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" Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When... "
A Treatise on the Elements of Algebra - Side 113
av Bewick Bridge - 1821 - 227 sider
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Easy Introduction to Mathematics, Volum 2

Charles Butler - 1814 - 582 sider
...as the excess of the third above the fourth to the fourth. 70. If four quantities be proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth to their difference. Let a : b : : c : d, then will a + b : a—b :: t+d : c—d; for a + bc + da —...
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The Elements of Algebra: Designed for the Use of Students in the University

James Wood - 1815 - 338 sider
...inversely, a : a—b :: c : c — d., (182.) When four quantities are proportionals, the sum of the Jirst and second is to their difference, as the sum of the third and fourth, to their difference. Let a : b :: c : d ; then, ' + b : ab :: c + d: «— d. G Ey ac , If possible,...
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An Elementary Treatise on Algebra

Bewick Bridge - 1818 - 254 sider
...inversely a : a±e : : с : c±.d. Til. 8. " If four quantities be proportional, then the sum " of (.he first and second is to their difference, as the sum...the third and fourth is to their difference." For by THEOR. 6, £L+Ô=ÎI±^ and ^=£^; invert the two last udud .. . , bd , a + bbc + dd fractions, then...
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The Elements of Algebra ...

James Wood - 1825 - 322 sider
...a :: cd : c; and inversely, a : ab :: с : c — d. (182.) When four quantities are proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth, to their difference. Let a : b :: с : d; then, a + b : a — b :: c + d : c—d. By Art. 179, °—...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 sider
...therefore, by again alternating, a: a — b::c:c — rf. 116. When four quantities are proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth to their difference. This readily appears from Nos. 114 and 115. For, (No. 114.) a+b:b::c+d : d, therefore,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 210 sider
...•'• A : B j- A : .- C : D ± C. Cor. B^fA^::D^C:C (35). 40. If four quantities be proportional, the sum of the first and second is to their difference,...sum of the third and fourth is to their difference. Let A : B : : C : D, then (by mixing) A+B:AB::CJ+D:C — D. ForA + B:B::C +D;D(37), .-. A + B : C •+...
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The student's algebra

John Darby (teacher of mathematics.) - 1829 - 212 sider
...fourth. Thus,ifa:6::e;rf; then will a— b ; b : ; c — did. 5. If four quantities be proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth is to thejr difference. Thus, if a;b:;c:d, then will a+b;a— b: ;c+d;c — d. 6. If four quantities be proportionals,...
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A Treatise on Algebra

George Peacock - 1830 - 732 sider
...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 is to their difference...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 6-3' x, , a + bc + da...
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Mathematical Problems and Examples, Arranged According to Subjects, from the ...

1836 - 366 sider
...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 to their difference as 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 -|-...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 290 sider
...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, as 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...
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