| 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... | |
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