 | John Playfair - 1819 - 354 pages
...', have to N a ratio compounded of the same ratios, which compound the ratio of A to D ; that is, a ratio compounded of the ratios of E to F, G to H, and K to L. XI. if three magnitudes are continual proportionals, the ratio of the first to the third is... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...bt-ing supposed, if M has to N the same ratio which A has to D ; then, for shortness sake, M is said to have to N, the ratio compounded of the ratios of E to F, G to H, and К to L. ELEMENTS 07 EUCLID. XII. ID proportionale, the antecedent terms are called homologous to one another,... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...being supposed, if M has to N the same ratio which A has to I); then, for shortness sake, M is said to have to N the ratio compounded of the ratios of E to F, G to H, and K to L. XII. In proportionals, the antecedent terms are called homologous to one another, as also the... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...being supposed, if M has to N the same ratio which A has to D ; then, for shortness' sake, M is said to have to N the ratio compounded of the ratios of E to F, G to H, and K to L. The term compound ratio, like all other technical terms, is used for brevity, and to avoid... | |
 | Euclid - 1835 - 540 pages
...being supposed, if M has to N the same ratio which A has to D ; then, for shortness sake, M is said to have to N the ratio compounded of the ratios of E to F, G to H, and K to L. XII. In proportionals, the antecedent terms are called homologous to one another, as also the... | |
 | Oliver Byrne - Mathematics - 1841 - 144 pages
...to L. And the same thing is to be understood when it is more briefly expressed by saying, A has to D the ratio compounded of the ratios of E to F, G to H, and К to L. In like manner, the same things being supposed ; if M has to N the same ratio which A has to D, then,... | |
 | Euclides - Geometry - 1841 - 378 pages
...to L. And the same thing is to be understood when it is more briefly expressed by sayipg, A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. compounded of the ratios of E to F, G to H, and KtoL. XII. In proportionals, the antecedent... | |
 | Oliver Byrne - Mathematics - 1841 - 140 pages
...then, by this definition, A is said to have to D the ratio compounded of ratios which are the same with the ratios of E to F, G to H, and К to L. And the same thing is to be understood when it is more briefly expressed by saying, A has to D the... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...to have to N a ratio compounded of the same ratios which compound the ratio of A to D ; that is, a ratio compounded of the ratios of E to F, G to H, and K to L. 11. If three magnitudes are continual proportionals, the ratio of the first to the third is... | |
 | Euclid - Geometry - 1845 - 218 pages
...being supposed, if M has to N the same ratio which A has to D ; then, for shortness' sake, M is said to have to N the ratio compounded of the ratios of E to F, G to H, and K to L. XII. In proportionals, the antecedent terms are called homologous to one another, as also the... | |
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And the same thing is to be understood when it is more briefly expressed by saying, A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if M has to N the same ratio which A has to... 
