...Y) 7. If»a :Ъ= c: d= e:f, then a + с + e : b + d+f— a: b. If a number of ratios are equal, then the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let - = - = - = r, then a = br, c= dr, e =fr. oaf e br drr= .. b+d+f b+d+f •'• 1а + л + ! = Г'...

...bk + dk+fk= (b + d+f)k, and a + c + e=fc=g = £ = g. b+d+fbdf That is, If several ratios are equal, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. EXERCISES 1. If ad = bc, show that - = - • Hint. Divide by bd. bd Z If ad=bc, show that- = -• 3....

...c/d, to prove that (a + 6)/(« - 6) = (c+d)/(c- d). Proof. We have = . = . bdbd Th E' p Theorem H. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. Given a/6 = c/d = e/f= —, to prove that ace Proof. Let k be the value of any one of the equal ratios...

...that (a + b)/(a — 6) = (c+d)/(c— d). Proof. We have a±b = c_ + d> mda^b = ed. Th. E,F Theorem H. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. Given a/6 = c/d = e/f= —, to prove that . ace b+d+f+- bdf Proof. Let A; be the value of any one of...

...last equation. A similar result holds for any number of equal ratios, and may be stated as follows : In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. CHAPTER XV QUADRATIC EQUATIONS 156. In § 108 the student learned how to solve certain quadratic equations,...

...last equation. A similar result holds for any number of equal ratios, and may be stated as follows : In a series of equal ratios the sum, of the antecedents...consequents as any antecedent is to its consequent. CHAPTER XV QUADRATIC EQUATIONS 149. In § 108 the student learned how to solve certain quadratic equations,...

...If four quantities are in proportion, they are in proportion by composition and division. Theorem H. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. PART II. PROPORTIONAL LINE-SEGMENTS 145. Theorem I. A line parallel to the base of a triangle divides...

...c + eH =(6 + d +/+ -")r. And, £Or, (a + c + e + •••): (6 + d +/+•••) = a:6. That is : In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. 382. Given a:b = b:c. Then a : c = a2 : b2. Proof: Since - = -, 6 c 4t follows that, °x^ = ?x2. 6...

...257. QED In a similar manner it may be shown that o — b:a = c — die. PROPOSITION VI. THEOREM 269. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Given a: b=c:d=e:f=g : h. To prove that a + c + e + g:b + d +/+ h==a:b. r, <• T iaoeg Proof. Let...

...d EXAMPLE. Since — = Щ- , then, ™±1. should equal ^JJ . Does it ? 2 3 10 — 2 15 — 3 196. In a series of equal ratios, the sum of the antecedents is to ¡he sum of the consequents as any antecedent is to its consequent. If «=« = !, etc, prove « + c...