| 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... | |
| 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... | |
| 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,... | |
| 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.... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| William Frothingham Bradbury - Algebra - 1889 - 444 pages
...: b = с : d that is, т = -, о а Clearing of fractions, ad=bc 311. If the product of two numbers **is equal to the product of two others, the factors...factors of the other the means, of a proportion. Let ad** — b с Dividing by bd, -, = -j that is, a : b — с : d Let a : b — с ; d Вy Art. 310, ad^bc... | |
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