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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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A Treatise on Algebra

George Peacock - Algebra - 1830 - 732 pages
...= =-, and mvertcndo, ac ac a — bc — d' or a : a — b :: c : c — d. 411. " If four magnitudes be proportionals, the sum of the first and second...their difference as the sum of the third and fourth is to their difference." Let a : b :: c : d, then also a + b : a — b :: c + d : c — d. T. .ac Forif...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...miscendo .-* viz. If four magnitudes A, B, C, D be proportionals, the sum of the first and second will be to their difference, as the sum of the third and fourth to their difference. For, since A : В : : С : D, componenda A + B : В : : С +D : D. And again, because nvertendo В...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...miscendo :* viz. If four magnitudes A, B, C, D be proportionals, the sum of the first and second will be to their difference, as the sum of the third and fourth to their difference. For, since A : В : : С : D, componenda A + B : В : : С +D : D. And again, because invertendo В...
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Mathematical Problems and Examples, Arranged According to Subjects, from the ...

Mathematics - 1836 - 366 pages
...other fraction equal to j whose terms are not equimultiples of a and b. 232. When four quantities are proportionals, the sum of the first and second is...the sum of the third and fourth to their difference. 234. Express a + b . Jl]. and log, (a + 6 v'~) in the c + v __ l form A -|- BV _ 1. 235. Shew how...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...to its excess above the second, as the third is to its excess above the fourth. 27- By mixing, when the sum of the first and second, is to their difference,...the sum of the third and fourth to their difference. 28. By equality, when there is any number of magnitudes more than two, and as many others, so that...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...B:: C + D:C — D: that is, if four numbers be proportional, the sum of the first and second terms is to their difference, as the sum of the third and fourth terms \a to their difference. It is evident that if B be greater than A, the analogy will become B...
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The elements of algebra

Andrew Bell (writer on mathematics.) - 1839 - 498 pages
...is to the secoml, as the excess of the third above the fourth to the fourth ; (332.) By mixing, when the sum of the first and second is to their difference,...the sum of the third and fourth to their difference ; (333.) By direct equality, when there are several analogies, and two homologous terms in each are...
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A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1839 - 282 pages
....-. inversely a : a :: c : cd. TH. 8. " If four quantities be proportional, then the sum of Ihe first and second is to their difference as the sum of the third arid fourth is to their difference." For by TH. 6, — =— = — 5- , and od a — bc — d . , ,...
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An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ...

John D. Williams - Algebra - 1840 - 636 pages
...: crf : с ; .•. inversely a : z& : : с Тн. 8. If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. For, by theorem 6, g ' c~*~ ; ; ' bd . a — bb — d ... bd and — — —...
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A Practical System of Algebra in Theory and Practice in Two Parts: With a ...

John D. Williams - Algebra - 1840 - 193 pages
...a4 : a :: cd : c; .-. inversely a : ab ;• c TH. 8. If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. For, by theorem 6, ~|~ ~\ • od , a — bb — d , . . . . . bd and — ;...
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