 | Franklin Ibach - Geometry - 1882 - 208 pages
...d : c. Take the form — = — • о а Divide 1 by each member. Then 1-1, а с THEOREM VII. 162. If four quantities are in proportion, they are in proportion by composition. Let a : b :: с : d. To prove that a .\- b : b : : с -fd : d. Take the form .7- = -=-• о а To... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...have, I = -g, or A : B :: C : D; in like manner, we have, £ = £, or B : A :: D | C; PROPOSITION III. THEOREM. If four quantities are in proportion, they are in proportion by alternation. • Assume the proportion, BD A : B : : C : D ; whence, T" = ~C" Q Multiplying each member... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...bd .• . a — b : b = c — d : d. QED Similarly, a — b : a = c — d : c. Proposition 7. 289. If four quantities are in proportion, they are in proportion by composition and division; that is, (he sum of the first and second is to their difference as the sum of the third... | |
 | 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 :... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...= ~Tc <AXIOM vI-> ; BD by canceling, —- = — ; or, B : A : : D : CQE D, AC 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 / to... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...alternation. PROP. III. If four quantities are in proportion, they are in proportion by inversion. PROP. IV. If four quantities are in proportion, they are in proportion by composition. PROP. V. If four quantities are in proportion, they are in proportion by division. SECTION II.— EQUAL... | |
 | Seth Thayer Stewart - Geometry - 1891 - 426 pages
...consequents (AXIOM vi.), AD BC , ,. AB which is the same as A : C : : B : DQED PROPOSITION III. 315. Theorem : if four quantities are in proportion, they are in proportion by inversion. Statement : If A : B : .- C : D, then, B : A : : D : C. Demonstration : BC = AD (PROP, i.)... | |
 | William Chauvenet - Geometry - 1894 - 380 pages
...then or, reducing, A + B ^ A' + B' \ B ~ B' ' and dividing this by [1], A + B A' + B' A ' ' A' ' I [2] results which are briefly expressed by the theorem,...[1], we should have found A — B A' — B' B A — B A B' A' — B' A' [3] results which are briefly expressed by the theorem, if four quantities are in... | |
 | 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
...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... | |
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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. 
