The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 98
... ratio to c , and has the same ratio to each of the magnitudes a and b . Take of a and b any equimultiples whatever d and e , and of c any multiple whatever f . Then , because d is the same multiple of a that e is of b , and that a is ...
... ratio to c , and has the same ratio to each of the magnitudes a and b . Take of a and b any equimultiples whatever d and e , and of c any multiple whatever f . Then , because d is the same multiple of a that e is of b , and that a is ...
Σελίδα 99
... ratio than bc has to d . Also d has to bc a greater ratio than it has to ab . For , having made the same construction , it may be shewn , in like manner , that 1 is greater than fg , but that it is not greater than eg . And 1 is a mul ...
... ratio than bc has to d . Also d has to bc a greater ratio than it has to ab . For , having made the same construction , it may be shewn , in like manner , that 1 is greater than fg , but that it is not greater than eg . And 1 is a mul ...
Σελίδα 100
... ratio than it has unto another magnitude is the lesser of the two . b d LET a have to c a greater ratio than b has to c ; a is greater than þ : for because a has a greater ratio to c than b has to c , there are ( v . def . 7 ) some ...
... ratio than it has unto another magnitude is the lesser of the two . b d LET a have to c a greater ratio than b has to c ; a is greater than þ : for because a has a greater ratio to c than b has to c , there are ( v . def . 7 ) some ...
Σελίδα 101
... ratios , & c . Q. E. D. PROPOSITION XII . THEOREM . If any number of magnitudes be proportionals , as one of the antecedents is to its consequent , so shall all the antecedents taken together be to all the con- sequents . LET any number ...
... ratios , & c . Q. E. D. PROPOSITION XII . THEOREM . If any number of magnitudes be proportionals , as one of the antecedents is to its consequent , so shall all the antecedents taken together be to all the con- sequents . LET any number ...
Σελίδα 102
... ratio which the third has to the fourth , but the third to the fourth a greater ratio than the fifth has to the sixth , the first shall also have to the second a greater ratio than the fifth has to the sixth . LET a the first , have the ...
... ratio which the third has to the fourth , but the third to the fourth a greater ratio than the fifth has to the sixth , the first shall also have to the second a greater ratio than the fifth has to the sixth . LET a the first , have the ...
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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