A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 66
... number of times we shall arrive at numbers in the ratio of equality . C. 6 is preliminary to the subject of polygonal numbers and their respective gnomons . The ... polygonal number with one more side . In fact , an 66 PYTHAGOREAN ARITHMETIC.
... number of times we shall arrive at numbers in the ratio of equality . C. 6 is preliminary to the subject of polygonal numbers and their respective gnomons . The ... polygonal number with one more side . In fact , an 66 PYTHAGOREAN ARITHMETIC.
Pagina 67
... number , the pyramid . The base of the pyramid may be a triangular number , a square , or any polygonal number , but Nico- machus only mentions the first triangular pyramids 1 , 4 , 10 , 20 , 35 , 56 , 84 , and explains ( c . 14 ) the ...
... number , the pyramid . The base of the pyramid may be a triangular number , a square , or any polygonal number , but Nico- machus only mentions the first triangular pyramids 1 , 4 , 10 , 20 , 35 , 56 , 84 , and explains ( c . 14 ) the ...
Pagina 508
... polygonal 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 ...
... polygonal 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 ...
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