A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 161
... Solution attributed to Plato . This solution , which Eutocius alone gives or mentions , can hardly be Plato's , if only because we know that Plato objected on principle to solutions by mechanical means as destroying the good of geometry ...
... Solution attributed to Plato . This solution , which Eutocius alone gives or mentions , can hardly be Plato's , if only because we know that Plato objected on principle to solutions by mechanical means as destroying the good of geometry ...
Pagina 234
... solution in the figure corresponds to the negative sign before the radical x = 1a- √ ( za2 . ; c m but Euclid was , of course , aware that there are two solutions , and how he could exhibit the second in the figure . For a real solution ...
... solution in the figure corresponds to the negative sign before the radical x = 1a- √ ( za2 . ; c m but Euclid was , of course , aware that there are two solutions , and how he could exhibit the second in the figure . For a real solution ...
Pagina 470
... solution of the equations u + v = n ( x + y ) , xy = n . uv , ( 1 ) ( 2 ) and the solution in the text is equivalent to x = 2n3 - 1 , u = n ( 4n3 —2 ) , y = 2n3 , v = n . It is not shown how the solution was arrived at ; but Zeuthen ...
... solution of the equations u + v = n ( x + y ) , xy = n . uv , ( 1 ) ( 2 ) and the solution in the text is equivalent to x = 2n3 - 1 , u = n ( 4n3 —2 ) , y = 2n3 , v = n . It is not shown how the solution was arrived at ; but Zeuthen ...
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