Books Books 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

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.... ## Plane Geometry

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... ## Plane Geometry

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 =... ## Elementary Algebra

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... ## Elementary Algebra

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/ íAe 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... ## Robbin's New Plane Geometry

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... ## Plane and Solid Geometry

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... ## Plane Geometry

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... ## Solid Geometry

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... 