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PROP. VII. THEOR.
On the same base, and on the same side of it, there cannot be two triangles having their conterminous sides at both extremities of the base, equal to each other.
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PROP. VIII. THEOR.
If two triangles have two sides of the one respectively equal to two sides of the other, and also their bases equal; then the angles contained by their equal sides are also equal.
PROP. XII. PROB.
To draw a straight line perpendicular to a given indefinite straight line from a given point without.
PROP. XIII. THEOR.
When a straight line standing upon another straight line makes angles with it; they are either two right angles, or together equal to two right angles.
Since the angles made at any point on one side of a straight line, are equal to two right angles; it is manifest that the angles at any point in a straight line, on both sides of it, or all the angles round a point, are together equal to four right angles.
If two straight lines, meeting a third straight line, at the same point, and at opposite sides of it, make with it the adjacent angles equal to two right angles; these straight lines lie in one continuous straight line.
PROP. XV. THEOR.
Where two straight lines intersect each other, the vertically opposite angles made by them are equal.
If a side of a triangle is produced, the external angle is greater than either of the internal remote angles.