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Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
The Elements of Euclid: viz. the first six books, together with the eleventh ... - Page 11
by Robert Simson - 1835 - 513 pages

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

Euclides - 1842 - 316 pages
...if two angles, &c. QED COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. UPON the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated in one extremity of the base equal to one another, and likewise...

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

John Playfair - Euclid's Elements - 1844 - 338 pages
...then, upon the same base EF, and upon the same side of it, there can be two triangles EDF, EGF.that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity ; but this is impossible (7. 1.); therefore, if the base...

## Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volume 2

Church schools - 1844 - 456 pages
...of another, of which the solidity is three times that of the former ; 1841. GEOMETRY. 1 . Prove that upon the same base, and on the same side of it, there cannot be two triangles which have the sides terminated in one extremity of the base equal to one another, and likewise those...

## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...different situation as EG, FG, then upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated...extremity of the base equal to one another, and likewise their sides terminated in the other extremity: but this is impossiblef; therefore, * 7. i. if the base...

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

Euclides - 1845 - 546 pages
...as EG, FG: Then, upon the same base, and upon the same side of it, there can be two triangles which have their sides which are terminated in one extremity...the base equal to one another, and likewise those sides which are terminated in the other extremity; but this is impossible. (i. 7.) Therefore, if the...

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

Euclides, James Thomson - Geometry - 1845 - 382 pages
...FG ; then, upon the same base EF, and upon the same side of it, there would be two triangles having their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity; but (I. 7) this is impossible: therefore, if the base...

## Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J. Butler Williams - Geodesy - 1846 - 368 pages
...the triangle possesses this property is evident from the theorem, (Euclid, 7, I.) which proves that, "Upon the same base, and on the same side of it, there...triangles that have their sides which are terminated at one extremity of the base equal to one another, and likewise those which are terminated in the other...

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

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...FG ; then, upon the same base EF, and upon the same side of it, there can he two triangles EDF, EGF, that have their sides which are terminated in one...extremity of the base equal to one another, and likewise their sides terminated in the other extremity ; but this is impossible (7. 1.) ; therefore, if the...