| Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1892 - 544 pages
...application of their methods. For instance, under the theory of proportion, it is sometimes stated that : " **In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent."** This is a true proposition applied to numbers, but is not true of geometrical magnitudes unless these... | |
| George W. Lilley - Algebra - 1892 - 420 pages
...163), íSr;-7?H-í»HTherefore, a + c + e + g :l+d+f + h::a:b. Hence, XI. In a continued proportion **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** a2 + Ь* а Ъ + b с EXAMPLE 1. .If ~ï~v~î~ = ~j,z 4. г > Prove that о as a mean proportional... | |
| George Albert Wentworth - Algebra - 1893 - 370 pages
...ос Multiplying by -, — = — -. с ос cd ab or - = -у с d .'. a : с = b : d. 317. In a aeries **of equal ratios, the sum of the antecedents is to...consequents as any antecedent is to its consequent.** •c, -ta с ea For'lf ¿=5=7=f' r may be put for each of these ratios. Then |=г,.=^=г,j,.r. .-.... | |
| James Morford Taylor - Algebra - 1893 - 358 pages
...ma : mb = гtc : nd ; (ii.) ma : nb= me: nd. The proof is left as an exercise for the student. 224. **In a series of equal ratios, the sum of the antecedents is to the** киm of the consequents as any one antecedent is to its consequent. For assume a: b = c: d= e:f= ...,... | |
| James Morford Taylor - Algebra - 1893 - 362 pages
...mb = nc : nd ; (ii.) ma : nb = me : nd. The proof is left as an exercise for tl1e student. 224. L1 **a series of equal ratios, the sum of the antecedents is to the** кит of the consequents as any one antecedent is to its consequent. For assume a:b = c: d = e:f=... | |
| George P. Lilley - Algebra - 1894 - 522 pages
...= d = = д • Therefore, a + c + e + rj : b + d+f+h :: a : b. Hence, XI. In a continued proportion **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** a2 + b3 ab + Ь с EXAMPLE 1. .If — r-^_- j- = -rj-x~-j-, prove that b is a mean proportional between... | |
| George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...conversely, the greater angle is opposite the greater side. 2.- Show that in any continued proportion, **the sum of the antecedents is to the sum of the consequents as any antecedent** to its corresponding consequent. 3. Prove that, in equal circles, incommensurable angles at the centre... | |
| William Freeland - Algebra - 1895 - 328 pages
...composition, (л By division, iZ=°ri (2) Dividing (1) by (2), we have, a + b _c + d a — b с — d 292. IX. **In a Series of Equal Ratios the sum of the antecedents...consequents as any antecedent is to its consequent.** If a:b = c:d = e:f=g:h. To prove (a + b + e + g) : (b + d +f+ K)=a:b. If a:b=c:d = e:f=g:h, н=нALGEBPA.... | |
| John Macnie - Geometry - 1895 - 390 pages
...(232") PROPOSITION XII. THEOREM. 251. If any number of like quantities are in continued proportion, **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** Given : A : B = C : D = K : V ; To Prow : A + C + E : B + D + F = A : B. Since a:b = c:d = e:f, (Hyp.... | |
| George Albert Wentworth - Geometry - 1895 - 458 pages
...+ d : c - d. as. D. PROPOSITION IX. 303. In a series of equal ratios, the sum of the an~ tecedents **is to the sum of the consequents as any antecedent is to its consequent. Let** a:b = c:d = e :/= g : ft. To prove a + c + e+^r : 6+<f+/+ h = a : b. Denote each ratio by r. N rm_... | |
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