A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 43
... triangular number . Hence Lucian's story that Pytha- goras once told some one to count , and , when he had said 1 , 2 , 3 , 4 , Pythagoras interrupted ' Do ... number . This is seen FIGURED NUMBERS 43 Figured numbers (a) Triangular numbers.
... triangular number . Hence Lucian's story that Pytha- goras once told some one to count , and , when he had said 1 , 2 , 3 , 4 , Pythagoras interrupted ' Do ... number . This is seen FIGURED NUMBERS 43 Figured numbers (a) Triangular numbers.
Pagina 50
... triangular numbers , and that any square number is the sum of two successive • · • . C • triangular numbers . The annexed diagrams illustrate these facts ; the second is proved by the identity In ( n - 1 ) + n ( n + 1 ) = n2 . Another ...
... triangular numbers , and that any square number is the sum of two successive • · • . C • triangular numbers . The annexed diagrams illustrate these facts ; the second is proved by the identity In ( n - 1 ) + n ( n + 1 ) = n2 . Another ...
Pagina
... numbers . Nico- machus in particular has rules for obtaining a polygonal number of ( a + 1 ) sides from a polygonal number of a sides . Thus he says : 1. If we put two consecutive triangular numbers to- gether , we get a square . In ...
... numbers . Nico- machus in particular has rules for obtaining a polygonal number of ( a + 1 ) sides from a polygonal number of a sides . Thus he says : 1. If we put two consecutive triangular numbers to- gether , we get a square . In ...
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