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If four quantities are in proportion, they will be in proportion by INVERSION ; that is, the second will be to the first as the fourth to the third.
Principles of Plane Geometry - Page 24
by James Wallace MacDonald - 1889 - 63 pages

## 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...

## 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...

## 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,...

## 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...

## 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...

## 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...

## 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...

## 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...