A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 484
... equation reduces to x3 + x = 4x2 + 4 , and we can divide out by the factor x2 + 1 . ( B ) Indeterminate equations ... equation . In most of the cases treated the equation takes a simpler form in consequence of one or other of the terms ...
... equation reduces to x3 + x = 4x2 + 4 , and we can divide out by the factor x2 + 1 . ( B ) Indeterminate equations ... equation . In most of the cases treated the equation takes a simpler form in consequence of one or other of the terms ...
Pagina 490
... equation in y . 2. Double equations of the second degree . The double equations in which one or both of the ... equation of the first degree by substituting 1 / y for x , but Diophantus makes a different substitution . = He assumes that ...
... equation in y . 2. Double equations of the second degree . The double equations in which one or both of the ... equation of the first degree by substituting 1 / y for x , but Diophantus makes a different substitution . = He assumes that ...
Pagina 492
... equation by one which he can solve rationally . He ultimately obtains the equation x4 + 337 = y2 , and also a suitable assumption for y , namely y = x2 — 25 , which produces a rational result , x = 12 . 5. x6 - Ax3 + Bx + c2 = y2 ...
... equation by one which he can solve rationally . He ultimately obtains the equation x4 + 337 = y2 , and also a suitable assumption for y , namely y = x2 — 25 , which produces a rational result , x = 12 . 5. x6 - Ax3 + Bx + c2 = y2 ...
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