 Proportion is when, of three numbers, the first has the same proportion to the third, as the difference between the first and second, has to the difference between the second and third. As in these three, 6, 8, 12 ; where 6 : 12 : : 8 — 6 : 12 — 8,...  A Treatise on Algebra: Embracing, Besides the Elementary Principles, All the ... - Page 205by George Roberts Perkins - 1842 - 360 pagesFull view - About this book
 | Charles Hutton - Mathematics - 1811 - 406 pages
...suffice. Musical Proportion is when, of three numbers, the first has the same proportion to the third, as the difference between the first and second, has to the difference between the second and third. As in these three, 6, 8, 12 ; where 6 : 12 :: 8 - 6 : 12 - 8, that is 6 : 12 :: 2... | |
 | Charles Hutton - Mathematics - 1812 - 620 pages
...suffice. Musical Proportion is when, of three numbers, the first has the same proportion to the third, as the difference between the first and second, has to the difference between the second and third. As in these three, 6, 8, 12 ; where 6 : 12 : : 8 — 6 : 12 — 8, that is 6 : 12... | |
 | John Bonnycastle - Algebra - 1813 - 456 pages
...ar + or* + ar* -t- ar*, &c. continued ad infinitum, will be lr 13. Three quantities are said to be in harmonical proportion, when the first has the same ratio to the third, as the difference between the first and second has to the difference between the second and... | |
 | Charles Hutton - Mathematics - 1816 - 610 pages
...Musical Proportion is when, of three numbers, the first has the same proportion to the third, as ihe difference between the first and second, has to the difference between the second and third. As in these three, 6, 8, 12 ; where 6 : 12 : : 8 — 6 : 12 — 8, that is 6 : 12... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...suffice. Musical Proportion is when, of three numbers, the first has the same proportion to the third, as the difference between the first and second, has to the difference between the second and third. As in these three, 6, 8, 12 ; where 6: 12 :: 8-6: 12-8, that is 6 : 12 :: 2:4. When... | |
 | Charles Hutton - Mathematics - 1825 - 608 pages
...12 — G, that is 6 : 12 : : 2 : 4. When four numbers are in musical proportion ; then the first haa the same ratio to the fourth, as the difference between...has to the difference between the third and fourth. As in these, 6, 8, 12, 18 ; where 6 : 18 : : 8—6: 18—12. that is 6 : 18 : : 2: 6. When numbers... | |
 | John Radford Young - Algebra - 1832 - 408 pages
...quantities are said to be in harmonical proportion,, when the first has the same ratio to the third, as the difference between the first and second has to the difference between the second and third. (36.) And four quantities are in harmonical proportion, when the first has the same... | |
 | James Bryce - Algebra - 1837 - 322 pages
...cubes triplicate, of the ratio of the first powers.f 168. IX. Three or four quantities are said to be in harmonical proportion, when the first has the same ratio to the last that the difference of the first and second has to the difference of the last and last but one.... | |
 | John Radford Young - 1839 - 332 pages
...quantities are said to be in harmonical proportion, when the'first has the same ratio to the third, as the difference between the first and second has to the difference between the second and third. (78.) And four quantities are in harmonical proportion, when the first has the same... | |
 | 1841 - 524 pages
...three numbers representing the relations of sounds, the first has the same proportion to the third as the difference between the first and second has to the difference between the second and third ; as in the numbers 6, 8, 12 ; where 6 : 12 : ; se : 12-8; that is to say, 6 ; 1 2... | |
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