 | David Martin Sensenig - Algebra - 1890 - 556 pages
...whence a — b : a ::c — d:c by alternation, and a — b : b : : e — d : d by alternation. 436. If four quantities are in proportion, they are in proportion by composition and division. Given a : Ъ : : с : d to prove a-\-b : a — Ъ : : c-\-d : c — d Demonstration : Since... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...: d. Proof. Since a : b — c : d, .-. ad = be. (281) .-. a:c = b:d. (283) QED Proposition 5. 287. If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first and second is to the second as the sum of the third and fourth is to... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...~7 * J bd a — bc ^?d thatls, __ = ___. .- . a — b : b = c — d : d. QED Proposition 7. 289. ff 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 and... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...(AxiOM vI.); BD by canceling, — = — ,- or, B : A : : D : CQED A (f PROPOSITION IV. 316. Theorem : If four quantities are in proportion, they are in proportion by composition. Statement : If A : B : : C : D, then, A + B : B : : C + D : D. AC Demonstration : — = — ; adding... | |
 | William Benjamin Smith - Geometry, Modern - 1892 - 314 pages
...proportions as a continued proportion, thus : u :x : :v :y ::w : z. 210. Theorem CXII. — If four tracts are in proportion, they are in proportion by composition, and by division, and by composition and division {Componendo, dividendo, componendo et dividendo) . Datum : u : x :... | |
 | William Benjamin Smith - Geometry, Modern - 1893 - 330 pages
...three proportions as a continued proportion, thus : u:x::v:y::wz 210. Theorem CXII. — If four tracts are in proportion, they are in proportion by composition, and by division, and by composition and division ( Componendo, dividendo, componendo et dividendo) . Datum : u: x:\v\y.... | |
 | William Freeland - Algebra - 1895 - 328 pages
...= d:c. That is, the second term is to the first as the fourth is to the third. 9. VI. Composition. If four quantities are in proportion, they are in proportion by composition. If a:b = c:d. To prove a + b :b = c + d:d. Let a:b = c:d. Then, £ = £• bd Adding 1 to each member,... | |
 | Joe Garner Estill - 1896 - 186 pages
...have used in preparation. A. 1. Prove that, in a circle, a diameter is greater than any other chord. 3. Prove that an angle formed by a tangent and a chord...certain circumference. The arcs AB, BC, and CD, are of 7C", 5:i ' , and 118° respectively. Find the angle between the chords AC and BD, and also the angle... | |
 | 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 and... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...he = ad. § 327 Divide each member of the equation by ac. Then bd ac PROPOSITION VI. THEOREM. 332. If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to... | |
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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. 
