In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Solid Geometry - Page 254by John H. Williams, Kenneth P. Williams - 1916 - 162 pagesFull view - About this book
| George Albert Wentworth - Geometry - 1904 - 496 pages
...A'B' = BC : B'C' = CD : C'D', etc. § 351 .-. AB + BC + etc. : A'B' + B'C' + etc. = AB : A'B', § 335 (in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent). That is, ' = AB:A'B'. QED Ex. 252. If the line joining the middle points of the bases of a trapezoid... | |
| John Henry Tanner - Algebra - 1904 - 398 pages
...first (or the second) as the sum of the third and fourth is to the third (or the fourth). PRINCIPLE 6. In a series of equal ratios the sum of the antecedents is to the sum of tl<e consequents as any antecedent is to its own consequent. Thus, if a : b = c : d = e :f=g : A= •••... | |
| John Henry Tanner - Algebra - 1904 - 398 pages
...first (or the second) as the sum of the third and fourth is to the third (or the fourth}. PRINCIPLE 6. In a series of equal ratios the sum of the antecedents is to tlie sum of tJie consequents as any antecedent is to its own consequent. Thus, if a: b = c: d = e :f=g:... | |
| John Charles Stone, James Franklin Millis - Algebra - 1905 - 776 pages
...And O2 = «c. §195. Hence, ¿>=j/ac. Thus, in the proportion 9: 18=18: 36, we have 18=1/8 x 36. 205. In a, series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. ampx Suppose that _=_=£.=_== onqy Ti a Let Ъ=г' mpx . . Then — =r. -=r. -—r, etc. Axiom 7. n... | |
| Walter Randall Marsh - Algebra - 1905 - 446 pages
...(1) bd raising each member of (1) to the nth power, whether n is integral or fractional, 6"~d"' XI. In a series of equal ratios the sum of the antecedents...sum of the consequents as any antecedent is to its own consequent. If a_c._m_x si*. , . a с mx /г,-. let - = r, - = r, - = r, -=r, (2) bdny clearing... | |
| Walter Randall Marsh - Algebra - 1905 - 412 pages
...each member of (1) to the nth power, whether n is integral or fractional, an _ cn b'1 ~ cF XI. _Zn д series of equal ratios the sum of the antecedents...sum of the consequents as any antecedent is to its own consequent. К а с т х ,л^ T=J=— = -•> t1) о dn у let f.* «-,,»_,, S.,, (2) о а... | |
| Walter Nelson Bush, John Bernard Clarke - Geometry - 1905 - 378 pages
...is said to be derived from the given proportion by compositivn and division.) XI. 2. In any number of equal ratios, the sum of the antecedents is to...consequents as any antecedent is to its consequent. Hyp. If a: 6 : : c : e : :/: g : : etc., Cone.: then a + c+/+ ...: b + e + g+ ... : : a: 6 : : c: e... | |
| George Albert Wentworth - Algebra - 1906 - 440 pages
...this in any particular case, it will be found sufficient to substitute ra for b and re for d. 388. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. For, if ? = £ = ! = £=..., bdfh we may put r for each of these ratios. • Then ? = r, C = r, l =... | |
| William James Milne - Algebra - 1906 - 444 pages
...to b + d +f+ h ? Compare this ratio with the ratio a : b ; with the other ratios. PRINCIPLE 13. — In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Thus, when a:6 = C:d = g: ft and so on, a + с + e + g + - : Ь + d +f+ Л + ••• : : a : Ь.... | |
| International Correspondence Schools - Building - 1906 - 634 pages
...antecedents and the denominators the consequents. The general truth was shown in that article, that in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. AREAS OF POLYGONS 36. Definitions. — The area of a surface is the superficial space included within... | |
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