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AC is equal angle ABC angle ACB angle BAC angle BCD angle contained angle EDF angle equal base base BC BC is greater bisects the angle centre circle circumference coincide common constr Construction Demonstration describe the circle distance draw a straight equal angles equal to CD equidistant equilateral triangle Euclid exterior angle extremities fall figure Find a point four given point given straight line greater Hence impossible intersect isosceles triangle join length less Let ABC likewise line BC meet middle point namely opposite sides perpendicular placed plane position PROBLEM produced proof prop PROPOSITION Prove Q.E.D. Exercises quadrilateral remainder respects right angles shew shewn side AC sides equal stands taken terminated THEOREM thing triangle ABC triangle DEF triangles be equal unequal whole
Page 39 - IF two triangles have two sides of the one equal to two sides of the...
Page 4 - 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 7 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 7 - Notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.
Page 36 - 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.
Page 37 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Page 18 - 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 29 - 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. At the point B in the straight line AB, let the two straight lines...