A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 155
... mean proportionals in continued proportion between two given straight lines ( cf. p . 131 above ) . Again , after a ... mean proportionals between two given straight lines . We will now give the recorded solutions in order . Archytas ...
... mean proportionals in continued proportion between two given straight lines ( cf. p . 131 above ) . Again , after a ... mean proportionals between two given straight lines . We will now give the recorded solutions in order . Archytas ...
Pagina 158
... mean proportionals between two straight lines a , b , that is , if a : x = x : y = y : b , then clearly x2 = ay , y2 = bx , xy = ab . The properties of the parabola and hyperbola used by Menaechmus 158 PROBLEM OF TWO MEAN PROPORTIONALS.
... mean proportionals between two straight lines a , b , that is , if a : x = x : y = y : b , then clearly x2 = ay , y2 = bx , xy = ab . The properties of the parabola and hyperbola used by Menaechmus 158 PROBLEM OF TWO MEAN PROPORTIONALS.
Pagina 169
... mean proportionals between two straight lines a , b thus . Take K on OB such that DO : OK a : b . = Join DK , and produce it to meet the cissoid in Q. Through Q draw the ordinate LM perpendicular to DC . Then , by the property of the ...
... mean proportionals between two straight lines a , b thus . Take K on OB such that DO : OK a : b . = Join DK , and produce it to meet the cissoid in Q. Through Q draw the ordinate LM perpendicular to DC . Then , by the property of 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