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MAGNITUDES which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another.
The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ... - Page 16
by Thomas Gaskin - 1847 - 263 pages

## Manual of Euclid. Books IV. V. VI.

Euclid - 1859 - 150 pages
...áXX»)Xoiç tari' <cai irpоç а rо aura TOV aiiruv íjcei \oyov, íKtu»a ïffrt «XA//Xiuï iarív. Magnitudes which have the same ratio to the same magnitude are equal to one another: and magnitudes to which the same magnitude has the same ratio are equal to one another. PART L Statement...

## The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...> C i A. PROPOSITION IX. THEOBEM. — If magnitudes have the same ratio to the same magnitude, they are equal to one" another : and those to which the...magnitude has the same ratio are equal to one another. Let A, B have each of them the same ratio to C ; then A shall be equal to B. DEMONSTRATION. For, if...

## The Collected Works of Dugald Stewart: Dissertation : exhibiting the ...

Dugald Stewart - 1860 - 390 pages
...the Fates dispense Pomp, power, and everything but sense. P. 377, n. F, n. 1. — Magnitudes having the same ratio to the same magnitude are equal to one another. — Euclid. P. 378, n. G, n. 2. — Those alone that have been mentioned are properly called quantities,...

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

Robert Potts - Geometry, Plane - 1860 - 380 pages
...it has to AB. (v. def. 7.1 ' Wherefore, of two unequal magnitudes, &c. QED PROPOSITION IX. THEOREM. Magnitudes which have the same ratio to the same magnitude are equal lo tme another : and those to which the same magnitude has the same ratio an tqual to one another....

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

Euclides - 1861 - 464 pages
...10. Hence 3 (5+4) > (3—1) 10. bnt3 X 5 > (3—1) 10, Л 5 + 4 : 10 > 5 : 10. PROP. IX.— THEOn. Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. Cox. Pst. 1, V. DRM. 8, V.— Def. 7, V.— Dei. 5, V. E. l Hyp. 1. ,, 2Cone. Let A : C = B : C ; or...

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

George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...ba greater ratio than с has to a. Therefore, of unequal magnitudes, &c. — (¿. ED PROPOSITION IX. Magnitudes which have the same ratio to the same magnitude,...magnitude has the same ratio, are equal to one another. a, b, c. Because a : с : : b : c, .. fab therefore - = - j с с and therefore a = b. Secondly, let...

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

Euclides - 1864 - 448 pages
...than it has to AB. (v. def. 7.) Wherefore, of two unequal magnitudes, &c. QED PROPOSITION IX. THEOREM. Magnitudes which have the same ratio to the same magnitude are equal to one another : and those to which tlut same magnitude has the same ratio arc equal to one another. Let, A, B have each of them the same...

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

Euclides - 1865 - 402 pages
...than it has to AB. (T. def. 7.) Wherefore, of unequal magnitudes, &c Q, E. T>. PROP. EX.— THEOREM. Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. (Reference — v. def. 5.) Let A and B have each of them the same ratio to C. Then A shall be equal...