Elements of Geometry and Trigonometry |
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Page 5
... Book , 68 888 98 BOOK V. Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid Angles , 126 BOOK VII . Polyedrons , 142 BOOK VIII . The three round bodies , 166 BOOK IX . Of Spherical Triangles and ...
... Book , 68 888 98 BOOK V. Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid Angles , 126 BOOK VII . Polyedrons , 142 BOOK VIII . The three round bodies , 166 BOOK IX . Of Spherical Triangles and ...
Page 43
... ( Book I. Prop . VII . * ) ; A or AD AB . Cor . ( Hence the greatest line which can be inscribed in a circle is its diameter . ) PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points ...
... ( Book I. Prop . VII . * ) ; A or AD AB . Cor . ( Hence the greatest line which can be inscribed in a circle is its diameter . ) PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points ...
Page 45
... ( Book I. Prop . XVII . ) . Again , since AD , DB , are equal , CG is a perpendicular erected from the mid- A H dle of AB ; hence every point of this perpendicular must be ... VII . THEOREM . Through three given points not BOOK III . 45.
... ( Book I. Prop . XVII . ) . Again , since AD , DB , are equal , CG is a perpendicular erected from the mid- A H dle of AB ; hence every point of this perpendicular must be ... VII . THEOREM . Through three given points not BOOK III . 45.
Page 46
Adrien Marie Legendre Charles Davies. PROPOSITION VII . THEOREM . Through ... ( Book I. Prop . XX . Cor . 1. ) . But BK , the prolongation of BD , is a ... ( Book I. Prop . XIV . ) ; hence DE , FG , will always meet in some point O. And ...
Adrien Marie Legendre Charles Davies. PROPOSITION VII . THEOREM . Through ... ( Book I. Prop . XX . Cor . 1. ) . But BK , the prolongation of BD , is a ... ( Book I. Prop . XIV . ) ; hence DE , FG , will always meet in some point O. And ...
Page 49
... ( Book I. Prop . VII . ) . And , whenever the triangle CAD can be constructed , it is plain C D B that the circles described from the centres C and D , will cut each other in A and B. E PROPOSITION XIII . THEOREM . If the distance between ...
... ( Book I. Prop . VII . ) . And , whenever the triangle CAD can be constructed , it is plain C D B that the circles described from the centres C and D , will cut each other in A and B. E PROPOSITION XIII . THEOREM . If the distance between ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex