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

## Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...proposition may be easily extended to any number of magnitudes. QED PROPOSITION XXII. (Eucl. v. 24.) If the first have to the second the same ratio which the third has to the fourth, and the fifth have to the second the same ratio which the sixth has to the fourth, then the first and...

## Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...the sign + , the other has the sign — .] PROP. A. If the first have to the second the same ratio as the third has to the fourth : then, if the first be greater than the second, the third is greater than the fourth ; if equal, equal ; if less, less. [If the first (a) have...

## Euclid, book v. proved algebraically, so far as it relates to commensurable ...

Charles Lutwidge Dodgson - 1874 - 96 pages
...the sign + , the other has the sign — .] PROP. A. If the first have to the second the same ratio as the third has to the fourth : then, if the first be greater than the second, the third is greater than the fourth ; if equal, equal ; if less, less. [If the first (a) have...

## The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...together (V. Def. 5). Wherefore, if any number, &c. Q ED PROPOSITION 13. — Theorem. 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...

## Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin SMITH - 1876 - 382 pages
...proposition may be easily extended to any number of magnitudes. 0. ED PROPOSITION XXII. (Eucl. v. 24.) // the first have to the second the same ratio which the third has to the fourth, and the fifth have to the second the same ratio which the sixth has to the fourth, then the first and...

## Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...II. Ratios that are equal to the same ratio are equal to one another. .. .. 191 13. 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 to the sixth, the first shall have to the...

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

Robert Potts - Geometry - 1876 - 446 pages
...magnitudes. Therefore, if there be any number, &c. QED PROPOSITION XXIV. THEOREM. If the first hat 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...

## The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...whatever be the number of magnitudes. Wherefore, ifthere^be any number &c. QED PROPOSITION 24. THEOREM. If the first have to the second the same ratio which the third has to the fourth, and the ffth have to the second the same ratio which the sixth has to the fourth, then the first and...