A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 250
... less than the sum of the prisms in P ' : which is impossible . Therefore W is not less than P ' . II . Suppose We have , inversely , B ' : B W : P = W > P ' . = P ' : V , where V is some solid less than P. But this can be proved ...
... less than the sum of the prisms in P ' : which is impossible . Therefore W is not less than P ' . II . Suppose We have , inversely , B ' : B W : P = W > P ' . = P ' : V , where V is some solid less than P. But this can be proved ...
Pagina 273
... less than twenty times the distance of the moon from the earth ; ( 2 ) that the diameter of the sun has the same ... less than 43 : 6 . Aristarchus is as good as his word , for these results are rigorously established in Propositions 7 ...
... less than twenty times the distance of the moon from the earth ; ( 2 ) that the diameter of the sun has the same ... less than 43 : 6 . Aristarchus is as good as his word , for these results are rigorously established in Propositions 7 ...
Pagina 329
... less than one - third of 1,000 times the sun's diameter and therefore again a fortiori less than one - third of 30,000 times the earth's diameter , that is to say , less than 10,000,000,000 stades . But , on our assumptions , the ...
... less than one - third of 1,000 times the sun's diameter and therefore again a fortiori less than one - third of 30,000 times the earth's diameter , that is to say , less than 10,000,000,000 stades . But , on our assumptions , the ...
Inhoudsopgave
INTRODUCTORY 157 | 5 |
NUMERICAL NOTATION AND PRACTICAL CAL | 11 |
PYTHAGOREAN ARITHMETIC | 36 |
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algebra Apollonius Archimedes Archytas arithmetic assumes astronomy axis base bisects Book centre of gravity chord circle circumscribed commentary cone conics contained cube curve cylinder definition diameter Diophantus divided edition equal equation equivalent Eratosthenes Eucl Euclid Eudemus Eudoxus Eutocius figure geometry given ratio given straight line gives Greek height Heron Hipparchus hyperbola inscribed lemmas length loci mathematics mean proportionals method method of exhaustion moon multiplied namely Pappus parabola parallel parallelogram pentagon perpendicular plane Plato polygonal number Porisms Posidonius problem Proclus proof Prop propositions proved Ptolemy pyramid Pythagoras Pythagoreans quadratic quadratic equations radius rectangle respectively right angles right-angled triangle segment semicircle sexagesimal sides similar solid solution solved sphere square number surface tangent Theon Theon of Alexandria theorem theory tion translation treatise triangular number volume whence