The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and Exercises
Macmillan, 1867 - Euclid's Elements - 400 pages
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ABCD angle ABC angle ACB angle BAC Axiom base BC is equal bisected Book centre circle ABC circumference common Construction contained Corollary Definition demonstration described diameter divided double draw drawn equal equal angles equiangular equilateral equimultiples Euclid extremities fall figure four fourth given circle given point given straight line greater half Hypothesis inscribed intersect join less Let ABC magnitudes manner meet multiple namely parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals Q.E.D. PROPOSITION quadrilateral ratio reason rectangle rectangle contained rectilineal figure remaining right angles segment shew shewn sides similar square square on AC straight line &c suppose Take taken THEOREM third triangle ABC Wherefore whole
Page 286 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 30 - 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 34 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Page 37 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Page 12 - 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 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Page 220 - If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Page 354 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
Page 104 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Page 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.