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If the product of two quantities is equal to the product of two others, the...
An Elementary Geometry - Page 27
by William Frothingham Bradbury - 1872 - 110 pages

## New Practical Algebra: Adapted to the Improved Methods of Instruction in ...

James Bates Thomson - Algebra - 1878 - 322 pages
...e By Art. 363, | = * Clearing of fractions, at = 6s. Again, 9:6:: 6-4, and 4 xg = 62. THEOREM III. If the product of two quantities is equal to the product of two others, the four quantities are proportional j the factors of either product being taken for the extremes, and...

## Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips, Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...AC, we have, £ = £, or, A:B = C:DL, £ = 5, or, A:C=B:DIL, ~ = ~, or, B : A = D : C III. CA Hence, if 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...

## An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...extremes equal to the product of the meaiis ia merely clearing the equation of fractions. THEOREM II. 14i If the product of two quantities is equal to the product...factors of the other the means of a proportion. Let ad = be ac Dividing by bd - = ^ that is a : b = c : d THEOREM III. 15. If four quantities are in proportion,...

## The Inductive Algebra: Embracing a Complete Course for Schools and Academies

William James Milne - Algebra - 1881 - 360 pages
...3. What does ad, the first member of the equation, form in the proportion? What be? PRINCIPLE 3. — If the product of two quantities is equal to the product of two otlier quantities, two of them may be made the extremes, and the other two the means, of a proportion....

## The national encyclopædia. Libr. ed, Volume 11

National cyclopaedia - 1884 - 668 pages
...fourth term) can be obtained as easily ; for be . ad , ad a=— ,6 = — , and c = — . dcb Conversely, if the product of two quantities is equal to the product of two others, these four are proportionals ; example, 4 times 6 = 3 times 8 ; whence we see that 3 is to 4 as 6 is...

## The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...be 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...

## 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 means of a proportion. or Thus,...

## A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 272 pages
...the product of the means). Whence, extracting the square root, 6.= Vac. QED PROPOSITION III. 297. // the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion in which the other two are made the means. Let...