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" : b : : mx : y, For the product of the means is, in both cases, the same. And if na : b : : x : y, then a : b : : x :ny. 375. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities... "
An Introduction to Algebra: Being the First Part of a Course of Mathematics ... - Page 188
by Jeremiah Day - 1827 - 332 pages
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...: B : : B : C ; then, by the proposition, I BOOK H. PROPOSITION ii. THEOREM (Converse of Prop. /.). If the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion....
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1850 - 348 pages
...For the product of the means is, in both cases the same. And if na : b : : x : y, then a : b : : x : ny. 375. On the other hand, if the product of two...equation shall constitute the means., and those on l lie other side, the extremes. If my—nh, then m in:: h: y, that is, _=„ n V „,,..,. 7 ii my...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1850 - 356 pages
...mx : y. For the product of the means is, in both cases the same. And if na:b : :x:y, then a:b: : x :ny. 375. On the other hand, if the product of two...proportion, when they are so arranged, that those OK one side of the equation shall constitute the means, and those on the other side, the extremes....
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An Elementary Treatise on Algebra: Designed as First Lessons in that Science

Horatio Nelson Robinson - Algebra - 1850 - 256 pages
...first term. This is a part of the well known rule of three, in Arithmetic. PROPOSITION II. Conversely. If the product of two quantities is equal to the product of two others, then two of them may be taken for the means, and the other two for the extremes of a proportion. Let...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - Algebra - 1852 - 408 pages
...to 2X8, we infer that 2, 3, 5, and 8, are not in proportion. ART. 268. PROPOSITION II. Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let be— ad. Dividing...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 250 pages
...equal to 8X2, we infer that the proportion is false. ART. 345. — PROPOSITION II. — Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad. Dividing...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1854 - 428 pages
...product of the means is, in both cases, the same. And if na : b: '.x '. y, then a : b'. '.x '. ny. 383. On the other hand, if the product of two quantities...means, and those on the other side, the extremes. tc i • mh If my=nh, then m '. n'. '.h '. y, that is, — = •ni , , T i . my nh ror by dividing...
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A treatise on the elements of algebra, by G. Ainsworth and J. Yeats

G. Ainsworth - 1854 - 216 pages
...d, then -=-, and multiplying both sides by ac, —= — , Л С ' <to . • . bc=ad. And conversely, if the product of two quantities is equal to the product of two other quantities, the four are proportional. For (by hyp.) ad=bc, and dividing both sides by bd, we...
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The Popular Educator, Volume 6

1855 - 424 pages
...the product of the means in both cases is the same. So, if na : Ь : : x : y, then a : Ь : : x : ny. On the other hand, if the product of two quantities...others, the four quantities will form a proportion, if they are so arranged that those on one side of the equation shall constitute the means, and those...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...definition, that the product of the extremes is equal to the product of the menus ; and conversely, if the product of two quantities is equal to the product of two others, the first two may be taken as the structed with a groove in each leg, so that extremes, and the last two...
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