 ... multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth...  A Treatise on Elementary Algebra - Page 293by James Hamblin Smith - 1869Full view - About this book
 | James Hamblin Smith - Algebra - 1882 - 414 pages
...less than nd, and if ma be equal to nb, me will also be equal to nd, and if ma be greater than rib, me will also be greater than nd. Since then of the...c, d are proportionals according to the geometrical test. 362. II. To deduce the algebraic test of proportionality from that given by Euclid. Let a, b,... | |
 | James Hamblin Smith - 1883 - 466 pages
...third is also equal to that of the fourth : or, " If the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth." We shall now show, first, how to deduce Euclid's test of the equality of ratios... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...the third is also equal to that of the fourth, and if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth. When four magnitudes are proportionals it is usually expressed by saying, the first... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...the second and fourth, namely, the arc EJ and the angle EPJ, and we have proved that, according as the multiple of the first is greater than, equal to,...multiple of the second, the multiple of the third is greater than, equal to, or less than the multiple of the fourth. Hence [v. DeJE. vJ BC : EF : : the... | |
 | Euclides - 1885 - 340 pages
...and third being taken, and any equimultiples whatsoever of the second and fourth, if, according as the multiple of the first is greater than, equal to,...multiple of the second, the multiple of the third is greater than, equal to, or less than the multiple of the fourth. vi. Magnitudes which have the same... | |
 | Charles Smith - Algebra - 1888 - 680 pages
...of the third is always greater than, equal to or less than the multiple of the fourth, according as the multiple of the first is greater than, equal to or less than the multiple of the second. If the four quantities a, b, c, d satisfy the algebraical CÍ f* test of proportionality, we have г... | |
 | Euclid - Geometry - 1890 - 442 pages
...third ; and let any equimultiples be taken of the second and fourth. Then, if it is found that always the multiple of the first is greater than, equal to, or less than the multiple of the second, according as the multiple of the third is greater than, equal to, or less than the multiple of the... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...the multiple of the third is greater than, equal to, or less than that of the fourth, according as the multiple of the first is greater than, equal to, or less than that of the second. This may be symbolically expressed thus : The ratio P : Q is said to be the... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1891 - 606 pages
...multiple of the third is greater than, equal to, or less than the multiple of the fourth, according as the multiple of the first is greater than, equal to, or less than the multiple of the second. In algebraical symbols the definition may be thus stated : Four quantities a, b, c, d are in proportion... | |
 | Charles Smith - Algebra - 1894 - 620 pages
...of the third is always greater than, equal to, or less than the multiple of the fourth, according as the multiple of the first is greater than, equal to, or less than the multiple of the second. If the four quantities a, b, c, d satisfy the algebraical test of proportionality, we have a _c. Ь... | |
| |
