Difference between revisions of ".Mzcw.NzE5Mg"
| Line 8: | Line 8: | ||
proportional between two quantities, you | proportional between two quantities, you | ||
need only multiply the quantities together | need only multiply the quantities together | ||
| − | & extract the square root of the product. | + | & extract the square root of the product. |
| + | Thus if it were required to ding a mean | ||
| + | proportional between 20 & 180: their product | ||
| + | is 3600, the square root of which [[deletion]] [[unclear]] [[/deletion]] [[addition]] is [[/addition]] 60 | ||
| + | the mean required; for 20:60::60:180. | ||
| + | |||
| + | 77. The first term in a continued proportion | ||
| + | is to the third in a duplicate ratio of the | ||
| + | first to the second. For in the geometric | ||
| + | proportion a:am::am:amm, the ratio of a to am, | ||
| + | is expressed by [[formula]] & the ratio of a to am is | ||
| + | expressed by a/am = 1/m; but the ratio 1/m2 is duplicate | ||
| + | of 1/m. Because [[formula]] Q.D.E. | ||
Latest revision as of 18:36, 11 August 2018
(17) And in general if a:b::b:c, then will ac = bb see § 52.
76. Hence it follows, that to find a geometric mean proportion unclear, or simply a geometric mean, or as it is often expressed a mean proportional between two quantities, you need only multiply the quantities together & extract the square root of the product. Thus if it were required to ding a mean proportional between 20 & 180: their product is 3600, the square root of which deletion unclear /deletion addition is /addition 60 the mean required; for 20:60::60:180.
77. The first term in a continued proportion is to the third in a duplicate ratio of the first to the second. For in the geometric proportion a:am::am:amm, the ratio of a to am,
is expressed by formula & the ratio of a to am is
expressed by a/am = 1/m; but the ratio 1/m2 is duplicate of 1/m. Because formula Q.D.E.
