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" 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. "
A Text-book of Geometry - Page 128
by George Albert Wentworth - 1888 - 386 pages
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Shorter Course in Algebra

George Albert Wentworth - Algebra - 1886 - 284 pages
...a : b : : с : d, then а.1 od By multiplying by bd, ad= be. 287. If the product of two numbers be 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, by dividing by bd, ^- = —, bd bd M 288. The equation...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...a : b = b : c. Then by §242, 62=ac. Whence, b = Vac. PROPOSITION II. THEOREM. 244. CONVERSELY, if the product of two quantities is 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...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...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 we have given ah 9 = a\ then, dividing by bb...
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A College Algebra

George Albert Wentworth - Algebra - 1888 - 514 pages
...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 = be, then, dividing by bd, a- = —, bd bd H.'. a : b = С...
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Sheldons' Complete Algebra: Part I Being Sheldon's Elements of ..., Parts 1-2

Algebra - 1888 - 492 pages
..., bc . ad ad From this equation, a = -=• , d =. — , о = — , с ==-=-• aa с b 368. IV. // the product of two quantities is equal to the product of two others, the factors of either product ni.ay be made the extremes, and the factors of the other product the...
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New Practical Algebra

James Bates Thomson - 1888 - 336 pages
...Art. 363, J = £ Clearing of fractions, ae = JV Again, 9 : 6 : : 6:4, and 4x9 = 6*. THEOREM Ш. [f (he product of two quantities is equal to the product of two others, the four quantities arc proportional ; the factors of either product being taken for ¿he extremes,...
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University Algebra: Embracing a Logical Development of the Science with ...

Charles Davies - Algebra - 1889 - 330 pages
...if we divide both members of ( 2 ) by ca, we shall have, - . = - ; or, a : b : : c : d. Hence, ac If the product of two quantities is equal to the product, of two other quantities, the first two may be made the means, and the second two the extremes, of a proportion....
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College Algebra

Webster Wells - Algebra - 1890 - 604 pages
...is equal to the product of the extremes divided by the other mean. 384. (Converse of Art. 381.) If the product of two quantities is 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 = 6e. Dividing...
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A Higher Algebra

George Albert Wentworth - Algebra - 1891 - 550 pages
...the above that the fourth term can have one, and but one, value. 280. 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 = bc, then, dividing by bd, ad_ be bd-bd' iz л a : b = с...
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A School Algebra

George Albert Wentworth - Algebra - 1891 - 380 pages
...the above that the fourth term can have one, and but one, value. 315. 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 = bc, then, dividing by bd, or / (л- с'- v / 316. Transformations...
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