 | Joe Garner Estill - Geometry - 1896 - 168 pages
...the point of contact of the tangent, is measured by one-half of the included arc. B. 4. Prove that if four quantities are in proportion, they are in proportion by composition and by division. 5. Show how to construct a triangle equal to a given pentagon. 6. Show how to inscribe... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...Therefore (by 201), ab: a = c - d: c. Similarly, a — b :b = c — d: d. QED PROPOSITION VII. 206. If four quantities are in proportion, they are in proportion by Composition and Division; that is, the sum of the first and second is to their difference as the sum of the third... | |
 | William Chauvenet - Geometry - 1898 - 376 pages
...memhers of [1] ; then or, reducing, A + B = A' + B' B B' and dividing this by [1], A + B A' + B' A " A' ' [2] results which are briefly expressed by the theorem, if four quantitiet are in proportion, they are in proportion by composition ; the term composition being employed... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...5-1; od a — bc— d that is, -y- = — Or a — b .b = c — d:d. PROPOSITION VIII. THEOREM. 334. If four quantities are in proportion, they are in proportion by composition and division; that is, the sum of the first two terms is to their difference as the sum of the last... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...simplifying as in § 97, a - b:b::c - d: d. The student should prove that a — b : a : : c - d : c. 99. If four quantities are in proportion, they are in proportion by composition and division. Let the proportion be a : 6 : : c : d. a+b c+d Then by § 97, bd a — bc — d ' 6 d... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...Then bd that is, —7— —-j— bd Or a — b : b — c — d : d. PROPOSITION VIII. THEOREM. 334. If four quantities are in proportion, they are in proportion by composition and division; that is, the sum of the first two terms is to their difference as the sum of the last... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...Transform the proposition, m : x = p : q, so that x becomes the fourth term. PROPOSITION VI. THEOREM 270. If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...—, arranged by composition and division, 0 Ci becomes a + b _c + d PROPOSITION VII. THEOREM 431. If four quantities are in proportion, they are in proportion by composition and division. H. a — bc — d Proof. [Analyze and solve.] 432. EXERCISE. If 2 = -, bd prove ^l«... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...of x and y. Ex. 524. If x - y : y = 2 : 3, find the ratio of x and y. PROPOSITION VIII. THEOREM 272. If four quantities are in proportion, they are in proportion by composition and division, ie the sum of the first two terms is to their difference as the sum of the last two terms... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...of x and y. Ex. 524. If x - y : y = 2 : 3, find the ratio of x and y. PROPOSITION VIII. THEOREM 272. If four quantities are in proportion, they are in proportion by composition and division, ie the sum of the first two terms is to their difference as the sum of the last two terms... | |
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If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term. 
