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 73
... 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 the circles are tangent externally . For , they have at least one point , A , on the line ...
... 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 the circles are tangent externally . For , they have at least one point , A , on the line ...
Page 74
... tangent to the other internally ; which was to be proved . Cor . 1. If two circles are tangent , either externally or internally , the point of contact is on the straight line drawn through their centres . Cor . 2. All circles whose ...
... tangent to the other internally ; which was to be proved . Cor . 1. If two circles are tangent , either externally or internally , the point of contact is on the straight line drawn through their centres . Cor . 2. All circles whose ...
Page 75
... tangent , externally : 3 ° . When this distance is less than the sum , and greater than the difference of the radii , they intersect each other : 4 ° . When this distance is equal to the difference of their radii , one is tangent to the ...
... tangent , externally : 3 ° . When this distance is less than the sum , and greater than the difference of the radii , they intersect each other : 4 ° . When this distance is equal to the difference of their radii , one is tangent to the ...
Page 83
... tangent and a chord meeting it at the point of contact , is measured by half the included arc . Let BE be tangent to the circle AMC , and let AC be a chord drawn from the point of contact A : then BAC is measured by half of the arc AMC ...
... tangent and a chord meeting it at the point of contact , is measured by half the included arc . Let BE be tangent to the circle AMC , and let AC be a chord drawn from the point of contact A : then BAC is measured by half of the arc AMC ...
Page 90
... tangent to DG , the angle opposite DE is a right angle , and there is but one solution . If the side opposite the given angle is shorter than the distance from E to DG , there is no solution . PROBLEM XII . Given , two adjacent sides of ...
... tangent to DG , the angle opposite DE is a right angle , and there is but one solution . If the side opposite the given angle is shorter than the distance from E to DG , there is no solution . PROBLEM XII . Given , two adjacent sides of ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence