A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 57
... bisected in C and produced to D , then AD2 + DB2 = 2AC2 + 2CD2 . If AC = CB = x , and BD = y , this proposition gives or ( 2x + y ) 2 + y2 = 2x2 + 2 ( x + y ) 2 , ( 2x + y ) 2 - 2 ( x + y ) 2 = 2x2 — y2 , which is the formula required ...
... bisected in C and produced to D , then AD2 + DB2 = 2AC2 + 2CD2 . If AC = CB = x , and BD = y , this proposition gives or ( 2x + y ) 2 + y2 = 2x2 + 2 ( x + y ) 2 , ( 2x + y ) 2 - 2 ( x + y ) 2 = 2x2 — y2 , which is the formula required ...
Pagina 83
... bisected by its diameter ( = Eucl . I , Def . 17 ) ; ( 2 ) that the angles at the base of an isosceles triangle are equal ( = Eucl . I. 5 ) ; ( 3 ) that , if two straight lines cut one another , the ver- tically opposite angles are ...
... bisected by its diameter ( = Eucl . I , Def . 17 ) ; ( 2 ) that the angles at the base of an isosceles triangle are equal ( = Eucl . I. 5 ) ; ( 3 ) that , if two straight lines cut one another , the ver- tically opposite angles are ...
Pagina 189
... bisected by , the zodiac circle . In the case of the sun and moon Eudoxus used three spheres only ; the two outer ... bisecting it is the zodiac circle . B The hippopede is really the intersection of the sphere about the earth as centre ...
... bisected by , the zodiac circle . In the case of the sun and moon Eudoxus used three spheres only ; the two outer ... bisecting it is the zodiac circle . B The hippopede is really the intersection of the sphere about the earth as centre ...
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