 | George Alfred - 1834 - 336 sider
...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... | |
 | John Playfair - 1836 - 148 sider
...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... | |
 | A. Turnbull - 1836 - 368 sider
...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|... | |
 | Silas Totten - 1836 - 360 sider
...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 - 1837 - 376 sider
...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... | |
 | 1838 - 372 sider
...the other. 178. If we have the proportion A : B : : C : D, BD we have -r-= -=, (Art. 169); -4l. '-' and by clearing the equation of fractions, we have...extremes is equal to the product of the two means. 179. If four quantities, A, B, C, and D, are so related to each other that AxD=B*C, i „ , , BD we... | |
 | Charles Davies - 1838 - 292 sider
...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 :... | |
 | Bourdon (M., Louis Pierre Marie) - 1839 - 368 sider
...by the other. 178. If we have the proportion A : B : : C : D, nr\ we have —— — , (Art. 169); AO and by clearing the equation of fractions, we have...four proportional quantities, the product of the two ext'emes is equal to the product of the two means. 179. If four quantities, A, B, C, and D, are so... | |
 | Richard W. Green - 1839 - 156 sider
...numerator. These were the two means. And hence we learn, that if four quantities are proportional, the product of the two extremes is equal to the product of the means. , §115. Therefore, whenever in our operations we find a proportion, we can easily reduce... | |
 | George Leonard - 1841 - 354 sider
...fractions when changed to a common denominator, always have equal numerators ? Therefore in a proportion, The product of the two extremes is equal to the product of the two means. So if we divide the product of the two means by one extreme, the quotient will be the other. In order... | |
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AC and by clearing the equation of fractions we have BO=AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means. 
