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 Books Bücher If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes, the same ratio which the first of the others has to the last. NB This is usually... Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Seite 217
von Euclides - 1861
Vollansicht - Über dieses Buch An elementary course of practical mathematics, Teil 1

James Elliot - 1860
...cequali, ex atquali distantta, or by direct equality. THEOREM XI. If there be any Number of Quantities, and as many others, which, taken two and two in a cross Order, have the same Ratios, the first shall have to the last ofthefirst Quantities, the same Ratio which the first of the...
Vollansicht - Über dieses Buch The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - 1862 - 79 Seiten
...rightly said that 3 cwt. has any ratio to £1, or 6 cwt. to £8. PROP. XX. — It is further true, that if there be any number of magnitudes and as many others, which taken two and two in order, have the same ratio; if the first be greater than the last of the first magnitudes, the first...
Vollansicht - Über dieses Buch The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...is to D as E is to H; EFOII I Because A, B and C are three magnitudes, and F, G and H other three, which, taken two and two in a cross order, have the same ratio. Therefore, by the first case, A is to C ~ l and so on, whatever be the number of magnitudes. ! Therefore,...
Vollansicht - Über dieses Buch The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...so is D to F. (v. def. 0.) Next, let there be four magnitudes A, B, C, D, and other four E, F, G, H, which taken two and two in a cross order have the same ratio, viz. A to B, as G to H; B to C, as Fto G; and Cto D, as E to F. Then A shall be to D, as E to H. Because...
Vollansicht - Über dieses Buch The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...third, the fourth shall be greater than the sixth ; and if equal, equal ; and if less, less. Prop. 22. If there be any number of magnitudes, and as many others, which taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes, the same ra'io...
Vollansicht - Über dieses Buch Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1855 - 317 Seiten
...magnitudes. PROP. XXIII THEOR. If there be any number of magnitudes, and as many others, which, taken (to* and two, in a cross order, have the same ratio ; the. first will have to the last of the first magnitudes the same ratio which the first of the others has to the...
Vollansicht - Über dieses Buch The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 Seiten
...whatever be the number of magnitudes. Wherefore, if there be any number &c. QED PROPOSITION 23. THEOREM. If there be any number of magnitudes, and as many others, which have the same ratio, taken two and two in a cross order, the first shall have to the last of the first...
Vollansicht - Über dieses Buch The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 Seiten
...whatever be the number of magnitudes. Wherefore, if there be any number &c. QED PROPOSITION 23. THEOREM. If there be any number of magnitudes, and as many others, which have the same ratio, taken two and two in a cross order, the first shall have to the last of the first...
Vollansicht - Über dieses Buch Manual of Euclid: Books IV, V, VI, and Propositions 1-21 of Book XI

Euclid - 1868 - 141 Seiten
...то irX^боc, avvSvo \afißavofiiva Kai ¿v тф avry Xóy^* кaí Siîaov iv Tif avru \oyil> iarai. If there be any number of magnitudes, and as many others, which, taken two and two, have the same ratio; they shall be in the same ratio by equality. Statement. — Let there be three...
Vollansicht - Über dieses Buch Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 Seiten
...is D to F. (v. def. 5.) Next, let there be four magnitudes A, B, C, Z), and other four E, F, G, H, which taken two and two in a cross order have the same ratio, viz. A to B, as G to H; Bio C, as Fto G; and Cto D, as .Eto F. Then A shall be to D, as E to H. by...
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