Elements of Geometry and Trigonometry |
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Page 57
Adrien Marie Legendre Charles Davies. Let BE be the tangent , and AC the chord . From A , the point of contact , draw the diameter AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by o half the semicircumference AMD ...
Adrien Marie Legendre Charles Davies. Let BE be the tangent , and AC the chord . From A , the point of contact , draw the diameter AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by o half the semicircumference AMD ...
Page 62
... tangent to the line DG , the triangle would be right angled , and there would be but one solution . The problem would be impossible in all cases , if the side B were less than the perpen- dicular let fall from E on the line DF . PROBLEM ...
... tangent to the line DG , the triangle would be right angled , and there would be but one solution . The problem would be impossible in all cases , if the side B were less than the perpen- dicular let fall from E on the line DF . PROBLEM ...
Page 64
... tangent to a given circle . If the given point A lies in the circum- D ference , draw the radius CA , and erect AD perpendicular to it : AD will be the tangent required ( Prop . IX . ) . If the point A lies without the circle , join A ...
... tangent to a given circle . If the given point A lies in the circum- D ference , draw the radius CA , and erect AD perpendicular to it : AD will be the tangent required ( Prop . IX . ) . If the point A lies without the circle , join A ...
Page 65
... tangent ; and the same thing is true of the sides BC , AC . Scholium . The three lines which bisect the angles of a tri- angle meet in the same point . PROBLEM XVI . On a given straight line to describe a segment that shall contain 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 meet in the same point . PROBLEM XVI . On a given straight line to describe a segment that shall contain a ...
Page 95
... tangent and a secant be drawn , the tangent will be a mean proportional between the secant and its external segment . From the point O , let the tangent OA , and the secant OC be be drawn ; then will ........ OCOA OA : OD , or OA2 = OC ...
... tangent and a secant be drawn , the tangent will be a mean proportional between the secant and its external segment . From the point O , let the tangent OA , and the secant OC be be drawn ; then will ........ OCOA OA : OD , or OA2 = OC ...
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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