Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" 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
Full view - About this book

Manual of Euclid. Books IV. V. VI.

Euclid - 1859 - 150 pages
...XX)Xoi tari' <cai irpо а rо aura TOV aiiruv jcei \oyov, Ktua ffrt XA//Xiu iarv. 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...
Full view - About this book

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...
Full view - About this book

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,...
Full view - About this book

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....
Full view - About this book

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...
Full view - About this book

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...
Full view - About this book

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...
Full view - About this book

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...
Full view - About this book

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

Robert Potts - 1865 - 528 pages
...7.) Wherefore, of two unequal magnitudes, &c. QED PROPOSITION IX. THEOREM. Magnitudes which have tlie same ratio to the same magnitude are equal to, one another : and those to whieh the tame magnitude has the same ratio ar equal to one another. Let A, B have each of thorn...
Full view - About this book

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 350 pages
...A+B by m, C has a greater ratio to A than it has to A+B (def. 7. 5.). . ...... 15 PROP. IX. THEOR. Magnitudes which have the same ratio to the same magnitude are equal to on* another ; and those to which the same magnitude has the same ratio are equal to one another. If...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF