| 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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