 | Thomas Hunter - 1878 - 142 σελίδες
...when the first is to the second as the second to the third. Four quantities are in proportion when the first is to the second as the third to the fourth. For example, A:B::B:C. Let A=2,B=4,and C= 8. Then2:4::4:8; that is, - =-; the equality of ratios. 4... | |
 | Alexis Claude Clairaut - 1881 - 184 σελίδες
...to the base B c, it may be demonstrated also that when four lines BF, B c, AB, and BG, are such that the first is to the second as the third to the fourth, then the rectangle having for height and base the first and the fourth of these lines, is equal to... | |
 | Homersham Cox (the younger) - 1885 - 254 σελίδες
...10 : 6 :: 25 : 15. We have then the general theorem — If four quantities are in proportion so that the first is to the second as the third to the fourth, then the first will be to the third as the second to the fourth. If the ratio of two numbers 221 and... | |
 | Henry Martyn Taylor - 1893 - 486 σελίδες
...the second of four magnitudes be to the sum of the third and the fourth as the second to the fourth, the first is to the second as the third to the fourth*. Let A, B, C, D be four magnitudes of the same kind, such that the sum of A and B is to the sum of C... | |
 | Henry Martyn Taylor - 1895 - 708 σελίδες
...the second of four magnitudes be to the second as the sum of the third and the fourth to tlie fourth, the first is to the second as the third to the fourth*. Let A, B, C, D be four magnitudes, A and B being of the same kind and C and D of the same kind, such... | |
 | Joseph Battell - 1903 - 722 σελίδες
...taken separately, are proportionals, they will also be proportionals when taken jointly, that is, if the first is to the second as the third to the fourth, the first and second together will be to the second as the third and fourth together to the fourth.'... | |
 | Euclid - 1908 - 456 σελίδες
...first be the same multiple of the second, or the same part of it, that the third is of the fourth, the first is to the second as the third to the fourth. Let the first A be the same multiple of B the second that C the third is of the fourth D ; A is to... | |
 | Hans Niels Jahnke - 436 σελίδες
...both by one difference, that is smaller than any given magnitude, as the third to the fourth, then the first is to the second as the third to the fourth. (Liber II, Proposition II) Here in proportions. quite in consonance with geometric theory, magnitudes... | |
 | Laurence Sigler - 2003 - 652 σελίδες
...[On Four Proportional Nambers,] It is sought how to find four proportional integral nmubers, of which the first is to the second, as the third to the fourth, that is the ratio of the first namber to the second is the same as the ratio of the third namber to... | |
 | Luke Hebert - 1829 - 392 σελίδες
...weight, as the Telocity of the weight to the velocity of the power $ and as, in these •*•quantities, the first is to the second as the third to the fourth, it follows,, that the 1st multiplied by the 4th, equals the 2nd multiplied by the 3rd. Therefore, the... | |
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NB When four magnitudes are proportionals, it is usually expressed by saying, the first is to the second, as the third to the fourth.' VII. When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater... 
