 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...  The elements of algebra - Page 139by James Wood - 1845 - 287 pagesFull view - About this book
 | 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...their difference, as the sum of 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... | |
 | 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,... | |
 | 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... | |
 | 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... | |
 | 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...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,... | |
 | 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 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,...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 •+... | |
 | 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...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,... | |
 | George Peacock - Algebra - 1830 - 732 pages
...=-, and 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...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... | |
 | Mathematics - 1836 - 366 pages
...prime to b, there is no other fraction equal to j whose terms are not equimultiples of a and b. 232. When four quantities are proportionals, the sum of...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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