 | Benjamin Greenleaf - Algebra - 1864 - 336 pages
...6 : b : : c — d : d. THEOREM Vin. 322. If four quantities be in proportion, the sum of the jirst and second is to their difference as the sum of the third and fourth is to their difference. Let a : b : : c : d; Then, a + b : a — b : : c + d : c — d ByTheo.VL, and... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 472 pages
...is to the difference between the third and fourth. THEOREM IX. If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. Let A, B, C, and D be the four magnitudes which give the proportion A : B :... | |
 | Isaac Todhunter - Algebra - 1866 - 614 pages
...inversely, a : a — b :: с : c — d. This operation is called converlendo. 396. W/ten four quantities are proportionals, the sum of the first and second is...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,... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1866 - 546 pages
...third. Let the student prove this. PROPOSITION (393.) 12. W/ien four quantities 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. DEMONSTRATION. Let a:b::e:d. We are to prove that a + b :a—b :: c + d : ca... | |
 | Isaac Todhunter - Algebra - 1866 - 576 pages
...inversely, a : a — b : : 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.... | |
 | 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 as the sum of the third and fourth is to their difference. This change is called proportion by Mixing. /- • ii. *. ac i_ .. й + ^ c... | |
 | 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 as the 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 ::... | |
 | 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, as the 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,... | |
 | Benjamin Greenleaf - Geometry - 1868 - 338 pages
...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 is to their difference as the 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... | |
 | Ontario Chief Superintendent of Education - Education - 1869 - 450 pages
...the ordinary rule for Equation of Payments. 3. Prove that if any four quantities are in proportion the sum of the first and second is to their difference as the sum of the third and fourtli is to their difference. 4. Define what is meant by " Compound Proportion." 5. Give and prove... | |
| |
If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. 
