 | Olinthus Gregory - 1863 - 482 páginas
...series of equal ratios represented by f we shall have - « - * - V - ««• T • - Tj Therefore, in a series of equal ratios, the sum of the antecedents...its consequent. If there be two proportions, as 30 : 1 5 : : 6 : 3, and 2 : 3 : : 4 : 6, then multiplying them term by term we shall have 30 x 2 : 15... | |
 | Adrien Marie Legendre - 1863 - 464 páginas
...shall have, A±PA : B±*-B :: C ±2,0 : 2>±^D; PEOPOSITION XI. THEOEEM. In any continued proportion, the sum of the antecedents is to the sum of the consequents, as any antecedent to its corresponding consequent. From the definition of a continued proportion (D. 3), A... | |
 | Edward Brooks - 1868 - 284 páginas
...THEOREM XII. If any number of quantities are in proportion, any antecedent will be to its consequent as the sum of the antecedents is to the sum of the consequents. Let A:B:: C: D:\E\F, etc. A : B : : E : F; we have A x .D = S X C, and AXF= B X E; adding to these,... | |
 | Charles Davies - 1872 - 464 páginas
...have, DD* A±*-A : *± P -B :: C±$C : D ± *D; PBOPOSITION XI. THEOREM. In any continued proportion, the sum of the antecedents is to the sum of the consequents, as any antecedent to its corresponding consequent. From the definition of a continued proportion (D. 3), A.... | |
 | Aaron Schuyler - 1873 - 536 páginas
...give the continued proportions: AB : AE : : BC : BF :: CD : CG. AB : EB :: BC : FC :: CD : GD. Since the sum of the antecedents is to the sum of the consequents as one antecedent is to its consequent, we have, AD : AE+BF + CG : : AB : AE. NAVIGATION. Now let a right... | |
 | Adrien Marie Legendre - 1874 - 500 páginas
...±2,0 : D ±^D -t qy T f which was to be proved. PEOPOSITION XI. THEOREM. In any continued proportion, the sum of the antecedents is to the sum of the consequents, as any antecedent to its corresponding consequent. From the definition of a continued proportion (D. 3), Adding... | |
 | George Albert Wentworth - 1877 - 436 páginas
...of similar polygons are proportional). .-. AB + BC, etc. : A'B' + B'C', etc. : : AB : A'B', § 266 (in a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to it That is P : P' A П : A' B'. GEOMETRY. BOOK III. PROPOSITION XVII. THEOREM. 296.... | |
 | George Albert Wentworth - 1877 - 426 páginas
...Then 2 _ ! = f _ lf that is, _, bd or, a — 6 : 6 : : с — d : d. QED PROPOSITION VIII. 266. 1n a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let a : b = с : d ! = e : f = g : h. We are to prove a + с + e +... | |
 | George Albert Wentworth - 1877 - 416 páginas
...of similar polygons are proportional). .-.A£ + BC, etc. : A'B' + B'C', etc. : : AB : A'B', § 266 (in a series of equal ratios the sum of the antecedents is to the sum of the consequents ns any antecedent, is to its consequent). That is P : P' : : A£ : A'B'. GEOMETRY. BOOK III. PROPOSITION... | |
 | George Albert Wentworth - 1877 - 416 páginas
...proportional). .-.AB+ BC, etc. : A'B' + B'C', etc. : : AB : A'B', § 266 (in a series of equal ratins the sum of the antecedents is to the sum of the consequents an any an1ecedent is to its consequent). That is P : P' : : A Б : A'В'. GЕOMETRY. BOOK III. PROPOSITION... | |
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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. 
