 | National cyclopaedia - 1884 - 670 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... | |
 | 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... | |
 | James Bates Thomson - 1888 - 336 pages
...Art. 363, J = £ Clearing of fractions, ae = JV Again, 9 : 6 : : 6:4, and 4x9 = 6*. THEOREM Ш. [f (he product of two quantities is equal to the product of two others, the four quantities arc proportional ; the factors of either product being taken for ¿he extremes, and the factors of... | |
 | 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... | |
 | 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... | |
 | Charles Davies - Algebra - 1889 - 330 pages
...Conversely, if we divide both members of ( 2 ) by ca, we shall have, - . = - ; or, a : b : : c : d. Hence, ac If the product of two quantities is equal to the product, of two other quantities, the first two may be made the means, and the second two the extremes, of a proportion.... | |
 | Webster Wells - Algebra - 1890 - 560 pages
...mean is equal to the product of the extremes divided by the other mean. 384. (Converse of Art. 381.) 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... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...are in proportion, they are in proportion by division. SECTION II.— EQUAL PRODUCTS. 297. PROP. VI. If the product of two quantities is equal to the product of two other quantities, the two quantities that form either product may be made the extremes, and the other... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...the antecedent or the consequent. SECTION II.— EQUAL PRODUCTS. PROPOSITION VI. 31§. Theorem : // the product of two quantities is equal to the product of two other quantities, the two quantities that form either product may be made the extremes, and the other... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...from (1), &2 = ac. (§231.) Whence, b = -Vac. PROPOSITION II. THEOREM. 233. (Converse of Prop. I.) Jf 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. To prove... | |
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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... 
