 | Isaac Todhunter - Algebra - 1866 - 618 pages
...:: с : c — d. This operation is called converlendo. 396. W/ten four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to t/ieir difference. If a : b : : с : d, then a + b : a—I : : c + d : c — d. By Art. 393, = 0 Cv... | |
 | Isaac Todhunter - Algebra - 1866 - 580 pages
...: с : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fowrtii is to tlieir difference. If a : b :: с : d, then a + b : a — b :: с +d : c — d. By Art.... | |
 | Joseph Ray - Algebra - 1866 - 252 pages
...Illustration, 8 : 5 : : 16 : 10 8— 5: 5: : 16-10:10; Or, 3 : 5 : : 6 : 10. *. Proposition IX. — If four quantities are in proportion, the sum of the first and second will be to their difference, as the sum of the third and fourth is to their difference. Let a : b :... | |
 | Joseph Ray - Algebra - 1852 - 422 pages
...ihejirst, as the difference of the third and fourth is to the third. ART. 275. PROPOSITION IX. — If four quantities are in proportion, the sum of the first and second will lie to their difference, as tht sum of the third and fourth is to their difference, Let a:b::c:d... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...:10. In a similar manner it may be shown that a — 6 : a : : c — d : c. 275. Proposition IX. — If four quantities are in proportion, the sum of the first and second will be to their difference as the sum of the third and fourth is to their difference. Let a : b :... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...the first, as the difference of the third and fourth is to the third. 2«>2. Proposition IX. — If four quantities are in proportion, the sum of the first and second will be to their difference, as the sum of the third and fourth is to their difference. Let a: b: :... | |
 | James Pryde - Navigation - 1867 - 506 pages
...and therefore (29, e) a—bc—db — ad—c 41. THEOREM.. — If four quantities be proportional, the sum of the first and second is to their difference...sum of the third and fourth is to their difference. This change is called proportion by Mixing. /- • ii. *. ac i_ .. й + ^ c + d Given that -т = ->... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...Hence, by Prop. II., A:B::A+C + E:B + D + F. PROPOSITION XII. — THEOREM. 148. If four magnitudes are in proportion; the sum of the first and second...sum of the third and fourth is to their difference. Let A : B : : C : D ; then will A + B:A — B : : C + D : C — D. For, from the given proportion,... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...is to the difference between ihe third and fourth. THEOREM IX. If four magnitudes are proportional, the sum of the first and second is to their difference...sum of the third and fourth is to their difference. Let A, B, C, and D he the four magnitudes which give the proportion A : B :: C : D; we are then to... | |
 | Elias Loomis - Algebra - 1868 - 386 pages
...b :: m:'n 9 m: U) c: d. n n c d : c : d. (i-) (2.) f f " 306." If four quantities are proportional, the sum of the first and second is to their difference,...sum of the third and fourth is to their difference. Let a : b : : c : d. By composition, Art. 304, d+b : b :: c+d: d. By alternation, Art, 301, a + b :... | |
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If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. 
