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Equal triangles on the same base, and on the same side of it, are between the same parallels.
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Σελίδα 47
των Euclid, Rev. John Allen - 1822 - 494 σελίδες
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## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 σελίδες
...equal to the triangle CDE: and they are on the same base DE; but equal triangles on the same base, and on the same side of it, are between the same parallels ;* * 39. i therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROP. III. THEOR....

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

John Playfair - 1844 - 317 σελίδες
...ABC is equal to the triangle DEF. PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Join AD ; AD is parallel to BC ; for, if it is not, through the point A draw (31. 1.) AE parallel to BC, and...

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

Euclid, James Thomson - 1845 - 352 σελίδες
...the straight line joining their vertices is parallel to the base. Let the equal triangles ABC, DBC be on the same base BC and on the same side of it ; join AD : AD is parallel to BC. For, if it be not, through A draw (I. 31 )AE parallel to BC, and...

## A system of practical mathematics; being no.xvi. of a new series of school-books

...passing through A, except AD, which therefore is || to BF. QED Cor. 1. Equal triangles on the same base and on the same side of it, are between the same parallels. Cor. 2. In the same manner it might be shown that equal triangles between the same parallels are upon...

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

Euclides - 1845
...proof depends on Theorem 66, p. 303. 58. Let ABC, EBC, DBC (DB being joined) be three equal triangles on the same base BC and on the same side of it (fig. Euc. i. 41). Join AD, DE. Then AD is parallel to BC, and DE .is parallel to BC. 59. The diameters...

## The Elements of Geometry, Symbolically Arranged

...same base, and upon the same side of it, are between the same parallels. Let the = <£^s ABC, DEC, be on the same base BC, and on the same side of it ; then the will be between the same ||s. A B c For if not, Prop. so. draw AE || BC, and join EC. H,...

## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 σελίδες
...(4)p.36; (c) p. 34 ; (d) ox. 7. 89 Th. Equal triangles (ABC, DBC), upon the same base (BC), and upon the same side of it, are between the same parallels. Join AD; — AL> is parallel to BC: for if not, A through the point A draw AE parallel to BC (a), and join CE....

## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...triangles upon S,c, QED PROP. XL. THEOR. Equal triangles upon equal bases, in the same straight line, and on the same side of it, are between the same parallels. Let the equal triangles, ABC, DEF, be upon equal bases BC, EF, in the same straight line BF, and on...

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

John Playfair - 1846 - 317 σελίδες
...ABC is equal to the triangle DEF. PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Join AD ; AD is parallel to BC ; for, if it is not, through the point A draw (31. 1.) AE parallel to BC, and...