...QED 251. THEOREM. Conversely, if the product of two numbers equals the product of two others, either pair may be made the extremes and the other pair the means of a proportion. GIVEN ad=bc. (2) To PROVE - = _. (i) bd Divide both sides of (2) by bd, the product of the denominators...

...296. A mean proportional between two quantities is equal to the square root of their product. 297. If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion in which the other two are made the means. 298....

...equations, such as squaring the equation, are applicable to proportions. PROPOSITION II 188. Theorem. //' the product of two quantities is equal to the product of two others, the factors of either product may be made the extremes, and the factors of the other product the means...

...mean is equal to the product of the extremes divided by the other mean. 309. (Converse of § 306.) If the product of two quantities is equal to the product...the other pair the means, of a proportion. Let ad = bс. Dividing by H S-£,«HWhence by § 301, a : b = с : d. In like manner, we may prove that a...

...mean is equal to the product of the extremes divided by the other mean. 309. (Converse of § 306.) If the product of two quantities is equal to the product...the other pair the means, of a proportion. Let ad = bс. Dividing by M, f! = Ë'ort = §ou od о a Whence by § 301, a : b = с : d. In like manner,...

...mean is equal to the product of the extremes divided by the other mean. 309. (Converse of § 306.) If the product of two quantities is equal to the product...the other pair the means, of a proportion. Let ad = ос. Dividing by H ^ = bc ra с bd bd bd Whence by § 301, a : b = с : d. In like manner, we may...

...divided by the other mean. 309. (Converse of § 306.) If the product of two quantities is equal to thé product of two others, one pair may be made the extremes,...the means, of a proportion. Let ad = be. Dividing, g-£,.fS. Wlience by § 301, a : 6 = с : d. In like manner, we may prove that a : с = b : d, с :...

...Then ma :mb = nc: nd, And ma : pb = me : pd. 290. Equal Products made into a Proportion ; that is, if the product of two quantities is equal to the product of two other quantities, either two may be made the means, and the other two the extremes of a proportion....

...Vac. Proof. From (1), b 2 = ac. (§ 232) /. b =Vac. PROP. II. THEOREM. 234. (Converse of Prop. I.) If the product of two quantities is equal to the product...extremes, and the other pair the means, of a proportion. Given ad = bc. (1) To Prove a : b = c: d. Proof. Dividing both members of (1) by bd, ad _ bc bd~bd...

...product of the two numbers that represent them when the quantities are expressed in a common unit. 338. If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = be, then,...