Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 60
... TANGENT is a straight line which touches the circumference in one point . This point is called , the point of contact , or , the point of tangency . 12. Two circles are tangent to each other , when they touch each other in one point ...
... TANGENT is a straight line which touches the circumference in one point . This point is called , the point of contact , or , the point of tangency . 12. Two circles are tangent to each other , when they touch each other in one point ...
Page 68
... tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it will be perpendicular to the radius drawn to that point . 1o . Let BD be perpendicular to the radius CA , at A then will it ...
... tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it will be perpendicular to the radius drawn to that point . 1o . Let BD be perpendicular to the radius CA , at A then will it ...
Page 69
... tangent ; or , both may be tangents . 1o . Let the secants AB and DE be parallel : then will the intercepted arcs MN and PQ be equal . For , draw the radius . CH perpendicular to the chord MP ; it will also be per- pendicular to NQ ...
... tangent ; or , both may be tangents . 1o . Let the secants AB and DE be parallel : then will the intercepted arcs MN and PQ be equal . For , draw the radius . CH perpendicular to the chord MP ; it will also be per- pendicular to NQ ...
Page 70
From the Works of A. M. Legendre Adrien Marie Legendre. 3o . Let the tangents DE and IL be parallel , and let H and K be their points of contact : then will the in- tercepted arcs HMK and HPK be equal . For , draw the secant AB parallel ...
From the Works of A. M. Legendre Adrien Marie Legendre. 3o . Let the tangents DE and IL be parallel , and let H and K be their points of contact : then will the in- tercepted arcs HMK and HPK be equal . For , draw the secant AB parallel ...
Page 71
... tangent externally . Let C and D be the centres of two circles , and let the distance between the centres be equal to the sum of the radii : then will the circles be tangent externally . For , they will have a point A , on the line CD ...
... tangent externally . Let C and D be the centres of two circles , and let the distance between the centres be equal to the sum of the radii : then will the circles be tangent externally . For , they will have a point A , on the line CD ...
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Common terms and phrases
ABē 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