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" 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 - Página 320
por Frederick Howland Somerville - 1913 - 447 páginas
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The Popular Educator, Volúmenes1-2;Volumen12

1867 - 964 páginas
...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 - 1844 - 108 páginas
...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) - 1858 - 262 páginas
...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 - 1866 - 268 páginas
...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 - 1871 - 380 páginas
...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 - 1872 - 382 páginas
...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 páginas
...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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Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - 1878 - 236 páginas
...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...
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University Algebra

Webster Wells - 1879 - 468 páginas
...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...
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A Complete Course in Algebra

Webster Wells - 1885 - 368 páginas
...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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