The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 89
... magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have ...
... magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have ...
Σελίδα 90
... four proportionals , and it is inferred that the second is to the first as the fourth to the third . Prop . B. Book ... magnitudes are taken , two and two . XIX . Ex æquali , from equality . This term is used simply by itself ; when the ...
... four proportionals , and it is inferred that the second is to the first as the fourth to the third . Prop . B. Book ... magnitudes are taken , two and two . XIX . Ex æquali , from equality . This term is used simply by itself ; when the ...
Σελίδα 93
... fourth d . If , therefore , the first , & c . Q. E. D. e b g c PROPOSITION IV . - THEOREM . If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the ...
... fourth d . If , therefore , the first , & c . Q. E. D. e b g c PROPOSITION IV . - THEOREM . If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the ...
Σελίδα 95
... magnitudes , & c . Q. E. D. a h b a f PROPOSITION A. - THEOREM . If the first of four magnitudes has to the second the same ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also ...
... magnitudes , & c . Q. E. D. a h b a f PROPOSITION A. - THEOREM . If the first of four magnitudes has to the second the same ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also ...
Σελίδα 96
... magnitude a be to b as c is to d , then also inversely b is to a as d to C. Take of b and d any equimultiples ... four magnitudes , & c . Q. E. D. PROPOSITION C. — THEOREM . If the first be the same multiple of the second , or the ...
... magnitude a be to b as c is to d , then also inversely b is to a as d to C. Take of b and d any equimultiples ... four magnitudes , & c . Q. E. D. PROPOSITION C. — THEOREM . If the first be the same multiple of the second , or 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