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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. "
An Easy Introduction to the Mathematics: In which the Theory and Practice ... - Page 66
by Charles Butler - 1814
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Algebra

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...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

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 ::...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

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. distantiÓ) or ex œquo, from equality of distance;...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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...
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Elements of Geometry and Trigonometry: With Practical Applications

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...
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Algebra for Beginners: With Numerous Examples

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/.*...
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New Elementary Algebra: in which the First Principles of Analysis are ...

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....
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Elements of Geometry: With Practical Applications to Mensuration

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...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

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....
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New Higher Algebra: An Analytical Course Designed for High Schools ...

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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