A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 49
... fact . They would also observe that the ' oblong ' number is double of a triangular number . These facts would be brought out by taking two dots representing 2 , and then placing round them , as successive gnomons , dots representing ...
... fact . They would also observe that the ' oblong ' number is double of a triangular number . These facts would be brought out by taking two dots representing 2 , and then placing round them , as successive gnomons , dots representing ...
Pagina 68
... facts the summation of any number of terms of the series of natural cubes . In general , n3 is the sum of n successive odd num- bers beginning with a certain number determined by the fact that the number of terms preceding it in the ...
... facts the summation of any number of terms of the series of natural cubes . In general , n3 is the sum of n successive odd num- bers beginning with a certain number determined by the fact that the number of terms preceding it in the ...
Pagina
... fact , { ( n − 1 ) n + 1 n ( n + 1 ) = n2 . 2. If we add to a square a triangular number with side less by 1 than that of the square , we obtain a pentagon ; if we add to a pentagon a triangular number with side less by 1 than that of ...
... fact , { ( n − 1 ) n + 1 n ( n + 1 ) = n2 . 2. If we add to a square a triangular number with side less by 1 than that of the square , we obtain a pentagon ; if we add to a pentagon a triangular number with side less by 1 than that of ...
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