Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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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 . 1 ° . 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 . 1 ° . 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 ( B. I. ...
... 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 ( B. I. ...
Page 70
... 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 to DE ; then , from what has just been shown , we shall have HM ...
... 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 to DE ; then , from what has just been shown , we shall have HM ...
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
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence