The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance with the Reports of the Cambridge Board of Mathematical Studies, and the Oxford Board of the Faculty of Natural Science, Book 1

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Longmans, Green, 1894 - Geometry - 515 pages
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Page 97 - Let it be granted :— 1. That a Straight Line may be drawn from any one point to any other point. 2. That a Terminated Straight Line may be produced to any length in a straight line. 3. And that a Circle may be described from any centre, at any distance from that centre.
Page 60 - PROPOSITION 32. THEOREM. 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. Let ABC be aA having one side BC produced to D; then ext. L
Page 130 - PROPOSITION 4. THEOREM. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts. Let AB be divided in C; then sq. on AB=sqs. on AC, CB, with twice rect. AC,
Page 26 - DEF. 10.—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 said to be perpendicular, or at right angles, to it. The symbol for
Page 26 - PROPOSITION 11. PROBLEM. To draw a straight line at right angles to a given straight line from a given point in the same. Let AB be the given straight line, and C the given point in it; it is required to draw from the point Ca straight line at right angles to AB. AD CEB
Page 202 - segment of a circle is the figure contained by a straight line and the circumference it cuts off. PROPOSITION 21. THEOREM. The angles in the same segment of a circle are equal to one another. Let ABCD be a 0, and BAD, BED LS in the same segment BAED; then
Page 217 - join CF.) PROPOSITION 32. THEOREM. . If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle shall be equal to the angles in the alternate segments. Let ABCD be a
Page 42 - PROPOSITION 21. THEOREM. If from the ends of a 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. From the ends B, C of the side BC of the A
Page 136 - PROPOSITION 7. If a straight line is divided into two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and that part together with the square on the other part. Let AB be divided at C. Then the sqs. on AB,
Page 407 - figuris ab Euclide in Elementorum libro VI. allatam' (1668) :— Ex. 740.—The equilateral triangle described on the hypotenuse of a right.angled triangle is equal to the sum of the equilateral triangles described upon the other two sides. Let BLC, CM A, ANB be the equilateral

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