Elements of Geometry and Trigonometry |
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Page 7
... Half Arcs , Additiona . Formulas , ..... Method of Computing a Table of Natural Sines ,. SPHERICAL Spherical Trigonometry Defined , General Principles , .... TRIGONOMETRY . Formulas for Right - angled Triangles , Napier's Circular Parts ...
... Half Arcs , Additiona . Formulas , ..... Method of Computing a Table of Natural Sines ,. SPHERICAL Spherical Trigonometry Defined , General Principles , .... TRIGONOMETRY . Formulas for Right - angled Triangles , Napier's Circular Parts ...
Page 34
... half of AF , is shorter than AC , the half of ACF ; which was to be proved . 2. In the triangles ABC and ABE , we have the side BC equal to BE , by hypothesis , the side AB com mon , and the included angles ABC and ABE equal , because ...
... half of AF , is shorter than AC , the half of ACF ; which was to be proved . 2. In the triangles ABC and ABE , we have the side BC equal to BE , by hypothesis , the side AB com mon , and the included angles ABC and ABE equal , because ...
Page 35
... half of ADF , is greater than AC , the half of ACF ; which was to be proved . Cor . 1. The perpendicular is the shortest distance from a point to a line . Cor . 2. From a given point to a given straight line , only two equal straight ...
... half of ADF , is greater than AC , the half of ACF ; which was to be proved . Cor . 1. The perpendicular is the shortest distance from a point to a line . Cor . 2. From a given point to a given straight line , only two equal straight ...
Page 77
... half or PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included between its sides . There may be three cases : the centre of the circle may lie on one of the sides of the angle ; it may lie within the ...
... half or PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included between its sides . There may be three cases : the centre of the circle may lie on one of the sides of the angle ; it may lie within the ...
Page 78
... half of the arc BED . For , draw the diameter AE . Then , from what has just been proved , the angle DAE is measured by half of DE , and the angle EAB by half of EB : hence , BAD , which is the sum of EAB and DAE , is measured by half ...
... half of the arc BED . For , draw the diameter AE . Then , from what has just been proved , the angle DAE is measured by half of DE , and the angle EAB by half of EB : hence , BAD , which is the sum of EAB and DAE , is measured by half ...
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Common terms and phrases
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence