The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 89
... equimultiples what- soever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that ...
... equimultiples what- soever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that ...
Página 91
... Equimultiples of the same or of equal magnitudes are equal to one another . II . Those magnitudes of which the same or equal magnitudes are equimultiples are equal to one another . III . A multiple of a greater magnitude is greater than ...
... Equimultiples of the same or of equal magnitudes are equal to one another . II . Those magnitudes of which the same or equal magnitudes are equimultiples are equal to one another . III . A multiple of a greater magnitude is greater than ...
Página 92
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . LET a the first , be the same multiple of b the second , that c the third is of d the fourth ; and of a , c , let the equimultiples ef ...
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . LET a the first , be the same multiple of b the second , that c the third is of d the fourth ; and of a , c , let the equimultiples ef ...
Página 93
... equimultiples of the second and fourth , viz . the equimultiple of the first shall have the same ratio to that of ... equimultiples what- ever e , f ; and of b and d any equimultiples whatever g , h : then e has the same ratio tog ...
... equimultiples of the second and fourth , viz . the equimultiple of the first shall have the same ratio to that of ... equimultiples what- ever e , f ; and of b and d any equimultiples whatever g , h : then e has the same ratio tog ...
Página 94
... equimultiples k , 1 : and of b and d have been taken certain equimultiples m , n ; if therefore k be greater than m , 1 is greater than n : and if equal , equal ; if less , less ( v . def . 5 ) . And k , 1 are any equimultiples whatever ...
... equimultiples k , 1 : and of b and d have been taken certain equimultiples m , n ; if therefore k be greater than m , 1 is greater than n : and if equal , equal ; if less , less ( v . def . 5 ) . And k , 1 are any equimultiples whatever ...
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Términos y frases comunes
ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle