| Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...word division is here used in a sense entirely different from its usual meaning. 206. Theorem VII. **In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.** Given the equal ratios : -?•=-=-; = oaf To Proof. be r. Then Or Adding: Therefore that a 4- c -\-... | |
| William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...proportion when written in any order that makes one pair the extremes and the other pair the means. 361. **In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.** 362. If four numbers are in proportion, they are in proportion by alternation ; that is, the first... | |
| John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...or like roots of the terms of a proportion are in proportion. (8) If two or more ratios are equal, **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** § 123. If DE is parallel to side AB of triangle ABC and meets AC at D and BC at E, then AC=BO dAC=BC... | |
| John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...first, and take the nth root of each member to prove the second. (8) If two or more ratios are equal, **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** That is, .* ace , , ia + c + e + etc. a if - = - = - = etc., then . , . - = T = etc. bdfb + d+f+etc..... | |
| Elmer Adelbert Lyman, Albertus Darnell - Algebra - 1917 - 520 pages
...12 21 3+9 + 12 + 21 45 of these fractions. This property of equal fractions may be stated thus : IX. **In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.** ._ т а с ex PEOOF. Let r = - = - = - • bdf у Also let each ratio equal Jc. -=k, from which a... | |
| William Charles Brenke - Algebra - 1917 - 212 pages
...d", then aa'a" : ЪЪ'Ъ" = cc'c" : dd'd". ., a_c a'_c' a"_c" lori1 ~' ~" *~'" 1hen _ _ b~d' V~d" 10. **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** Thus: a! : 02 = bi : 62 = Ci : C2 = ai + bi + Ci : 02 + 62 + Cj. For ]i— = — = -=••• =r,... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1917 - 674 pages
...; then a = bk, с = dk, c. =fk. bdf Hence a + с + к = bk + dk +fk =(b + d +f)k, 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. l I FURTHER... | |
| George Hervey Hallett, Robert Franklin Anderson - Algebra - 1917 - 432 pages
...; that is, This identity may be expressed in words as follows : In a number of equal ratios the gum **of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** ace b~T' d ~ Г' } .= r. Then, a = br, c = dr, e=fr. Adding, a + c + e=(b\-d+J Dividing, a + c+ e b+d+f... | |
| Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...equations: (1) a? - b2 = cd. (3) ax+bx+cx-rad+rih+rik. 403. Theorem. In a series of equal ratios, the aum **of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** _. acea Given I=^=7=l' To prove a+c+e+g =a^=e = g_ b+d+f+hbdfh Proof. Let - = r. Then -=r, -=r, -=r.... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...A'B' B'C' C'D' D'E' E'A'' . AB+BC+CD+DE+EA __ AB - 31g A'B' + B'C' + C'D' + D'E' + E'A' A'B' ' * ' ' ' **(In a series of equal ratios the sum of the antecedents is to the sum of,** etc.) QED That is. P-= AB . p' A'B' SIGHT WORK 1. If in the above figure AB = 6 inches and A'B' = 4... | |
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