A Manual of Greek MathematicsClarendon Press, 1931 - 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 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