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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... "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 117
by Euclides - 1860
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1762 - 466 pages
...and the fame thing is to be underftood when it is more briefly exprefled by faying A has ro D, the ratio compounded of the ratios of E to F, G to H, and K to L. In like manner, the fame things bemg fuppofed, if M has to N the fame ratio which A has to D, then,...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 520 pages
...by this definition, A is faid to have to I) the ratio compounded of ratios which are the fame with the ratios of E to F, G to H, and K to L : And the fame thing is to be underftood when it is more briefly exprefled, by faying A has to D the...
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The Geometrician: Containing Essays on Plane Geometry, and Trigonometry ...

Benjamin Donne - Geometry, Plane - 1775 - 159 pages
...L. And the fame Thing is to be underftood when it is more briefly expreiTed by faying A has to D the Ratio compounded of the Ratios of E to F, G to H, and KtoL. In like Manner, the fame Things being fuppofed, if M has to N the fame Ratio which A has to D,...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 550 pages
...has to N the fame ratio which A has to 1 > , then, for fhortnefs lake, M is faid 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 alfo the confequetns...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1781 - 466 pages
...this Definition, A is faid to have to D the Book V. ratio compounded of ratios which are the fame with the ratios of E to F, G to H, and K to L. and the fame thing is to be underftood when it is more briefty exprefted. by faying A has to D the...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - Euclid's Elements - 1795 - 444 pages
...ratio which A has to D, then, for fliormels fake, M is faid to have to N a ratio compounded of the fame ratios which compound the ratio of A to D ; that is,...compounded of the ratios of E to F, G to H, and K to L. A ratio which is compounded of two cquul ratios is faid to be duplicate of either of thefe ratios....
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The Elements of Mathematical Analysis, Abridged: For the Use of Students ...

Nicolas Vilant - Algebra - 1798 - 196 pages
...M has to N the fame ratio which A has to D ; then, for ihortnefs' fake, M is faid to have to N the ratio compounded of the ratios of E to F, G to H, and К to L. This definition is the addition of continued unequal ratios. DEFINITION XIII, XIV, XV, XVI,...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...if M has to N the fame ratio which A has to D, then, for fhdrtnefs fake, M is faid 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 alfo the confequents...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1804 - 470 pages
...to D ; A. maj alfo be faid to have to D the ratio compounded of the ratic; which are the fame with the ratios of E to F, G to H, and K to L. In like manner, the fame things being fuppofed, if M IK. the fame ratio which A has to D, then, for...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...the ratio compounded of the ratios which are the same with the ratios of E to F, G to H, and KtoL. In like manner, the same things being supposed, if...compounded of the ratios of E to F, G to H, and K to L. XL If three magnitudes are continual proportionals, the ratio of the first to the third is said to...
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