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" 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. "
A Theoretical and Practical Treatise on Algebra: In which the Excellencies ... - Page 198
by Horatio Nelson Robinson - 1850 - 328 pages
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An Elementary Treatise on Algebra

Bewick Bridge - Algebra - 1818 - 254 pages
...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...of " 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,...
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A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1821 - 284 pages
...± d : c, ,'. inversely a : a+_b : : с : c+_d. Tн. 8. " If four quantities be proportional, then the sum " of the first and second is to their difference,...of " the third and fourth is to their difference." For by _ ., a + bc + d , a— t c—d . , ,, , THEOR. 6, — : — =• , and — — = — — : invert...
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A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1821 - 648 pages
....'. inversely a : a+_b : : c : c£d. TH. S. " If four quantities be proportional, then the .•mm " of the first and second is to their difference, as...of " the third and fourth is to their difference." For by THEOR. 6, ^~=^—, and ^- =^^-; invert the two last bdba , , bd , a+bb c+dd fractions, then...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...A :: D± C : C, •'• 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...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 pages
...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 - Algebra - 1830 - 732 pages
...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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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 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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An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ...

John D. Williams - Algebra - 1840 - 634 pages
...: c±rf : с ; .•. inversely a : «z±& : : с Тн. 8. If four quantities be proportional, then the sum of the first and second is to their difference...sum of the third and fourth is to their difference. For, by theorem 6, g ' c~*~ ; ; ' bd . a — bb — d ... bd and — — — ; invert the last two...
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A Practical System of Algebra in Theory and Practice in Two Parts: With a ...

John D. Williams - Algebra - 1840 - 216 pages
...a±4 : a :: c±d : c; .-. inversely a : a±b ;• c TH. 8. If four quantities be proportional, then the sum of the first and second is to their difference...sum of the third and fourth is to their difference. For, by theorem 6, ~|~ ~\ • od , a — bb — d , . . . . . bd and — ; — = — j- ; invert the...
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A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1841 - 260 pages
...: c±d : c, .-. inversely a : a±6 : : c : c±d. TH. 8. " If four quantities be proportional, then the sum of the first and second is to their difference...sum of the third and fourth is to their difference." For by TH. 6^ — =— = — =- , and od — T— = — — ; invert the last two fractions, then £=...
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