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

J. Ernst, 1854 - 335 СЕКъДЕР
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### пЕЯИЕВЭЛЕМА

 General Principles 9 Theorems in reference to right lines and anglos 15 Proportion 42 BOOK III 61 BOOK IV 79 BOOK V 90 Exercises in geometrical investigation 100 BOOK VI 109
 PLANE TRIGONOMETRY 136 On the computation of sines and tangents 144 Application of Plane Trigonometry 156 Oblique angled Trigonometry 163 SPHERICAL TRIGONOMETRY 176 Napiers circular parts 186 CONIC SECTIONS 226 The Parabola 247

 BOOK VII 118
 The Hyperbola 263

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 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.
сЕКъДА 13 - AXIOMS. 1. Things which are equal to the same thing are equal to one another.
сЕКъДА 24 - If two triangles have two sides of the one equal to two sides of the...
сЕКъДА 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.
сЕКъДА 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.
сЕКъДА 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.
сЕКъДА 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.
сЕКъДА 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.
сЕКъДА 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.
сЕКъДА 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