| Alan Sanders - Geometry - 1903 - 392 pages
...successively equal to each other. Example : BOOK III PROPOSITION X. THEOREM 443. In a continued proportion **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let** To Prove Proof bdfh b+d+f+hf lj (2i H ^3> a) From (1). 7=7 ^4) H (5) a/= be (6) ] cf=de (7) «/ = /«... | |
| Alan Sanders - Geometry - 1903 - 396 pages
...other. Example : - = - = — = -, etc. bdf ti PROPOSITION X. THEOREM 443. In a continued proportion **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** (1) Let To Prove Proof bdfh o_±-2_±A+_fl! = ?. b+d+f+hf T = ~ (2) From (1). 5 = 7 (3) df - = - (4)... | |
| 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 - 396 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 - 400 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 - 792 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 - 462 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... | |
| International Correspondence Schools - Building - 1906 - 620 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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