A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 176
... solid and appropriates the first four solids to the four elements , the pyramid or tetrahedron to fire , the octahedron to air , the icosahedron to water , and the cube to earth , while the Creator uses the fifth solid , the ...
... solid and appropriates the first four solids to the four elements , the pyramid or tetrahedron to fire , the octahedron to air , the icosahedron to water , and the cube to earth , while the Creator uses the fifth solid , the ...
Pagina 301
... solid rhombi TCOT and TBOT . And so on . Archimedes proves that the volumes of the elements of the solid are equal respectively to a series of cones of height h , where h is the length of the perpendicular from O on any one of the sides ...
... solid rhombi TCOT and TBOT . And so on . Archimedes proves that the volumes of the elements of the solid are equal respectively to a series of cones of height h , where h is the length of the perpendicular from O on any one of the sides ...
Pagina 350
... solid ' , and ' linear ' respectively . ( 1 ) ' Plane loci ' are not merely loci in a plane ; they are actually only straight lines and circles ; ( 2 ) ' Solid loci ' are conics pure and simple , the idea being that they arise from ...
... solid ' , and ' linear ' respectively . ( 1 ) ' Plane loci ' are not merely loci in a plane ; they are actually only straight lines and circles ; ( 2 ) ' Solid loci ' are conics pure and simple , the idea being that they arise from ...
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