A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 249
... prisms and two equal pyra- mids AFGE , FBHK similar to the original pyramid ( the equality of the prisms is proved in XI . 39 ) , and that B H K L E the sum of the two prisms is greater than half the original pyramid . Proposition 4 ...
... prisms and two equal pyra- mids AFGE , FBHK similar to the original pyramid ( the equality of the prisms is proved in XI . 39 ) , and that B H K L E the sum of the two prisms is greater than half the original pyramid . Proposition 4 ...
Pagina 250
... prisms in P ' ) . But W is also 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 ...
... prisms in P ' ) . But W is also 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 ...
Pagina 520
... prism with equal base and height . Now the scientific proof of this is in two parts . The second part proves that any ... ( prisms ) . There is good evidence , as we have seen , that Democritus was capable of using this method ; but there ...
... prism with equal base and height . Now the scientific proof of this is in two parts . The second part proves that any ... ( prisms ) . There is good evidence , as we have seen , that Democritus was capable of using this method ; but there ...
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