| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| William Guy Peck - Algebra - 1875 - 348 pages
...both members of (1), we have, | = |; or, b:a :: d:c; . . . (6) hence, the following principle : 4°. **If four quantities are in proportion, they will be in proportion by** inversion. If we add 1 to both members of (1), and also subtract 1 from both members, we shall have,... | |
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