 | 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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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. 
