Books Books 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... Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 117
by Euclides - 1860 ## The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 pages
...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...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... ## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 333 pages
...the ratio compounded of the ratios which are the same with the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if...ratio which A has to D, then, for shortness' sake, Mis said to have to N a ratio compounded of the same ratios, which compound the ratio of A to D ; that... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 316 pages
...F, G to H, and K to L. In like manner, the same things being supposed, if M has to'N the sameratio which A has to D, then, for shortness' sake, M is...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 said to... ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...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...; 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... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
...ratio compounded of the ratios which -sJre the same with the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if...is, a ratio compounded of the ratios of E to F, G to Hr and K to L. XI. Ef three magnitudes are continual proportionals, tlie ratio of the first to the... ## The First Six Books of the Elements of Euclid: With a Commentary and ...

Dionysius Lardner - Geometry - 1838 - 386 pages
...expressed by saying, A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. I n like manner, the same things being supposed, if M...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... ## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...the ratios of E to F, G to H, and K to L. In like manner the same things being supposed, if M have 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... ## The Elements of Euclid

Euclid - Geometry - 1838 - 478 pages
...ratios of E to F, G to H, and K to L. In like manner the same things being supposed, if M have tl^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. 'Geometers make use of the following... ## The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Euclid's Elements - 1841 - 144 pages
...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...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. This definition may be better understood... 