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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.
Elements of Plane and Solid Geometry - Page 134
by George Albert Wentworth - 1877 - 398 pages

## Elements of Plane and Solid Geometry

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) «/ = /«...

## Elements of Plane and Solid Geometry

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)...

## Plane and Solid Geometry

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...

## Elementary Algebra

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= •••...

## Elementary Algebra

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:...

## Essentials of Algebra: Complete Course (an Adequate Preparation for the ...

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...

## Elementary Algebra

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...

## Elementary Algebra

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...