A Manual of Greek MathematicsDover Publications, 1963 - 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 • • · · • triangular numbers . The annexed diagrams illustrate these facts ; the second is proved by the identity { n ( n − 1 ) + n ( n + 1 ) = n2 . Another ...
... triangular numbers , and that any square number is the sum of two successive • • · · • triangular numbers . The annexed diagrams illustrate these facts ; the second is proved by the identity { n ( n − 1 ) + n ( n + 1 ) = n2 . Another ...
Pagina 508
... 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 157 | 5 |
NUMERICAL NOTATION AND PRACTICAL CAL | 11 |
PYTHAGOREAN ARITHMETIC | 36 |
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algebra Apollonius Archimedes Archytas arithmetic assumes astronomy axis base bisects Book centre of gravity chord circle circumscribed commentary cone conics contained cube curve cylinder definition diameter Diophantus divided edition equal equation equivalent Eratosthenes Eucl Euclid Eudemus Eudoxus Eutocius figure geometry given ratio given straight line gives Greek height Heron Hipparchus hyperbola inscribed lemmas length loci mathematics mean proportionals method method of exhaustion moon multiplied namely Pappus parabola parallel parallelogram pentagon perpendicular plane Plato polygonal number Porisms Posidonius problem Proclus proof Prop propositions proved Ptolemy pyramid Pythagoras Pythagoreans quadratic quadratic equations radius rectangle respectively right angles right-angled triangle segment semicircle sexagesimal sides similar solid solution solved sphere square number surface tangent Theon Theon of Alexandria theorem theory tion translation treatise triangular number volume whence