 | Horatio Nelson Robinson - Geometry - 1860 - 470 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 :: C : D; we are then to... | |
 | James Elliot - 1860 - 252 pages
...obtained by this theorem and its corollaries. THEOREM VII. When four Quantities are proportionals, the Sum of the first and second is to their Difference as the Sum of the tlurd and fourth to their Difference, DEM. If a : b : : c : d, then, by Th. 6, Cor. 2, a + b : a :... | |
 | Isaac Todhunter - 1860 - 620 pages
...: 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 - 1861 - 372 pages
...— c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to thfir difference, as the sum of the third and fourth is to their difference. Admitting that a : b : : c : d, we are to prove that a+b : a — b : : c+d : c — d • From the same... | |
 | 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,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...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...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 given proportion, by Prop.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 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...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 given proportion, by Prop.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...+ 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...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, by Prop.... | |
 | Benjamin Greenleaf - 1863 - 338 pages
...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...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. VL, -î-=^, "~ * c~d bd... | |
 | Isaac Todhunter - Algebra - 1863 - 302 pages
...ab : a :: c—d : c; therefore a : ab :: c : cd. 367. When four numbers are proportionals, the sum of the first and second is to their difference as...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/.* j ~ — By Arts. 364... | |
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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. 
