Difference between revisions of ".Mzcw.NzE4MA"
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64. If the first quantity is to the second as the second | 64. If the first quantity is to the second as the second | ||
| − | is to the | + | is to the third, the three quantities are said to be in |
| + | [[underline]] continued proportion. [[/underline]] Thus a:b::^ [[addition]] b: [[/addition]] d, or if 3:9::^ [[addition]] 9: [[/addition]] 27, | ||
| + | then are the quantities, a, b, c, or the numbers 3, 9, 27, | ||
| + | is continued proportion. The mark of this proportion | ||
| + | is [[image]]. Thus [[image]] a,b,c denotes that, a:b::b:c. And | ||
| + | [[image]] a, b, c, d, e, f, g, & c. denotes that, a:b::b:c::c:d::d:e::e:f::f:g\ | ||
| + | |||
| + | 65. And in this case the quantities, a, b, c, d, e, f, g, are | ||
| + | said to be in [[underline]] geometric progression. [[/underline]] | ||
| + | |||
| + | 66. In like manner an arithmetic proportion is | ||
| + | said to be continued when the first term differs | ||
| + | as much from the second as the second does from | ||
| + | the third. | ||
| + | |||
| + | 67. And if there be many quantities, & that | ||
| + | the difference of any two directly following | ||
| + | each other is always the same, those quantities | ||
| + | are said to be in [[underline]] arithmetic progression. [[/underline]] | ||
| + | Thus the numbers, 3, 0, 12 are in continued arithmetic | ||
Revision as of 16:45, 10 August 2018
(11) 64. If the first quantity is to the second as the second is to the third, the three quantities are said to be in underline continued proportion. /underline Thus a:b::^ addition b: /addition d, or if 3:9::^ addition 9: /addition 27, then are the quantities, a, b, c, or the numbers 3, 9, 27, is continued proportion. The mark of this proportion is image. Thus image a,b,c denotes that, a:b::b:c. And image a, b, c, d, e, f, g, & c. denotes that, a:b::b:c::c:d::d:e::e:f::f:g\
65. And in this case the quantities, a, b, c, d, e, f, g, are said to be in underline geometric progression. /underline
66. In like manner an arithmetic proportion is said to be continued when the first term differs as much from the second as the second does from the third.
67. And if there be many quantities, & that the difference of any two directly following each other is always the same, those quantities are said to be in underline arithmetic progression. /underline Thus the numbers, 3, 0, 12 are in continued arithmetic
