...ab or - = -• с d .'. a : с = b : d. 317. In a series of equal ratios, the sum of the antecedent? is to the sum of the consequents as any antecedent is to its consequent. n • » a с ea For, if _ = - = - = £, oafп r may be put for each of these ratios. rm.™ a_ r c_.-r...

...= -> = 7. , each of these ratios = , - =- . • b 9 f b+d+f a result which may be thus enunciated : In a series of equal ratios the sum of the antecedents is to ¡he sum of the consequents as any antecedent is to its consequent. Example. 1. If - = — find tho...

...cp: dq. THEOREM XVI. In a series of equal ratios, (he sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Let a : 6 = с : d, And m:n=p:q. Then а с t Ь d' And ™=£. Let а:Ь = c:d= e: f. Let г = the common ratio....

...the first two terms is to their difference as the sum of the last two terms to their difference. 303. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. 304. The products of the corresponding terms of two or more proportions are in proportion. 305. Like...

...obtained by: VI. Composition, и --\- c : c : : b + d : d. VII. Division. « — c:c::b — d : d. 350. In a series of equal ratios, the sum of the antecedents...sum of the consequents as any antecedent is to its т-. -taceg For-lf b = d = J=V r may be put for each of these ratios. , ., aeeg Then - = f,- = r,j=r,0...

...equations ma me multiplying as ot fractions a _ c PROPOSITION VIII 195. Theorem. In a continued proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let ————-- b~d~f'~ ['value of each ratio e=fr ,.] clearing of fractions separately a + c + e =...

...Dividing (1) by (2), member by member, _ ab~cd' that is, о + b • a — b = с + d : с — d. 530. In a series of equal ratios, the sum of the antecedents is tc the sum of the consequents as any antecedent is toits consequent. ï-ï-i-7-î' then, by § 522,...

...equal. 21. In every proportion the product of the extremes is equal to the product of the means. 22. lu a series of equal ratios, the sum of the antecedents is to the sum of the conseqnents as any antecedent is to its conseqnent. 23. If a line be drawn through two sides of a triangle...

...kind as a and b. In applying alternation, however, all four quantities must be of the same kind. 340. In a Series of Equal Ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. _, .. a с eg For'lf -b = d = f = -h' r may be put for each of these ratios. г_, a с eg Then, -b...

...however, all four quantities must be of the same kind. 340. In a Series of Equal Ratios, the sum of th e antecedents is to the sum of the consequents as any antecedent is to its consequent. _< .„ aeet) For, if - = - = - = £, bdfh r may be put for each of these ratios. . aeeg Then, - -...