...a :b :: c : d :: e :/&c. a : b :: a+c+e&c. : b+d+f&c. or - = ~ b + d+f&LC. ie as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. 49. Def. One quantity is said to vary directly as another when the...

...c + d : c — d. THEOREM IX. When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. Let a : b = c : d = e : f ; then a: b = a + c + e: b + d + f. Because...

...: the ALGH :: the A EDC : the ALKH. But when any number of ratios are equal, as each antecedent is to its consequent so is the sum of all the antecedents to the sum of all the consequents; v. 12. .'. the AABE : the A LFG :: the fig. ABCDE : the fig. FGHKL....

...whole journey. 7. Prove that when any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. 8. Extract the square root of — 47-12\/l5. 9. If A varies inversely...

...number of equal ratios, all the magnitudes being of the same kind, then as any of the antecedents is to its consequent so is the sum of all the antecedents to the sum of all the consequents. Given A :B = A' :B' = A": B" ; to prove A:B=A+A' + A":B+B'+ B". Prom...

...in Dynamics. Article VIII. — When any number of quantities' are proportional, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of ail the consequents ; that is, if a : b : : c : d : : e : f &c., or -; = -r == -~, &c.»...

...proportionals ? Prove that if any number of quantities be m continued proportion, as one of the antecedents is to its consequent so is the sum of all the antecedents to the sum of all the consequents. 9. Prove the rule for finding the sum to n terms of an Arithmetic Series...