Elements of Geometry and Trigonometry |
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Page 27
... remaining sides of the triangle . Let be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then will the sum of BO and 00 be less than the the sum of the sides BA and AC ...
... remaining sides of the triangle . Let be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then will the sum of BO and 00 be less than the the sum of the sides BA and AC ...
Page 61
... remaining common ; then will they coincide ; otherwise there would be some points in either one or the other of the curves unequally distant from the centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its ...
... remaining common ; then will they coincide ; otherwise there would be some points in either one or the other of the curves unequally distant from the centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its ...
Page 110
... remaining terms are proportional ( B. II . , P. IV . ) , hence , AD : DB : :: AE : EC ; which was to be proved . Cor . 1. We have , by composition ( B. II . , P. VI . ) , AD + DB : AD :: AE EC : AE ; + or , AB : AD :: AC : AE ; 110 ...
... remaining terms are proportional ( B. II . , P. IV . ) , hence , AD : DB : :: AE : EC ; which was to be proved . Cor . 1. We have , by composition ( B. II . , P. VI . ) , AD + DB : AD :: AE EC : AE ; + or , AB : AD :: AC : AE ; 110 ...
Page 127
... remaining segment of the second is to the remaining segment of the first . For , draw CA and BD . Then will the angles ODB and OAC be equal , because each is measured by half of the arc CB ( B. III . , P. XVIII . ) . The angles OBD and ...
... remaining segment of the second is to the remaining segment of the first . For , draw CA and BD . Then will the angles ODB and OAC be equal , because each is measured by half of the arc CB ( B. III . , P. XVIII . ) . The angles OBD and ...
Page 203
... remaining pyramid may be regarded as having the triangle FfH for its base , and the point g for its vertex . From g , draw gK parallel to fF , and draw also KH and Kf . Then will the pyramids K - FfH and g - FfH , be equal ; for they ...
... remaining pyramid may be regarded as having the triangle FfH for its base , and the point g for its vertex . From g , draw gK parallel to fF , and draw also KH and Kf . Then will the pyramids K - FfH and g - FfH , be equal ; for they ...
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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
AB² ABCD AC² 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...