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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.
Elements of Plane and Solid Geometry - Page 134
by George Albert Wentworth - 1877 - 398 pages

Plane Geometry, with Problems and Application

Herbert Ellsworth Slaught - 1918 - 332 pages
...B'C' ~ C'D' ~ D'E' ~ E'A' . AB+BC+CD+DE + EA = AB . 31s A'B' + B'O'+ 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=AIL. p' A'B' SIGHT WORK 1. If in the above figure AB = 6 inches and A'B' = 4 inches,...

Plane Geometry

Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Modern - 1920 - 328 pages
...angle at which to cut the upper end ? the lower end ? 276. General addition theorem of proportion. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. Given • l = -d = -f- d) , a + c + eace .„. To prove that J±j±» ={=•.•. (2) Proof. Let l^'f^'...

Plane Geometry

Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Modern - 1920 - 328 pages
...angle at which to cut the upper end ? the lower end ? 276. General addition theorem of proportion. In a series of equal ratios the sum of the antecedents is to the gum of the consequents as any antecedent is to its consequent. Given ? = £ = £. (1) _ , a+c+eace...

Solid Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...they are in proportion by subtraction. This is sometimes called proportion by division. THEOREM 124. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. THEOREM 98. If three parallels cut two transversals, the segments on one transversal have the same...

Drill Book in Plane Geometry

Robert Remington Goff - 1922 - 136 pages
...similar to the given polygon. 288. Two regular polygons of the same number of sides are similar. 289. In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as ... what? *2Q0. The perimeters of two similar polygons are to each other as any two corresponding sides....

Essentials of Plane Geometry

David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...terms is to the second term as the difference between the last two terms is to the fourth term. 8. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. 9. If a:b = c:d, then a8 : 6s = c3 : cf . 10. If a:6 = 6:c, then a:c = a2:62. 11. If a : 6 = 6 : c,...

Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1923 - 408 pages
...bd " bd ' • r •„ , ' — *- I Jo ( \ III, § 144] GENERAL THEOREMS 145 Theorem H. In a scries of equal ratios the sum of the antecedents is to the...consequents as any antecedent is to its consequent. Given a/b = c/d = e/f = •••, to prove that a + c + e + ••• _?_£._£_ b+d+f+- -b=d=f= '••'...

Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...equations have the same denominators; then divide the first by the second. Proposition IX. Theorem 197. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. „ „ . ace Hyp.: Grant -r— = = -,- . Det.: To prove that (a + c + e) : (b + d + f) = a : b. Proof:...