| 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.... | |
| 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... | |
| 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:... | |
| 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 îi, or -. = v, ~ = v, -f = v, — . di... | |
| 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... | |
| 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,... | |
| 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.... | |
| 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... | |
| 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,... | |
| 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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