solid lighter than a fluid be at rest in it, the weight of the solid will be to that of the same volume of the fluid as the immersed portion of the solid is to the whole.
Page 402 - BC) we first find the formula for the area of a triangle in terms of its sides, K=Vs(s — a) (s — b) (s — c).
Page 40 - ... is equal to a triangle with base equal to the circumference and height equal to the radius of the circle, I apprehended that, in like manner, any sphere is equal to a cone with base equal to the surface of the sphere and height equal to the radius*.
Page 206 - Hence it is plain that triangles on the same or equal bases, and between the same parallels, are equal, seeing (by cor.
Page 17 - Archimedes possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit...
Page 21 - as it were of set purpose to have covered up the traces of his investigation, as if he had grudged posterity the secret of his method of inquiry, while he wished to extort from them assent to his results".