 | Ferdinand Rudolph Hassler - Arithmetic - 1826 - 224 pages
...3+5 x 3-t-5a X.'H-6» X 3+5« x 3+5" X 3+5« x 3 &c. The law of continued geometric proportion, that the product of the two extremes is equal to the product of the mean term into itself, evidently holds good here, and we have, for instance, by the product of... | |
 | Jeremiah Day - Algebra - 1827 - 352 pages
...d+b — 1. 8. Reduce the equation x X(0+6)— a — 6= Dividing by a+b (Art. 118.) x — 1 =d And • x=d+l. 187. Sometimes the conditions of a problem...arithmetic. See Webber's Arithmetic. * Thus, if a : 6: ;c : d, Then ad=bc And if 3 : 4: :6 ; 8; And 3X8=4X6. Hence, 188. A PROPORTION IS CONVERTED INTO... | |
 | Ira Wanzer - Arithmetic - 1831 - 408 pages
...reason of the practice in the Rule of Three. THEOREM 2. — In any continued geometrical progression, the product of the two extremes is equal to the product of any two means that are equally distant from them, or equal to the second power of the middle term when... | |
 | Charles Davies - Arithmetic - 1833 - 284 pages
...since the product of th« divisor by the quotient is equal to the dividend, it follows, That in any geometrical proportion the product of the two extremes is equal to the product of the two means. Thus in the first example, 1 : 6 :: 2 : 12 we have, 1 X 12=frx2=12 and in the second, 4 : 12 : : 8... | |
 | George Alfred - Arithmetic - 1834 - 336 pages
...called the ratio. NB — In any rank or series of numbers, which increase or decrease by a common ratio, the product of the two extremes is equal to the product of any two means, equally distant from the said extremes, as in the series, 2, 4, 8, 16; the product of... | |
 | A. Turnbull - Arithmetic - 1836 - 368 pages
...term. Now if we call the unknown term x, then, as in every proportional series consisting of 4 terms, the product of the two extremes is equal to the product of the two means, the above question, as an equation, will stand thus, 1J a = 3J X 8, then * = 3£ x " ~j = — = 18|... | |
 | John Playfair - Geometry - 1836 - 148 pages
...divided by B is equal to C divided by D. PROPOSITION I. THEOREM. If four quantities are proportional, the product of the two extremes is equal to the product of the two means. Let A : B : : C : D ; then AD=BC. A /~1 Because A : B j: C : D, g=-(Def. 20. 4.) ; multiply both by... | |
 | Silas Totten - Algebra - 1836 - 360 pages
...which cannot be demonstrated without the aid of Algebra. (73.) 1st. In every geometrical progression, the product of the two extremes is equal to the product of any two terms equally distant from them, or equal to the square of the middle term, when there is an... | |
 | Adrien Marie Legendre - Geometry - 1837 - 376 pages
...othpr. and their nroHnrt '* <i<•—'•*-«* PROPOSITION I. THEOREM. When four quantities are in proportion, the product of the two extremes is equal to the product of the two means. Let A, B, C, D, be four quantities in proportion, and M : N • : P : Q be their numerical representatives... | |
 | Charles Davies - Arithmetic - 1838 - 292 pages
...since the product of the divisor by the quotient is equal to the dividend, it follows, That in every proportion the product of the two extremes is equal to the product of the two means. Thus in the first example, 1 : 6 : : 2 : 12 we have, 1 x 12 = 6 xi2 = 12 and in the proportion, 4 :... | |
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If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. 
