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" 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 the fourth term. "
A Text-book of Geometry - Page 130
by George Albert Wentworth - 1888 - 386 pages
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Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1872 - 268 pages
...extremes is equal to the square of the mean. Let a : b = b : c* By Theorem I. ac = 62 THEOREM VI. 207. If four quantities are in proportion, they will be in proportion by composition. Let a : b = c : d ac Adding 1 to each member, ^ + 1 = j a-\-bc 01 -- = ~ ie a-\-b:b = c-\-d:d THEOREM...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...have, AC M JJ ^f — ^ \ whence, JB : A : : D : C: which was to be proved. PROPOSITION VI. THEOREM. If four quantities are in proportion, they will be in. proportion by composition or division. Assume the proportion, A : B : : C : D ; whence, -j- = 7T • 7? 7) s*. \j If we add 1...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...of a proportion. Let ad = bc Dividing by bdr = 3 ™ •> ba that is a : b = c : d THEOREM III. 15, If four quantities are in proportion, they will be in proportion by alternation. Let a : b = c : d By (12) ad=bc THEOREM IV. 16, If four quantities are in proportion,...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...they will be in proportion by alIernation. Let a : b = c : d By (12) ad = bc By (14) a:c = b:d 16. If four quantities are in proportion, they will be in proportion by inversion. Let • a : b = c : d By (12) ad = bc By (U) ; b : a = d : c THEOREM V. 17. If four quantities...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...couplets may be made the consequents of the first, by alternation (P. HI.). PROPOSITION V. THEOREM. If four quantities are in proportion, they will be in proportion by inversion. Assume the proportion, . A : H : : G : D ; whence, -j- = -^ • vl O If we take the reciprocals...
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The Complete Algebra: Designed for Use in Schools, Academies, and Colleges

Joseph Ficklin - Algebra - 1874 - 446 pages
...of the proportions may be derived. Сок. 2. — Since (3) may be derived from (2), it follows that If four quantities are in proportion, they will be in proportion by alternation. COR. 3. — Since (4) may be derived from (2), it follows that If four quantities are...
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New Elementary Algebra: Containing the Rudiments of the Science for Schools ...

Horatio Nelson Robinson - Algebra - 1875 - 338 pages
...I e d a —c— or, a : b = c : d. From (A), T From(B), | = ^. Hence (Ax. 7), PROPOSITION VII. 269. If four quantities are in proportion, they will be in proportion by COMPOSITION or DIVISION ; that is, the sum of the first and second will be to the second, as the sum of the third...
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Eaton's Elementary Algebra, Designed for the Use of High Schools and Academies

William Frothingham Bradbury - 1875 - 280 pages
...extremes is equal to the square of Hie mean. Let a : b = Ь : с By Theorem I. a с = 62 THEOREM VI. 207. If four quantities are in proportion, they will be in proportion by composition. Let а : b = с : d а с >• e- l = d Adding 1 to each member, ^ -L- 1 = - -|- 1 —T~ ~d— ie a...
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Manual of Algebra

William Guy Peck - Algebra - 1875 - 348 pages
...= — or a: t, + a :: c: d + c, and a : b — a :: c : d — c hence, the following principle: 5. If four quantities are in proportion, they will be in proportion by composition or by division. — = - ; or. ma : mo :: a : b ; '. . . (8) ma a ^ mb bi , / 0 \ hence, the following...
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New University Algebra

Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...be, are the means, and the factors of the first product, ad, are the extremes. PROPOSITION III. — If four quantities are in proportion, they will be in proportion by ALTERNATION ; that is, the antecedents will be to each other as the consequents. Let a : b = c : d...
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