# Elements of Geometry, Plane and Spherical Trigonometry and Conic Sections

J. Ernst, 1854 - Conic sections - 335 pages
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### Contents

 BOOK VII 118 Elementary principles 136 On the computation of sines and tangents 144
 The Parabola 247 The Hyperbola 263

### Popular passages

Page 62 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
Page 13 - AXIOMS. 1. Things which are equal to the same thing are equal to one another.
Page 24 - If two triangles have two sides of the one equal to two sides of the...
Page 149 - If a perpendicular be let fall from any angle of a triangle to its opposite side or base, this base is to the sum of the other two sides, as the difference of the sides is to the difference of the segments of the base.
Page 48 - In place of adding unity, subtract it, and we shall find that a : a — b :: c : c — d. or a : b — a :: c : d — c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference.
Page 110 - If a straight line stand at right angles to each of two straight lines in the point of their intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which they are.
Page 21 - 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 20 - If a side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles.
Page 47 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 173 - I measured 312 yards in a right line by the side of the river, and then found that the two angles, one at each end of this line, subtended by the other end and the house, were 31° 15