| 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,... | |
| 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^'... | |
| 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... | |
| 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.... | |
| 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,... | |
| 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:... | |
| Edward Ira Edgerton, Perry Amherst Carpenter - Algebra - 1925 - 400 pages
...transformation, divide the proportion resulting in (3) by that resulting in (4). 22. Theorem. — (9) **In a series of equal ratios, the sum of the antecedents...consequents, as any antecedent is to its consequent.** /,. ac ,ea Glven_ . ~ =?= | to prove CL (* P Proof: Since -, ~, -, etc., are all equal, denote the... | |
| Education - 1893 - 648 pages
...Prove that if any number of quantities are in proportion any antecedent will be to its consequent as **the sum of the antecedents is to the sum of the consequents.** 9. The area of a circle is equal to the circumference multiplied by one-half the radius. Demonstrate.... | |
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