 If the product of two numbers is equal to the product of two other numbers, either two may be made the means, and the other two the extremes of a proportion.  Elementary Algebra - Page 225by Elmer Adelbert Lyman, Albertus Darnell - 1917 - 503 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 the... | |
 | Davis Wasgatt Clark - 1844 - 394 pages
...others, these four numbers will constitute a proportion when so arranged that the factors of one product be made the means, and the factors of the other product the extremes. Let ad=bc: Dividing by db, and reducing, °— £ ; bd Hence - - - - a:b::c:d. 365. — (3.) If three... | |
 | Davis Wasgatt Clark - Algebra - 1846 - 374 pages
...others, these four numbers will constitute a proportion when so arranged that the factors of one product be made the means, and the factors of the other product the extremes. Dividing by db, and reducing, -=_ ; bd Hence - - - - a:b;:c:d. 365.—(3.) If three numbers be proportional,... | |
 | 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 Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...proportional (II., 36) 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... | |
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