 | Walter Randall Marsh - Algebra - 1905 - 412 pages
...each member of (1) to the nth power, whether n is integral or fractional, an _ cn b'1 ~ cF XI. _Zn д series of equal ratios the sum of the antecedents...sum of the consequents as any antecedent is to its own consequent. К а с т х ,л^ T=J=— = -•> t1) о dn у let f.* «-,,»_,, S.,, (2) о а... | |
 | Walter Nelson Bush, John Bernard Clarke - Geometry - 1905 - 378 pages
...is said to be derived from the given proportion by compositivn and division.) XI. 2. In any number of equal ratios, the sum of the antecedents is to...consequents as any antecedent is to its consequent. Hyp. If a: 6 : : c : e : :/: g : : etc., Cone.: then a + c+/+ ...: b + e + g+ ... : : a: 6 : : c: e... | |
 | 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.... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...antecedents and the denominators the consequents. The general truth was shown in that article, that in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. AREAS OF POLYGONS 36. Definitions. — The area of a surface is the superficial space included within... | |
 | 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 =... | |
 | 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 - = -•... | |
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In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. 
