The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 89
... fourth , when any 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 ...
... fourth , when any 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 ...
Σελίδα 90
... fourth ; or that the first is to the third as the second to the fourth : as is shewn in the 16th Prop . of this 5th Book . XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred that the second is to ...
... fourth ; or that the first is to the third as the second to the fourth : as is shewn in the 16th Prop . of this 5th Book . XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred that the second is to ...
Σελίδα 91
... fourth of the first rank , so is the third from the last to the last but two of the second rank , and so on in a cross order : and the inference is as in the 18th definition . It is demonstrated in the 23d Prop . of Book 5 . AXIOMS . I ...
... fourth of the first rank , so is the third from the last to the last but two of the second rank , and so on in a cross order : and the inference is as in the 18th definition . It is demonstrated in the 23d Prop . of Book 5 . AXIOMS . I ...
Σελίδα 92
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . LET ab ...
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . LET ab ...
Σελίδα 93
... fourth d , and that the fifth kf is the same multiple of the second b , which the sixth 1h is of the fourth d ; ef the first together with the fifth , is the same multiple ( ii . 5 ) of the second b , which gh the third together with ...
... fourth d , and that the fifth kf is the same multiple of the second b , which the sixth 1h is of the fourth d ; ef the first together with the fifth , is the same multiple ( ii . 5 ) of the second b , which gh the third together with ...
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a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle