First Practical Lines of Geometrical Drawing ...

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Williams and Norgate, 1865 - Geometrical drawing - 169 pages

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Page 5 - 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 equal to two right angles.
Page 6 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.
Page 5 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Page 5 - If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite angle on the same side; and also the two interior angles on the same side together equal to two right angles.
Page 6 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Page 57 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 57 - A prism is a solid figure contained by plane figures, of which two that are opposite are equal, similar, and parallel to one another ; and the others parallelograms. XIV. A sphere is a solid figure described by the revolution of a semicircle about its diameter, which remains unmoved.
Page 58 - The base of .a cone is the circle described by that side containing the right angle which revolves.
Page 6 - In equal circles, angles, whether at the centres or circumferences, have the same ratio which the circumferences on which they stand have to one another ; so also have the sectors.
Page 5 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.

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