Books Books 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 73
by Zadock Thompson - 1832 - 168 pages ## Manual of Algebra

William Guy Peck - Algebra - 1875 - 348 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... ## Examination Christmas,1875

Education Department,London - 1876 - 1010 pages
...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... ## Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 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... ## The New American Arithmetic, Part 3

Samuel Mecutchen, George Mornton Sayre - Arithmetic - 1877 - 200 pages
...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... ## Bradbury's Elementary Algebra: Designed for the Use of High Schools and ...

William Frothingham Bradbury - Algebra - 1877 - 280 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... ## Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 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... ## Complete Arithmetic: Theoretical and Practical

William Guy Peck - Arithmetic - 1877 - 428 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°.... ## Complete Arithmetic: Comprising the New Intermediate Arithmetic and Part of ...

Stoddard A. Felter, Samuel Ashbel Farrand - Arithmetic - 1877 - 496 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... ## Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...circumference to the diameter is a mean proportional between the segments of the diameter). aXb, §259 (flu product of the means is equal to the product of the extremes). QEF 355. COROLLARY 1. A square may be constructed eqxiivalent to a triangle, by taking for its side... 