 | James Wharton - 1847 - 224 pages
...together, and also the two middle terms, their products are equal, or, as it is usually expressed, the product of the means is equal to that of the extremes ; thus 6 . 2 = 4 . 3, or 12=12. If one of these terms be wanting it can be found ; thus if it be required... | |
 | Education - 1855 - 436 pages
...which one number bears to another ; and that the ratio of 5 to 40 is the same as that of 7 to 56 : the product of the means is equal to that of the extremes in a proportion ; or that the product of the square roots of two numbers is equal to the square root... | |
 | Thomas Sherwin - Algebra - 1855 - 262 pages
...foregoing principles of proportions. The correctness of any proportion may be verified by ascertaining that the product of the means is equal to that of the extremes. 1. Illustrate (i) by the proportion 7 : 10 = 21 : 30. 2. Illustrate (n) by putting 12.8 = 32.3 into... | |
 | Cadmus Marcellus Wilcox - Rifle practice - 1859 - 308 pages
...to show. This property is indispensable to the existence of proportions. It can be shown that when the product of the means is equal to that of the extremes, the four numbers are in proportion, and they are not in proportion when this is not the case. KNOWING... | |
 | 1860 - 462 pages
...called the extremes, and the others, that is, В and C, are called the means. 81. Theorem. In every proportion the product of the means is equal to that of the extremes. — Proof. In any proportion, as M : N = P : Q, we wish to prove (using the mark X to signify " multiplied... | |
 | John Daniel Runkle - Mathematics - 1860 - 590 pages
...two quantities, bearing the same ratio to a third, must be equal to each other, we have proved that the product of the means is equal to that of the extremes. 82. Definition. When both the means are the same quantity, that quantity is called a mean proportional... | |
 | Thomas Hill - Geometry - 1862 - 148 pages
...two quantities, bearing the same ratio to a third, must be equal to each other, we have proved that the product of the means is equal to that of the extremes. 82. Definition. When both the means are the same quantity, that quantity is called a mean proportional... | |
 | Thomas Sherwin - 1862 - 252 pages
...foregoing principles of proportions. The correctness of any proportion may be verified by ascertaining that the product of the means is equal to that of the extremes. 1. Illustrate (i) by the proportion 7 : 10 = 21 : 30. 2. Illustrate (n) by putting 12.8 = 32.3 into... | |
 | Thomas Hill - Geometry - 1863 - 164 pages
...called the extremes, and the others, that is, B and C, are called the means. 81. Theorem. In every proportion the product of the means is equal to that of the extremes. Proof. In any proportion, as M : N — P : Q, we wish to prove (using the mark X to signify " multiplied... | |
 | Simon Newcomb - Algebra - 1882 - 302 pages
...When any three terms of a proportion are given, the fourth can always be found from the theorem that the product of the means is equal to that of the extremes. We have shown that whenever Ans. Alt. Inv. « 2 |V i 6 G = о О — 21 31 4 2i. 6; 7. Сoтр. •... | |
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HDG, the corresponding sides are proportional (page 70, 4thly) ; therefore we have the proportion ED : DG =AD : HD (II.) This last proportion has the first ratio common with the first proportion ; consequently the two remaining ratios are in a geometrical... 
