The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 89
... multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
... multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
Σελίδα 91
... multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION I. - THEOREM . If any number of magnitudes be equimultiples of as many others , each of each ; what multiple soever any one of ...
... multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION I. - THEOREM . If any number of magnitudes be equimultiples of as many others , each of each ; what multiple soever any one of ...
Σελίδα 92
... 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 the first , be the same multiple ...
... 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 the first , be the same multiple ...
Σελίδα 93
... multiple of b , that gl is of d . For the same reason , kf is the same multiple of b , that 1h is of d ; and so , if there be more parts in ef , gh , equal to a , c because , therefore , the first ek is the same multiple of the second b ...
... multiple of b , that gl is of d . For the same reason , kf is the same multiple of b , that 1h is of d ; and so , if there be more parts in ef , gh , equal to a , c because , therefore , the first ek is the same multiple of the second b ...
Σελίδα 94
... multiple of a that fis of c and of e and f have been taken equimultiples k , 1 ; therefore k is the same multiple of a , that 1 is of c ( v . 3 ) . For the same reason , m is the same multiple of b , that n is of d and because , as a is ...
... multiple of a that fis of c and of e and f have been taken equimultiples k , 1 ; therefore k is the same multiple of a , that 1 is of c ( v . 3 ) . For the same reason , m is the same multiple of b , that n is of d and because , as a is ...
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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