A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 256
... Prop . 59 ( the case of ' excess ' ) . Let the given area AB be applied to AC , exceeding by the figure CB given in species . I say that each of the sides HC , CE is given . E B A K сн to CB ( VI . 18 ) . diagonal ( VI . 26 ) . Bisect ...
... Prop . 59 ( the case of ' excess ' ) . Let the given area AB be applied to AC , exceeding by the figure CB given in species . I say that each of the sides HC , CE is given . E B A K сн to CB ( VI . 18 ) . diagonal ( VI . 26 ) . Bisect ...
Pagina 304
... ( Prop . 5 ) ; from a given sphere to cut off a segment having a given ratio to the cone with the same base and equal height ( Prop . 7 ) . The problems of Props . 1 and 5 are reduced to that of finding two mean proportionals . Two ...
... ( Prop . 5 ) ; from a given sphere to cut off a segment having a given ratio to the cone with the same base and equal height ( Prop . 7 ) . The problems of Props . 1 and 5 are reduced to that of finding two mean proportionals . Two ...
Pagina 432
... prop at each corner , he finds what weight is borne by each prop ( a ) when the props support the triangle only , ( b ) when to the triangle is added a given weight placed at any point on it ( cc . 38 , 39 ) ; lastly , he finds the ...
... prop at each corner , he finds what weight is borne by each prop ( a ) when the props support the triangle only , ( b ) when to the triangle is added a given weight placed at any point on it ( cc . 38 , 39 ) ; lastly , he finds the ...
Inhoudsopgave
INTRODUCTORY 1 157 | 1 |
NUMERICAL NOTATION AND PRACTICAL CAL | 11 |
PYTHAGOREAN ARITHMETIC | 36 |
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Veelvoorkomende woorden en zinsdelen
according added algebra Apollonius appears Archimedes assumes base begins Book called centre circle cone conics construction contained corresponding cube curve cylinder definition described diameter Diophantus divided draw drawn earth edition Elements equal equation equivalent Euclid expression fact figure five follows four geometry given gives greater Greek height Heron included inscribed Join known latter lemmas length less mathematics means measure meet mentioned method moon multiplied namely observations obtained original Pappus parallel particular perpendicular plane polygon position problem produced proof Prop proportion propositions proved Ptolemy pyramid Pythagoreans radius ratio rectangle reference regarded regular relation represented respectively result right angles segment shows sides similar solid solution solved sphere square straight line Suppose surface theorem theory tion translation treatise triangle volume whole