Elements of Geometry and Trigonometry |
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Page vii
... Half Arcs , Additional Formulas , Method of Computing a Table of Natural Sines , SPHERICAL TRIGONOMETRY . PAGE 55 57-59 60-62 63 64-66 67 68-70 71 Spherical Trigonometry Defined , 73 General Principles , 73 Formulas for Right - angled ...
... Half Arcs , Additional Formulas , Method of Computing a Table of Natural Sines , SPHERICAL TRIGONOMETRY . PAGE 55 57-59 60-62 63 64-66 67 68-70 71 Spherical Trigonometry Defined , 73 General Principles , 73 Formulas for Right - angled ...
Page 34
... half of AF , is shorter than AC , the half of ACF ; which was to be proved . 2o . 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 ...
... half of AF , is shorter than AC , the half of ACF ; which was to be proved . 2o . 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 ...
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 two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included between its sides . There may be three cases ...
... half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included between its sides . There may be three cases ...
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 of ...
... 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 of ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
ABē ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane 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.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...