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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. "
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 17
por International Correspondence Schools - 1906
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A Review of Algebra

Romeyn Henry Rivenburg - 1914 - 80 páginas
...pair, etc. 3. Alternation. 4. Inversion. 5. Composition. 6. Division. 7. Composition and division. 8. In a series of equal ratios, the sum of the antecedents...is to the sum of the consequents as any antecedent, etc. Special method .of proving four quantities in proportion. Let - = x, a = bx, etc. Development...
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Solid Geometry

Sophia Foster Richardson - 1914 - 209 páginas
...ratio of similitude of Fl and F2. Then m^_ _ m2 _ m3 _ ..._£» m/ m2' m3' (In a continued proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.) That is, area of surface of Fl ^ 3g area of surface of F2 477. THEOREM. The ratio of the volumes of...
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A Review of Algebra

Romeyn Henry Rivenburg - 1914 - 80 páginas
...etc. (c) Alternation. (e) Composition. (d) Inversion. (/) Division, (gr) Composition and division. (A) In a series of equal ratios, the sum of the antecedents is to the sum of the consequents etc. (г) Like powers or like roots of the terms of a proportion etc. 6. If x : m : : 13 : 7, write...
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Plane Geometry

Webster Wells, Walter Wilson Hart - 1915 - 309 páginas
...segments and XY : X' Y' equals the ratio of similitude. 296. Fundamental Theorem about Equal Ratios. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. If _ . . bdfh then g + c + e + g = g = g b+d+f+hbd Proof. 1. Let r = - and hence br = a. b PROPOSITION...
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Plane Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - 1915 - 277 páginas
...proportions from each of the following equations: (1) a*-V=cd. (3) ax+bx+cx=nd+nh+nk. 403. Theorem. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. _,. acea Given ---.--I. bdfh _ l - I To prove b+d+f+hbdfh Proof. Let - = r. Then - = r, -=r, g- = r....
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Plane Geometry

John Wesley Young, Albert John Schwartz - 1915 - 223 páginas
...dent and b is called the consequent; each is called a term of the ratio. 381. THEOREM. In a sequence of equal ratios, the sum of the antecedents is to...consequents as any antecedent is to its consequent. For, let - = - = - = 2 = r, where a, b, c ..• are positive numbers. bdfh Then a = br, c = dr, e =...
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Elementary Algebra

Herbert Ellsworth Slaught, Nels Johann Lennes - 1915 - 373 páginas
...dk, e =fk. bdf Hence a + c + e = bk + dk +fk =(b + d +f)k, da + c + e _ k = a_c _e b+d+fbdf That is, The sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Mean Proportional. If a : b ::b:x, then b is called a mean proportional between a and x. WRITTEN EXERCISES...
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Elementary Algebra

Herbert Ellsworth Slaught, Nels Johann Lennes - 1915 - 373 páginas
...+ c + e = bk + dk +fk =(b + d +f)k, and a+c + e = fc=g = g = g. &+d+/ bdf That is, 2%e sum o/ íAe antecedents is to the sum of the consequents as any antecedent is to its consequent. Mean Proportional. If a : b : : b : x, then b is called a mean proportional between a and x. WRITTEN...
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Robbin's New Plane Geometry

Edward Rutledge Robbins - 1915 - 264 páginas
...x ±y:x; (2) a ± 6 : 6 = x ± y : y ; (3) a ± 6 : x ± y = a : x, etc. NOTE 2. In any proportion the sum of the antecedents is to the sum of the consequents as either antecedent is to its consequent. Also, in any proportion the difference of the antecedents is...
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Plane and Solid Geometry

William Betz - 1916 - 507 páginas
..., — T, — —, ' etc. aoc a + b + c + • • • _ a a' + b' + c' + • • • ~ a' Why? §361 (In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.) 3. That is, p :p' = a : a'. EXERCISES 1. Two building lots have the same shape. It takes 400 ft. of...
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