Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 65
... passes through two of these points , will pass through the third , and be perpendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in the same straight line , one circumference may be made to pass , and ...
... passes through two of these points , will pass through the third , and be perpendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in the same straight line , one circumference may be made to pass , and ...
Page 66
... pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in more than two points ; for , if they could intersect in three points , there would be two circumferences . passing through ...
... pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in more than two points ; for , if they could intersect in three points , there would be two circumferences . passing through ...
Page 72
... pass through a common point of that line , are tangent to each other at that point . And if a straight line be drawn tangent to one of the circles at their common point , it will be tangent to them all at that point . Scholium . From ...
... pass through a common point of that line , are tangent to each other at that point . And if a straight line be drawn tangent to one of the circles at their common point , it will be tangent to them all at that point . Scholium . From ...
Page 77
... without the angle . 1o . Let EAD be an inscribed an- gle , one of whose sides AE passes through the centre : then will it be measured by half of the arc DE E For , draw the radius CD . The external angle BOOK III . 77.
... without the angle . 1o . Let EAD be an inscribed an- gle , one of whose sides AE passes through the centre : then will it be measured by half of the arc DE E For , draw the radius CD . The external angle BOOK III . 77.
Page 89
... pass a circumference through any three points not in a straight line . If the points are vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle ...
... pass a circumference through any three points not in a straight line . If the points are vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following