...numbers is equal to the square root of their product. PROP. II. THEOREM 218. (Converse of Prop. I.) If the product of two numbers is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Given ad...

...= — - • III ~"~ t7 Hence, m — V( — 4)( — 9) = — fi, which is a negative number, (iii.) If the product of two numbers is equal to the product of two others, the numbers of either xft may be made the, extremes, and those of the other set may be made...

...374. Given ad = be. Then a:b = c:d. Proof : ad = be. Dividing by bd, í = í. bd That is : If tl1e product of two numbers is equal to the product of two other numbers, one pair may be made the extremes, and the other pair the means, of a proportion. In like manner we...

...the extremes is equal to the product of the means. This is a convenient test of proportionality. 11. If the product of two numbers is equal to the product...two other numbers, either pair may be made the means and the other pair the extremes in a proportion. 12. A proportion is obtained from a given proportion...

...in like manner, illustrate each of the following principles by one or more numerical examples. (2) If the product of two numbers is equal to the product...other numbers, either pair may be made the means, and the other pair the extremes, of a proportion. Let mq = np. tYYl IY\ Divide by nq, — - - ; or...

...the extremes is equal to the product of the means. This is a convenient test of proportionality. 11. If the product of two numbers is equal to the product...two other numbers, either pair may be made the means and the other pair the extremes in a proportion. 12. A proportion is obtained from a given proportion...

...their product. Let the proportion be •. a : b = b : c. Then 62 = ac._(§ 163.) Hence b .= Vac. 165. If the product of two numbers is equal to the product...other numbers, either pair may be made the means, and the other pair the extremes, of a proportion. (Converse of § 163.) If mn=pq, and we divide both...

...if the product of two numbers, a and d equals the product of two other numbers, 6 and c, either two may be made the means of a proportion in which the other two are made the extremes. Considering this in terms of pressure and volume we shall find a valuable law. If...

...J£xiy = b:c, isdx:y = b :cd a, true proportionf PROPOSITION II. THEOREM (Converse of Prop. I) 393 If the product of two numbers is equal to the product...two other numbers, either pair may be made the means and the other pair the extremes of a proportion. Given ad = be. To prove a: 5 = c: d. ARGUMissrr REASONS...

...fourth proportional to a, b, and c. Find a fourth proportional to ¿, |, and \. 394. PRINCIPLE 3. — If the product of two numbers is equal to the product of two other numbers, one pair of them may be made the extremes and the other pair the means of a proportion. For, given...