Elements of Geometry and Trigonometry |
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Page 63
... serves for making a circum- E ference pass through three given points A , B , C ; and also for describing a circumference , in which , a given triangle ABC shall be inscribed . PROBLEM XIV . Through a given point , to draw BOOK III . 63.
... serves for making a circum- E ference pass through three given points A , B , C ; and also for describing a circumference , in which , a given triangle ABC shall be inscribed . PROBLEM XIV . Through a given point , to draw BOOK III . 63.
Page 64
... inscribed in a semicircle is a right . angle ( Prop . XVIII . Cor . 2. ) ; therefore AB is a perpendicular at the ... inscribe a circle in a given triangle . Let ABC be the given triangle . Bisect the angles A and B , by the lines AO and ...
... inscribed in a semicircle is a right . angle ( Prop . XVIII . Cor . 2. ) ; therefore AB is a perpendicular at the ... inscribe a circle in a given triangle . Let ABC be the given triangle . Bisect the angles A and B , by the lines AO and ...
Page 65
... inscribed in the triangle ABC .; for the side AB , being perpendicular to the radius at its extremity , is a tangent ; and the same thing is true of the sides BC , AC . Scholium . The three lines which bisect the angles of a tri- angle ...
... inscribed in the triangle ABC .; for the side AB , being perpendicular to the radius at its extremity , is a tangent ; and the same thing is true of the sides BC , AC . Scholium . The three lines which bisect the angles of a tri- angle ...
Page 94
... inscribed in the same segment ( Book III . Prop . XVIII . Cor . 1. ) ; for the same reason the angle C - B ; the triangles are there- fore similar , and the homologous sides give the proportion AO : DO :: CO : OB . A B Cor . Therefore ...
... inscribed in the same segment ( Book III . Prop . XVIII . Cor . 1. ) ; for the same reason the angle C - B ; the triangles are there- fore similar , and the homologous sides give the proportion AO : DO :: CO : OB . A B Cor . Therefore ...
Page 96
... inscribed circle . For , the triangles AOB , BOC , AOC , which have a common vertex at O , have for their com- mon altitude the radius of the inscribed circle ; hence the sum of these triangles will be equal to the sum of the bases AB ...
... inscribed circle . For , the triangles AOB , BOC , AOC , which have a common vertex at O , have for their com- mon altitude the radius of the inscribed circle ; hence the sum of these triangles will be equal to the sum of the bases AB ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex