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" If the product of two quantities be equal to the product of two other quantities, two of them " (any two, of course) " may be made the extremes, and the other two the means, of a proportion " ; eg 4 X 8 = 2 X 16 ; then, making 4 and 2 the extremes, we... "
An Essay Upon the Study of Geometry in Common Schools - Page 24
by Stephen Chase - 1847 - 26 pages
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The Youth's Assistant in Theoretic and Practical Arithmetic, : Designed for ...

Zadock Thompson - Arithmetic - 1828 - 230 pages
...stand — iem. lem. cts. cts. IMB. cts. Iem. cts. 4 : 6 : : 12 : x. or 4 : 12 : : 6 : *. Now, since the product of the extremes is equal to that of the means, 4 simes x equals 6 times 12, or, according to the second arrangement, 12 thnes 6. Hence, if 12 times...
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The Youth's Assistant in Theorhetic [sic] and Practical Arithmetic: Designed ...

Zadock Thompson - Arithmetic - 1832 - 182 pages
...— km. 1cm. els. cts. lem. cts. l«m. els. 4 : 6 : : 12 i x. or 4 I 12. : ! 6 : *. Now, since the product of the extremes is equal to that of the means, 4 times x equals 6 times 12, or, according to the second arrangement, 12 times 6. Hence, if 12 times...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...when a : b :: c: d, by definition, ^ =^, and multiplying both sides by bd, it becomes ad=zbc ; or the product of the extremes is equal to that of the means. 4. Given — ^— : — — :: 7 : 4; to find the value of x. 1 Oft 7 By multiplying extremes and means,...
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First Lessons in Geometry: Upon the Model of Colburn's First Lessons in ...

Alpheus Crosby - Geometry - 1847 - 190 pages
...this prop" Le circle eat 1'espace termini par cettelignecourbe."— £l£mentsde Gtomltrie, ll»e Ed., p. 33. osition. " If the product of two quantities...is equal to that of the means, 4 X 2 = 8 X 16, or 8 = 128. It should be, the two factors of one product may be made the extremes, &c. Nor is this a mere...
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First Lessons in Geometry: Upon the Model of Colburn's First Lessons in ...

Alpheus Crosby - Geometry - 1847 - 192 pages
...respect sometimes amounts to a gross error. Thus, in some of the books, we find this proposition. " If the product of two quantities be equal to the product...is equal to that of the means, 4 X 2 = 8 X 16, or 8 = 128. It should be, the two factors of one product may be made the extremes, &c. Nor is this a mere...
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