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" In any proportion, the product of the means is equal to the product of the extremes. "
The Youth's Assistant in Theoretic and Practical Arithmetic: Designed for ... - Page 67
by Zadock Thompson - 1848 - 168 pages
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The Art of Teaching School: A Manual of Suggestions for the Use of Teachers ...

Josiah Rhinehart Sypher - Teaching - 1872 - 327 pages
...and second terms of a proportion must be the same as the relation between the third and fourth terms. The product of the means is equal to the product of the extremes. A missing extreme may be found by dividing the product of the means by the given extreme. A mean may...
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The Quadrature and Geometry of the Circle Demonstrated

James Smith - Circle-squaring - 1872 - 269 pages
...the area of a circumscribing square to the latter = 16. Hence: r28 : 1-6384 :: 12-5 : 16 ; therefore, the product of the means is equal to the product of the extremes, and proves that the areas of circles are to each other as the areas of their circumscribing squares....
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The Art of Teaching School

J.R. Sypher - 1872
...second terms of a proportion must be the same as the relation between the third a^id fourth terms. The product of the means is equal to the product of the extremes. A missing extreme may be found by dividing the product of the means by the given extreme. A mean may...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 261 pages
...dividing the antecedent by the consequent is called the ratio. If four quantities are proportional, the product of the means is equal to the product of the extremes; in the proportion a : b : : c : d, a and d are the extremes, b and c the means. Wherefore, in order...
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New Practical Arithmetic: In which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1873 - 336 pages
...a term repeated between the other two. Thus, In 12 : 6 :: 6 : 3, 6 is a mean proportional. 328. 1. In every proportion the product of -the means is equal to the product of the extremes. For, in the proportion 6 : 3 : : 4 : 2, since the ratios are equal (Art. 326), we have f = -J- Now,...
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Manual of Algebra

William Guy Peck - Algebra - 1875 - 331 pages
...fractions, we have, bc — ad; (2) hence, the following principles: 1°. If four quantities are in proportion, the product of the means is equal to the product of the extremes. Conversely, if we divide both members of (2) by cq, we have, - = - ; or, a : b : : c : d ; hence, ac...
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Examination Christmas,1875

Education Department,London - 1876
...angle : find the area. SECTION X. 1. Define ratio and proportion. Shew that when four numbers are in proportion, the product of the means is equal to the product of the extremes. 3. State as precisely as possible your view« as to the value of Mental Arithmetic simply asan Educational...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 366 pages
...proportion is said to be transformed by division. PROPOSITION II. THEOREM. If four quantities are in proportion, the product of the means is equal to the product of the extremes. Assume the proportion, a : b :: c : d, whence - = - ; . . . (1) Multiplying both members of (1) by...
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Bradbury's Elementary Algebra: Designed for the Use of High Schools and ...

William Frothingham Bradbury - Algebra - 1877 - 269 pages
...fourth terms of a proportion are called the extremes, and the second and third the means. 106. In a proportion the product of the means is equal to the product of the extremes. Let a : b = с : d a с 6 = 5 Clearing of fractions, ad^bc A proportion is an equation ; and making...
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The New American Arithmetic, Part 3

Samuel Mecutchen, George Mornton Sayre - Arithmetic - 1877
...last terms of a proportion are called the Extremes, and the second and third terms the Means. In any proportion the product of the means is equal to the product of the extremes. Thus, in the proportion 4 : 8 :: 12 : 24, 8x 12 = 4 x 24. ORAL EXERCISES. 1. If 2 pounds of butter...
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