A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 248
... bases and equal in content , whence it follows that any pyramid with triangular base ( and therefore also any pyramid with polygonal base ) is equal to one third part of the prism having the same base and equal height . Lastly , we have ...
... bases and equal in content , whence it follows that any pyramid with triangular base ( and therefore also any pyramid with polygonal base ) is equal to one third part of the prism having the same base and equal height . Lastly , we have ...
Pagina 295
... base . That is , if s be a generator and r the radius of the base , the curved surface of the cone is ( as we should say ) πrs and that of the cylinder 2πrs . We will illustrate Archimedes ' working of the method of exhaustion by the ...
... base . That is , if s be a generator and r the radius of the base , the curved surface of the cone is ( as we should say ) πrs and that of the cylinder 2πrs . We will illustrate Archimedes ' working of the method of exhaustion by the ...
Pagina
... base being for them a figure of unique importance , they had arrived at an expression for its content by measuring how much corn , or what not , would go into a vessel of that shape . They must have seen that the height and the area of ...
... base being for them a figure of unique importance , they had arrived at an expression for its content by measuring how much corn , or what not , would go into a vessel of that shape . They must have seen that the height and the area of ...
Inhoudsopgave
INTRODUCTORY 1 157 | 1 |
NUMERICAL NOTATION AND PRACTICAL CAL | 11 |
PYTHAGOREAN ARITHMETIC | 36 |
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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