A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 45
... gnomon is interesting . The gnomon was originally the upright stick which cast shadows on the plane or hemispherical surface of a sun- dial to mark the hours ; and ' marker ' or ' pointer ' is the literal meaning of the word . It ...
... gnomon is interesting . The gnomon was originally the upright stick which cast shadows on the plane or hemispherical surface of a sun- dial to mark the hours ; and ' marker ' or ' pointer ' is the literal meaning of the word . It ...
Pagina 69
... ( gnomon BC'D ) = n . n2 = n3 . = Similarly ( gnomon B'C " D ' ) = ( n - 1 ) 3 , and so on . Therefore 13 + 23 + 33 + ... + n3 the sum of the gnomons down to the gnomon about the small square at A which has 1 for its side , plus that ...
... ( gnomon BC'D ) = n . n2 = n3 . = Similarly ( gnomon B'C " D ' ) = ( n - 1 ) 3 , and so on . Therefore 13 + 23 + 33 + ... + n3 the sum of the gnomons down to the gnomon about the small square at A which has 1 for its side , plus that ...
Pagina 233
... gnomon UWV , and the problem is therefore to find the gnomon UWV such that its area is equal to that of the given rectilineal figure C. And clearly the gnomon cannot be greater than the parallelo- gram EF . Therefore C must not be ...
... gnomon UWV , and the problem is therefore to find the gnomon UWV such that its area is equal to that of the given rectilineal figure C. And clearly the gnomon cannot be greater than the parallelo- gram EF . Therefore C must not be ...
Inhoudsopgave
INTRODUCTORY 157 | 5 |
NUMERICAL NOTATION AND PRACTICAL CAL | 11 |
PYTHAGOREAN ARITHMETIC | 36 |
Copyright | |
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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