The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 89
... proportion , is the similitude of ratios . IX . Proportion consists in three terms at least . X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second ...
... proportion , is the similitude of ratios . IX . Proportion consists in three terms at least . X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second ...
Σελίδα 90
... inference is as mentioned in the preceding definition , whence this is called " ordinate proportion . " It is demonstrated in 22d Prop . Book 5 .. XX . Ex æquali in proportione perturbata seu inordinata , 90 THE ELEMENTS OF EUCLID .
... inference is as mentioned in the preceding definition , whence this is called " ordinate proportion . " It is demonstrated in 22d Prop . Book 5 .. XX . Ex æquali in proportione perturbata seu inordinata , 90 THE ELEMENTS OF EUCLID .
Σελίδα 91
... proportion . * This term is used when the first magnitude is to the second of the first rank as the last but one is to the last of the second rank ; and as the second is to the third of the first rank , so is the last but two to the ...
... proportion . * This term is used when the first magnitude is to the second of the first rank as the last but one is to the last of the second rank ; and as the second is to the third of the first rank , so is the last but two to the ...
Σελίδα
... proportion of graceful com- positions by living writers . These impart much novelty , whilst they do not impair the soundness of the papers , many of which treat of the higher branches of study . The Illus- trations are tasteful ...
... proportion of graceful com- positions by living writers . These impart much novelty , whilst they do not impair the soundness of the papers , many of which treat of the higher branches of study . The Illus- trations are tasteful ...
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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