| 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... | |
| Charles Butler - Mathematics - 1814 - 528 pages
...to the first, 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...the third and fourth to their difference. Let a : b :: c : d, then will a+b : a—b : : c+d : c—d; for u + li c 4 </ a — bc — d since — - — =... | |
| Sir John Leslie - Geometry - 1817 - 456 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 :... | |
| 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 .. . ,... | |
| 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, as the sum of " the third and fourth is to their difference." For by _ ., a + bc + d , a— t c—d . , ,, , THEOR. 6, — : — =• ,... | |
| 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 the sum of " the third and fourth is to their difference." For by THEOR. 6, ^~=^—, and ^- =^^-; invert the two last bdba , , bd , a+bb... | |
| George Lees - 1826 - 276 pages
...111.) a : c : : a — b:c — d, and, therefore, by again alternating, a: a — b::c:c — rf. 116. When four quantities are proportionals, the sum of...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:... | |
| Enoch Lewis - Algebra - 1826 - 180 pages
...by bd, ad=bc. „ . ...-., ud be а с Keciprocally, if ad=bc, ,— ,=n. or -=-= — bd bd о а 63. When four quantities are proportionals, the sum of the first and second is to the second, as the sum of the third and fourth is to the fourth. c+d r Or, a+6:o :: c+d: d. If the... | |
| John Darby (teacher of mathematics.) - 1829 - 212 pages
...fourth is to the 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...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... | |
| John Playfair - Geometry - 1829 - 210 pages
...•'• 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),... | |
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