 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 = be. (1) To Prove - = -. bd Proof. Dividing both members of (1) by bd, ad_bc_ £_£ bd~bd'...  Elementary Algebra Revised - Page 320by Frederick Howland Somerville - 1913 - 447 pagesFull view - About this book
 | Geography - 1867 - 964 pages
...9. Sow, 12 and 3 are the extremes, and 4 and 9 are the means, oí tie given proportion. Conversely, if the product of two numbers is equal to the product of any other two numbers, the four numbers will form a proportion. Thus, since — 8 x 3 = « x 4 or,... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...the means is equal to the product of the extremes ; as, 6 : 4 : : 15 : 10, hence 10.6=15.4. Prop. 2. If the product of two numbers is equal to the product of two other numbers, the four may be arranged in a proportion; as, 8.3=12.2, hence 8: 12: : 2 : 3. Scholium. Remark that... | |
 | Bourdon (M., Louis Pierre Marie) - Arithmetic - 1858 - 262 pages
...multiplication, they must have been equal at first. Hence the property is proved. 161. Reciprocally. — If the product of two numbers is equal to the product of two other numbers, these four numbers form a proportion of which either pair of factors will constitute the means, the... | |
 | Thomas Percy Hudson - Arithmetic - 1866 - 268 pages
...45 ' Now, 12 and 3 are the extremes, and 4 and 9 are the means, of the given proportion. Conversely, if the product of two numbers is equal to the product of any other two numbers, the four numbers will form a proportion. Thus, since 8X3 = 6X4, 8, 4, 6, 3 form... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...mean proportional between two numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal to the product of two others, either two may be made the extremes, and the other two the means, of a proportion. For, if... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...mean proportional between two numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal to the product of two others, either two may be made the extremes, and the other two the means, of a proportion. For, if... | |
 | Richard Wormell - 1876 - 268 pages
...mark the fourth term by x — 12 : 108 : : n : x. And from what has already been said — («). When the product of two numbers is equal to the product of two othtrs they form a proportion in four different ways. Thus the four numbers (5, 54, 6, 45) form a proportion... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...the product of two quantities is equal to the product of two other quantities, one pair of factors may be made the extremes, and the other pair the means, of a proportion. EXERCISE 2. From AD = BC, write eight proportions. 5. Since the proportions II. and III. are true when... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...x = a 344. If the product of two quantities be equal to the product of two others, one pair of them may be made the extremes, and the other pair the means, of a proportion. Thus, if ad = b с , , ad be ao In a similar manner, we might derive from the equation ad = bc, the... | |
 | Webster Wells - 1885 - 368 pages
...296. (Converse of Art. 293.) If the product of two quantities be equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = be. Dividing by bd, g=«!с orf с bd bd bd • In a similar manner we may prove that : a... | |
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