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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. "
Easy Introduction to Mathematics - Σελίδα 58
των Charles Butler - 1814
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 493 σελίδες
...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 - 1817 - 432 σελίδες
...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 - 1818 - 227 σελίδες
...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 - 1821 - 227 σελίδες
...± 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 - 1821 - 227 σελίδες
....'. 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 - 1825 - 305 σελίδες
..., 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
...— 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 - 1826 - 166 σελίδες
...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...

Elements of geometry: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - 186 σελίδες
...•'• 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, as the 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),...

The student's algebra

John Darby (teacher of mathematics.) - 1829
...proportion by making the terms of one product the extremes, and the terms of the other product the means. 3. If four quantities be proportionals, the sum of the first and second is to the second, as the sum of the third and fourth is to the fourth. Thus, if a;b; ;c'd, then will a+b:by.c+d;d....




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