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" IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross 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... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Σελίδα 83
των Dennis M'Curdy - 1846 - 138 σελίδες
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An elementary course of practical mathematics, Μέρος 1

James Elliot - 1860
...greatest and consequently c the least, b + c > a + d. THEOREM X. If there be any Number of Quantities, and as many others, which, taken two and two in Order, have the same Ratios, tlie first shall have to the last ofthefirst Quantities the same Ratio which the first of the...

Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...to the last of the first magnitudes, the same ratio which the first has to the last of the others. ' If there be any number of magnitudes, and as many others, which taken two and two, have the same ratio, they shall have the same ratio by equality. "— EUCLID. CON. Pst. 1, V. DEM....

The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - 1862 - 79 σελίδες
...n : : p : z. PROPOSITION XXIII. " Ex jEQUALI IN PROPORTIONS PERTURBATA," OR " Ex jEQUO PERTURBATO." If there be any number of magnitudes, and as many others, which, taken two and two in a cross order, have the same ratio ; the first shall have to the last of the first magnitudes the same...

The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...than F. Therefore, if there be three, &c. QED PROPOSITION XXII. THEOREM. If there be any number nf 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 has to the...

The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...whatever be the number of magnitudes. Therefore, if there be any number, &c. QED PROP. XXm.— THEOREM. // there be any number of magnitudes, and as many others, which taken two and two in a cross order, have the same ratio ; then the first shall have to the last of the first magnitudes...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 σελίδες
...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...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 σελίδες
...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...

Manual of Euclid: Books IV, V, VI, and Propositions 1-21 of Book XI

Euclid - 1868 - 141 σελίδες
...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...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 σελίδες
...greater than D, by case first ; PROPOSITION XXII. THEOREM. If there be any number of magnitudes, and a3 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 has to the...

The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 285 σελίδες
...true whatever be the number of equal ratios and whatever be the magnitudes considered. PROPOSITION 12. If there be any number of magnitudes, and as many...which taken two and two in order have the same ratio, the first shall have to the last of the first set of magnitudes the same ratio as the first has to...




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