 | Isaac Todhunter - 1860 - 622 pages
...inversely, a : ab :: c : 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 tfte third and fourth is to their difference. If a : b : : c : d, then a + b : a — b :: c + d : c... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 472 pages
...third and fourth. THEOREM IX. If four magnitudes are proportional, the sum of the first and tecond 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 ::... | |
 | Euclides - 1861 - 464 pages
...sum or difference of the third and fourth is to the third or fourth ; — or the sum of the first und second is to their difference, as the sum of the third and fourth to their difference. F PВOt'ORTIONALS ABOvE TWO. XVIII. — Ex œquali (se. distantià) or ex œquo, from equality of distance;... | |
 | Benjamin Greenleaf - Geometry - 1862 - 514 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 — Ii. For, from the... | |
 | Benjamin Greenleaf - Geometry - 1862 - 520 pages
...+ E). Hence, by Prop. II., 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 — P. For, from the... | |
 | Isaac Todhunter - Algebra - 1863 - 302 pages
...or --- = - . bade ac or ab : a :: c—d : c; therefore a : ab :: c : cd. 367. When four numbers are proportionals, the sum of the first and second is...their difference as the sum of the third and fourth is to their difference ; that is, if a : b :: c : d, then a+b : ab :: c + d : c—d. T> t ! ,,.A jo/.*... | |
 | Benjamin Greenleaf - 1863 - 338 pages
...~1Г' whence, a — b : b : : с — d : d. THEOREM VIII. 322. If four quantities be 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 : : с : d; Then, а-\-b : a — 6: : с -\- d : с — d By Theo.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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 the... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...c,-\-d : с, a — 6 : ¿i =r <• — d : c. PROPOSITION VII. — If four quantities be 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. If a : b = с : d, we are to prove that a-{-b : a — b = c-\-d : с — d.... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...whence, a — b : b : : c — d : d. 317. 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. If a : b : : c : d, then a -j- b : a — b : : c -\- d : c — d. By Art. 315,... | |
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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. 
