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" In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art. "
Elements of Plane Geometry: For the Use of Schools - Page 54
by Nicholas Tillinghast - 1844 - 96 pages
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The Essentials of Geometry (plane)

Webster Wells - 1898 - 264 pages
...From(l), o_ = c- ( 237) ac and o^-ft^Cj-d. ac PROP. VIII. THEOREM. 240. In a series of equal ratios, the sum, of all the antecedents is to the sum of all the consequents as any antecedent 18 to its consequent. Given a:b = c:d=e:f. (1) To Prove a + c + e:b + d +/= a : b....
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Plane and Solid Geometry: Inductive Method

Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...: W~C'*— CD : C' D' . Now substitute these values in your first equations. By proportion, 198, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Can you write an equation so that the sum of the AS in the...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...bc — d .: a + b: a — 6 = c + d:c — d. PROP. VIII. THEOREM. 240. In a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Given a:b = c:d = e:f. (1) To Prove a + c + e :b + d+f= a:...
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Secondary Algebra

George Egbert Fisher - Algebra - 1900 - 438 pages
...b : c, we have, by Art. 8, &2 = ac ; whence b = 19. In a series of equal ratios, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let % : d = пi : d? = пя : d3 — ••• = v, П, Wo i, or -. = v, ~ = v, -f = v, — . di...
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Complete Secondary Algebra

George Egbert Fisher - 1901 - 622 pages
...have, by Art. 8, W = ас ; whence b = -/(ac). 19. In a series of equal ratios, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let n, : (2j = nt : d2 = Wj da = ••• = v, Then n1 = vd, n<i = vd2, n3 = vds, • ••. Ad...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 816 pages
...?^*. [{491] ac By dividing (1) by (2), 2-| = e- 493. THEOREM IX. — In a series of equal ratios the sum of all the antecedents is to the sum of all the consequents as any one antecedent is to its consequent. Let the 'ratios be (1) j- = J- = = = r. (2) a = Ar,...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 818 pages
...= e= [1491] ac By dividing (1) by (2), J| = ^ 493. THEOREM IX. — In a series of equal ratios the sum of all the antecedents is to the sum of all the consequents as any one antecedent w to its consequent. Let the ratios be (1) •• = -• = = ..... = r....
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 460 pages
...h.-.R, or - = ^-^, that P:R = hm: kn. ' kn R kn' 240. THEOREM. If any number of ratios are equal, then the sum of all the antecedents is to the sum of all the consequents as any one antecedent is to its consequent. Let a^ : 6! = 02 : 62 = a3 : 63 = •••. It is required...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1902 - 266 pages
...are in proportion. PROPOSITION IX. THEOREM. 209. In a series of equal ratios, any antecedent is to Us consequent as the sum of all the antecedents is to the sum of all the consequents. Let a:b = c:d=e:f. To prove a + c + e:b + d +f= a:b = c:d = e:f. Let r be the value of the equal ratios,...
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Mathematics

American School (Chicago, Ill.) - Engineering - 1903 - 428 pages
...either fractional or integral.) IX. If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Now, ab = ab (A) And,' ad = be (B) And also, af =. be (C) Adding ( A), (B), (C), a (b + d + /) = b...
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