Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, and Copious Notes and Illustrations

J. Ballantyne and Company, 1811 - 500 pages

Popular passages

Page 105 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 26 - 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 97 - In like manner, a figure is said to be described about another figure, when all the sides of the circumscribed figure pass through the angular points of the figure about which it is described, each through each. III. A rectilineal figure is said to be inscribed in a circle, when all the angles of the inscribed figure are upon the circumference of the circle.
Page 421 - The first of four magnitudes, is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 403 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Page 125 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Page 9 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 80 - The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same part of the circumference.
Page 34 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 358 - In any triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.