| Charles William Hackley - Algebra - 1846 - 542 pages
...VIII., -=~ ; and hence, subtracting these equal acbd quantities from unity, or 6 d a—6 c—d XII. **If four quantities be proportionals, the sum of the first and second** trill have to Oieir difference tfie same ratio that the sum of the third and fourth hat to their difference.... | |
| Euclid, Robert Potts - Euclid's Elements - 1847 - 118 pages
...similar triangles it may be proved that of any three of the consecutive circles, the sum of the radii **of the first and second, is to their difference, as the sum of the** radii of the second and third, is to their difference. HINTS, &c. TO THE THEOREMS. BOOK VI. 3. THIS... | |
| Horatio Nelson Robinson - Algebra - 1848 - 320 pages
...b : : c : c — a. or a : b — a : : c : d — c. (Theorem 4.) Jf four magnitudes be proportional, **the sum of the first and second is to their difference, as the sum of the third and fourth** i* to their difference. Admitting that a : b : : c : d , we are to prove that a+6 : a — b : : c+rf... | |
| Stephen Chase - Algebra - 1849 - 350 pages
...compound, hence componendo, by compounding. (o) Lat., from divide, to separate; by separating. Hence, Cor. **The sum of the first and second is to their difference, as the sum of the third and fourth** is to their difference. Thus 3:2 = 6:4; .-. 3+2 : 3—2 = 6+4 : 6—4. Hence (J§ 234-236), § 237.... | |
| Horatio Nelson Robinson - Conic sections - 1854 - 350 pages
...C—D Or . . A:B— A: : C:D— C. THEOREM 9. If four magnitudes be proportional, the sum of thefirsl **and second is to their 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... | |
| James William M'Gauley - 1854 - 284 pages
...means, ac — ad=ac — be ad=be 24. We may mix : and, then, " the sum of the first and second terms **is to their difference, as the sum of the third and fourth** is to their difference." a:b: :C:d Mixing, a-\-b:a — b: :c-\-d:C—d Multiplying extremes, and means,... | |
| John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...student prove this. PROPOSITION (393.) 12. When four quantities are in proportion, the sum of the ßrst **and second is to their difference as the sum of the third and fourth** is to their difference. DEMONSTRATION. Let a : b : : с : d. We are to prove that a + b : a—b : :... | |
| James B. Dodd - Algebra - 1859 - 368 pages
...v :: w : x : y : z. THEOREM XIII. (163.) The sum of the first, and second terms in any Proportion, **is to their difference, as the sum of the third and fourth** is to their difference. Let a : b : : x : y, then is a-\-b : a — b : : x-\-y : x — y. By Composition... | |
| Joseph Allen Galbraith - Optics - 1860 - 94 pages
...radius of the mirror, this relation becomes r:: alternmdo (Euc. V. 16) — A + |r : A- |r :: and since **the sum of the first and second is to their difference as the sum of the third and fourth** is to their difference, we have, componendo et dividendo (Euc. V. 1 7, 18), ^& : r : : r : ^8, or,... | |
| James Elliot - 1860 - 252 pages
...proportions that can be 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 :... | |
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