| Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...proportions from each of the following equations: (1) a*-V=cd. (3) ax+bx+cx=nd+nh+nk. 403. Theorem. **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** _,. acea Given ---.--I. bdfh _ l - I To prove b+d+f+hbdfh Proof. Let - = r. Then - = r, -=r, g- = r.... | |
| Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...segments and XY : X' Y' equals the ratio of similitude. 296. Fundamental Theorem about Equal Ratios. **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** If _ . . bdfh then g + c + e + g = g = g b+d+f+hbd Proof. 1. Let r = - and hence br = a. b PROPOSITION... | |
| John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...dent and b is called the consequent; each is called a term of the ratio. 381. THEOREM. In a sequence **of equal ratios, the sum of the antecedents is to...consequents as any antecedent is to its consequent.** For, let - = - = - = 2 = r, where a, b, c ..• are positive numbers. bdfh Then a = br, c = dr, e =... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1915 - 408 pages
...dk, e =fk. bdf Hence a + c + e = bk + dk +fk =(b + d +f)k, da + c + e _ k = a_c _e 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. WRITTEN EXERCISES... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1915 - 412 pages
...+ c + e = bk + dk +fk =(b + d +f)k, and a+c + e = fc=g = g = g. &+d+/ bdf That is, 2%e sum o/ ķAe **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. WRITTEN... | |
| Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...x ±y:x; (2) a ± 6 : 6 = x ± y : y ; (3) a ± 6 : x ± y = a : x, etc. NOTE 2. In any proportion **the sum of the antecedents is to the sum of the consequents as** either antecedent is to its consequent. Also, in any proportion the difference of the antecedents is... | |
| William Betz - Geometry - 1916 - 536 pages
..., — T, — —, ' etc. aoc a + b + c + • • • _ a a' + b' + c' + • • • ~ a' Why? §361 **(In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.)** 3. That is, p :p' = a : a'. EXERCISES 1. Two building lots have the same shape. It takes 400 ft. of... | |
| Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
..."division"; a + b _ c + d is called " composition and divia — b ~ c — d sion." 205. Theorem VII. **In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.** _. ,. ...ace Given the equal ratios: r = -j = 7 = . oaf ' „ , a + c 4- e. . . . ace To prove that... | |
| John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...first two terms is to the second term as the difference of the last two terms is to the fourth. 277. **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** 279. Like powers of the terms of a proportion are in proportion. 285. A line drawn through two sides... | |
| Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...E'B'D'. A BCD ~ A B'C'D'. Why? Why? Why? Why? Why? Why? Why? 296. Fundamental Theorem about Equal Ratios. **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** If " = _ = - = ? bdf h' then a + c + e + ga c_ = e^ b+d+f+hbd Proof. 1. Let r = - and hence br = a.... | |
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