Greek MathematicsDover, 1963 - 552 pagina's |
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Pagina 100
... proportion was only applicable to commensurable quan- tities . This would be no obstacle to the use of proportions in such a proof so long as the existence of the incom- mensurable remained undiscovered . But , when once the ...
... proportion was only applicable to commensurable quan- tities . This would be no obstacle to the use of proportions in such a proof so long as the existence of the incom- mensurable remained undiscovered . But , when once the ...
Pagina 227
... proportion alternando , separando , componendo respectively ; that is , they prove that , if the original proportion is true , the transformed proportion is also true . 19. If then a : b = c : d , ( ac ) ( b - d ) = a : b . The ...
... proportion alternando , separando , componendo respectively ; that is , they prove that , if the original proportion is true , the transformed proportion is also true . 19. If then a : b = c : d , ( ac ) ( b - d ) = a : b . The ...
Pagina 548
... Proportion : theory discovered by Pythagoras 51 , for commensur- able magnitudes only 110 : def . of numerical proportion 124 , 235 : ' perfect ' proportion 51-2 : Euclid's universally applicable theory due to Eudoxus 190-1 , 224 ...
... Proportion : theory discovered by Pythagoras 51 , for commensur- able magnitudes only 110 : def . of numerical proportion 124 , 235 : ' perfect ' proportion 51-2 : Euclid's universally applicable theory due to Eudoxus 190-1 , 224 ...
Inhoudsopgave
Classification of mathematical subjects | 5 |
NUMERICAL NOTATION AND PRACTICAL CAL | 11 |
B Addition and subtraction | 28 |
Copyright | |
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algebra Apollonius Archimedes Archytas Aristotle arithmetic assumed astronomy axis base bisected Book centre of gravity chord circle circumference circumscribed cone conics construction contained cube curve cylinder definition Democritus diameter Diophantus divided draw drawn earth Elements equal equation equilateral equivalent Eratosthenes Eucl Euclid Eudemus Eudoxus Eutocius figure geometry given ratio given straight line gives gnomon Greek height Heron Hipparchus Hippocrates hyperbola inscribed irrational isosceles lemmas length loci magnitudes mathematics mean proportionals method of exhaustion moon multiple namely Nicomachus Pappus parabola parallel parallelogram pentagon perpendicular plane Plato polygon Porisms problem Proclus produced proof Prop propositions proved Ptolemy pyramid Pythagoras Pythagoreans radius rectangle respectively right angles right-angled triangle says segment semicircle sides similar solution solved sphere square number surface tangent Thales Theaetetus Theon Theon of Alexandria theorem theory tion treatise volume