 | Euclides - 1846 - 292 pages
...E together to B, D, F together. Wherefore, If any number %c. QED PROP. Xni. THEOR. If the first has to the second the same ratio which the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the sixth, the first shall also have... | |
 | Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...same ratio to one another which their equimultiples have. When is the first of four magnitudes said to have to the second the same ratio which the third has to the fourth ; and when a greater ratio ? Do the definitions and theorems of Book v. include incommensurable magnitudes... | |
 | Harvey Goodwin (bp. of Carlisle.) - Mathematics - 1847 - 136 pages
...arithmetical, and the last three in harmonical progression ; it is required to prove that the first has to the second the same ratio which the third has to the fourth. 10. If P, Q, R be respectively the pth, </th and rth terms of an harmonical series, prove that (p -q)PQ... | |
 | Euclides - 1848 - 52 pages
...all the antecedents taken together be to all the consequents. PROP. XIII. THEOREM. If the first has to the second the same ratio which the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the sixth ; the first shall also... | |
 | James Elliot - 1850 - 116 pages
...л/20 or 3 4exactly, in numbers, at all. 2. When four quantities are proportional, the first is said to have to the second the same Ratio which the third has to the fourth. A proportion, therefore, expressing the equality of two ratios, is sometimes written thus, 16 : 4 =... | |
 | Harvey Goodwin - Mathematics - 1851 - 196 pages
...triangle having each angle at the base double of the third angle. 7. If the first of six magnitudes have to the second the same ratio which the third has to the fourth, but the third to the fourth a greater ratio than the fifth to the sixth, the first shall have to the... | |
 | Euclides - Geometry - 1853 - 334 pages
...A has a greater ratio to B than E has to r. "Which was to be proved. COB.— If the first magnitude have to the second the same ratio which the third has to the fourth, and the fifth have to the sixth a greater ratio than the first have to the second : then the fifth... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...etc. QED PROPOSITION A. THEOR. If the first of four magnitudes has to the second the same ratio rchich the third has to the fourth, then, if the first be greater than the second, the third is also greater than the fourth ; and if equal, equal ; if less, less. Take any equimultiples... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 474 pages
...former being called the antecedent and the latter the consequent. 94. If the first of four numbers has to the second the same ratio which the third has to the fourth, the four numbers are said to form a propor(i 10 2 lion. Thus the ratio of 2 : 3 is -, and the ratio... | |
 | Euclides - Geometry - 1853 - 176 pages
...there be any number, &c. QED a, b, С, d, e, f, g, h, PKOPOSITION XXIV. — .THEOREM, If the first has to the second the same ratio which the third has to the fourth, and the fifih to the second the same ratio which the sixth lias to the fourth ; the first and fifih... | |
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THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the... 
