Books Books
THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the...
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 79
by Dennis M'Curdy - 1846 - 138 pages

## The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Mathematics - 1841 - 140 pages
...... ad = »Т т a Т e Л а/ = »с • _ 9 h ... a A = * У. т PROP. XIII. THEO. If the first has to the second the same ratio which the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the sixth ; the first shall also...

## Algebraical Problems, Producing Simple and Quadratic Equations, with Their ...

Miles Bland - Algebra - 1841 - 458 pages
...three of which are in arithmetic and the last three in harmonic progression ; prove that the first has to the second the same ratio which the third has to the fourth. 18. The sum of three terms of an harmonic progression, «'hose first term is -, is = — ; determine...

## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...number of magnitudes. Therefore, if there be any number, &c. QED PROP. XXIV. THEOR. //' the first has to the second the same ratio which the third has to the fourth; and the fifth to the second the same ratio which the sixth has to the fourth; the first and fifth together...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...A : B : : C : D. Therefore mA7nB, and mE/nF, wherefore, A ; B7E : F (def. 7. 5.). PROP. XIV. THEOR. If the first have to the second the same ratio which the third has to the fourth, and if the first be greater than the third, the i the fourth; if equal, equal; and if less, less. If...

## Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...just as often as the third contains the fourth, or a like part of the fourth, the first is said to have to the second, the same ratio which the third has to the fourth ; or, the ratio of the first to the second is said to be equal to the ratio of the third to the fourth....

## A Treatise on Algebra: Arithmetical algebra

George Peacock - Algebra - 1842 - 426 pages
...observation would apply to the following proposition : " if there be six magnitudes, and if the first has to the second the same ratio which the third has to the fourth, but if the third has to the fourth a greater ratio than the fifth to the sixth : then the first has...

## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - Geometry - 1845 - 382 pages
...are A, C, E together, to B, D, F together : wherefore, if any number, &c. • PROP. XIII. THEOR. — If the first have to the second the same ratio which the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the sixth ; the first will also have...

## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...together. (v. def. 5.) Wherefore, if any number, &c. QED PROPOSITION XIII. THEOREM. Ifthefirst has to the second the same ratio which the third has to the fourth, but the third to the fourth a greater ratio than the Jifth has to the sixth ; thefirst shall also have...