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In any proportion, the product of the means is equal to the product of the extremes.
Treatise on the elements of algebra - Page 256
by James Bryce - 1837

## 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...

## 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...

## 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...

## New Practical Arithmetic: In which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1873 - 336 pages
...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,...

## Manual of Algebra

William Guy Peck - Algebra - 1875 - 331 pages
...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...

## Examination Christmas,1875

...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...

## Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 366 pages
...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) ac Multiplying both members of (1) by...

## Complete Arithmetic: Comprising the New Intermediate Arithmetic and Part of ...

Stoddard A. Felter, Samuel Ashbel Farrand - Arithmetic - 1877 - 471 pages
...numerator by the other denominator, the products are equal. Hence, iu every proportion, PRINCIPLE I. — The product of the means is equal to the product of the extremes. If multiplying either the means or extremes together produces the same product, dividing this product...

## Complete Arithmetic: Theoretical and Practical

William Guy Peck - Arithmetic - 1877 - 341 pages
...have equal denominators ; hence, their numerators are equal, that is, 5 x 8 = 2 x 20 ; in this case the product of the means is equal to the product of the extremes. But we can reason in like manner on any proportion ; hence, we have the following principle : 1°....

## Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 398 pages
...the diameter is a mem proportional between the segments of the diameter). Then tiCl = MCXCN, §259 (the product of the means is equal to the product of the extremes). QEF GEOMETRY. BOOK IV. PROPOSITION XXVI. PROBLEM. 359. To construct a parallelogram equivalent to a...