A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 252
... Join alternate angular points in one decagon , making a regular pentagon inscribed in the same circle ; do the same in the other circle , but so that the angular points of the second pentagon are not opposite those of the first pentagon ...
... Join alternate angular points in one decagon , making a regular pentagon inscribed in the same circle ; do the same in the other circle , but so that the angular points of the second pentagon are not opposite those of the first pentagon ...
Pagina 261
... Join A , B to the centre 0. Draw OC parallel to AB . Join CB , and draw DE parallel to BC meet- ing the circle again in E. Then shall BC , DE intercept between them an area equal to m / n of that of the circle . F E Join AC . Then the ...
... Join A , B to the centre 0. Draw OC parallel to AB . Join CB , and draw DE parallel to BC meet- ing the circle again in E. Then shall BC , DE intercept between them an area equal to m / n of that of the circle . F E Join AC . Then the ...
Pagina 429
... Join BE , and draw GH parallel to BE , meeting BC in H. Join CE , EH , EG . Then AGBE = △ HBE . Add to each AABE ; therefore AAGE = ( quadrilateral ABHE ) . A Therefore B C H E D ( quadrilateral ABHE ) : ACED AAGE : ACED = AE : ED ...
... Join BE , and draw GH parallel to BE , meeting BC in H. Join CE , EH , EG . Then AGBE = △ HBE . Add to each AABE ; therefore AAGE = ( quadrilateral ABHE ) . A Therefore B C H E D ( quadrilateral ABHE ) : ACED AAGE : ACED = AE : ED ...
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