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A B and CD A B is equal A C B A C equal adjacent angles alternate angle angle A B C angle A C D angle ABC angle B A C angle BAC angle BCD angle contained angle EDF angles B G H angles equal Axiom 2a Axiom 9 base B C base E F bisected coincide conclusion Construction enunciations of Euc equal angles equal to A C equal to angle equilateral triangle EXERCISES.—I exterior angle given line given point given straight line Given.—The triangle ABC Given.—The two triangles greater than angle included angle interior opposite angle isosceles triangle Join Let us suppose line CD major premiss parallelogram A B CD Particular Enunciation PROBLEM Euclid produced proposition prove that angle remaining angle Repeat.—The enunciations Required.—To prove right angles side A C sides equal square straight line A B THEOREM Euclid
Page 83 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 66 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Page 34 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Page 94 - 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.
Page 88 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Page 104 - If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Page 142 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Page 51 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.