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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

## Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...THEOR. The terms of an analogy are proportional by mixing ; or the sum of the first and second to the difference, as the sum of the third and fourth to their difference. For, by conversion, A: A+B:: C : C+1), and alternately A : C ::A+B: C+D. Again, by conversion A : A—B...

## Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 454 pages
...THEOR. The terms of an analogy are proportional by mixing ; or the sum of the first and second is to the difference, as the sum of the third and fourth to their difference. Let A : B : : C : D, and suppose A-^-B ; then A+B : A— B : : C+D : C— D. For, by conversion, A : A + B : : C : C + D,...

## An Elementary Treatise on Algebra

Bewick Bridge - Algebra - 1818 - 227 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 .. . ,...

## A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1821 - 288 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, as the sum of " the third and fourth is to their difference." For by _ ., a + bc + d , a— t c—d . , ,, , THEOR. 6, — : — =• ,...

## A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1821 - 227 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 the sum of " the third and fourth is to their difference." For by THEOR. 6, ^~=^—, and ^- =^^-; invert the two last bdba , , bd , a+bb...

## The Elements of Algebra ...

James Wood - Algebra - 1825 - 322 pages
..., that is, ab : a :: cd : c; and inversely, a : ab :: с : c — d. (182.) When four quantities are proportionals, the sum of the first and second is...the third and fourth, to their difference. Let a : b :: с : d; then, a + b : a — b :: c + d : c—d. By Art. 179, °— = C±d-; and by Art. 180, ^ cd...

## Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 pages
...— d, and, therefore, by again alternating, a: a — b::c:c — rf. 116. When four quantities are proportionals, the sum of the first and second is...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, (No. 112.) a+b:c+d:...

## The Practical Analyst: Or, A Treatise on Algebra, Containing the Most Useful ...

Enoch Lewis - Algebra - 1826 - 166 pages
...still be a true one. _ а с ас a^-bc^-d For T=-d-'- b^=^1' or —=Т' Or, a*rb : b : : c~rd : d. 64. If four quantities be proportionals, the sum of the first and second is to their difterence,.as the sum of the third and fourth is to their difference. * The terms are similarly designated...