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" If the product of two numbers -is equal to the product of two other numbers, either pair may be made the means, and the other pair the extremes, of a proportion. "
Elements of Algebra - Page 122
by Arthur Schultze - 1918 - 309 pages
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The Popular Educator, Volumes 1-2; Volume 12

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,...
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Elements of Plane Geometry: For the Use of Schools

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...
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Bourdon's Arithmetic: Containing a Discussion of the Theory of Numbers

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...
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Arithmetic for school and college use. With a chapter on the metric system

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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Modern geometry [ed.] with an appendix by W.B. Jack

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...
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Chauvenet's Treatise on Elementary Geometry

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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A College Algebra

George Albert Wentworth - Algebra - 1888 - 514 pages
...proportion are given, it appears from the above that the fourth term can have one, and but one, value. 191. If the product of two numbers 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...
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The Academic Algebra

William Frothingham Bradbury - Algebra - 1889 - 444 pages
...tlic product of the means. Let a : b = с : d that is, т = -, о а Clearing of fractions, ad=bc 311. If the product of two numbers is equal to the product of two others, the factors of either product may be made the extremes, and the factors of the other the means,...
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