| George Albert Wentworth - Algebra - 1906 - 440 pages
...this in any particular case, it will be found sufficient to substitute ra for b and re for d. 388. **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** For, if ? = £ = ! = £=..., bdfh we may put r for each of these ratios. • Then ? = r, C = r, l =... | |
| George Albert Wentworth - 1894 - 218 pages
...composition 7:2 = 21:0; by division, 3:2 = 0:0; and by composition and division 7 :3 = 21 : 9. 216. **In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.** aceg For, let - = j = - = f • bd / h Denote the value of each of these ratios by r. acea Then - =... | |
| William James Milne - Algebra - 1906 - 444 pages
...to b + d +f+ h ? Compare this ratio with the ratio a : b ; with the other ratios. PRINCIPLE 13. — **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** Thus, when a:6 = C:d = g: ft and so on, a + с + e + g + - : Ь + d +f+ Л + ••• : : a : Ь.... | |
| Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...±b:a = x±y: x; (2) a±b: b= x±y:y; (3) a ± b : x ± y = a : x, etc. NOTE II. In any proportion **the sum of the antecedents is to the sum of the consequents as** either antecedent is to its consequent. (Explain.) Also, in any proportion the difference of the antecedents... | |
| Charles Hamilton Ashton, Walter Randall Marsh - Algebra - 1907 - 304 pages
...roots of four quantities, a, b, c, d, which are in proportion, are in proportion ; or — =—• XI. **In a series of equal ratios the sum of the antecedents...sum of the consequents as any antecedent is to its** own consequent. If |=Л = ™ = *, (i) bdn у т : acmx УОЧ let - = r, - = r, - = r, - = r, (2)... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1907 - 328 pages
...Hence, a + c + e = bk + dk +fk =(b + d +/) k, a+c+e , ace "" That is, If several ratios are equal, **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** EXERCISES 1. If ad = bc, show that - = - . Hint. Divide by bd. bd 2. If ad = bc, show that- = -•... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1907 - 328 pages
...c + e = bk + dk +fk =(b + d +/) k, a+c+e . ace " --- That is, If several ratios are equal, the s?<m **of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** EXERCISES 1. If ad = bc, show that- = -• Hint. Divide by bd. bd 2. If ad = bc, show that - = -•... | |
| Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...(1) a ±b:a = x±y: x; (2) a±b:b = x±y:y; (3) a ± b: x± y = a: x, etc. NOTE II. In any proportion **the sum of the antecedents is to the sum of the consequents as** either antecedent is to its consequent. (Explain.) Also, in any proportion the difference of the antecedents... | |
| Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...first two terms is to their difference as the sum of the last two terms is to their difference. 334. **In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.** 336. A straight line parallel to the base of a triangle divides the other two sides proportionally.... | |
| Albert Harry Wheeler - Algebra - 1908 - 698 pages
...applying (vi.) to (1) by the corresponding ratios obtained by applying (vii.) to (1). (ix.) In a seríes **of equal ratios the sum of the antecedents is to the...consequents as any antecedent is to its consequent.** That is, if a : Ъ — с : d = e : f — = m : n, then (a + с + e + + m) : (Ь + d + f + + n) = a... | |
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