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" 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
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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...
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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...
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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,...
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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...
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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...
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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...
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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...
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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...
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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...
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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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