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 59
... radii of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any part of a circumference . 5. A CHORD is a straight line joining the extremities of an arc . Any chord belongs to two ...
... radii of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any part of a circumference . 5. A CHORD is a straight line joining the extremities of an arc . Any chord belongs to two ...
Page 63
... radii CD and OG . and EOG have all the sides of the one equal to the cor- responding sides of the other ; they are , therefore , equal in all their parts : hence , the angle ACD is equal to EOG . If , now , the sector ACD be placed upon ...
... radii CD and OG . and EOG have all the sides of the one equal to the cor- responding sides of the other ; they are , therefore , equal in all their parts : hence , the angle ACD is equal to EOG . If , now , the sector ACD be placed upon ...
Page 64
... radii CA and CB . Then , the right - angled triangles CDA and CDB will have the hypothenuse CA equal to CB , and the side CD common ; the triangles are , therefore , A G B equal in all their parts : hence , AD is equal to DB . Again ...
... radii CA and CB . Then , the right - angled triangles CDA and CDB will have the hypothenuse CA equal to CB , and the side CD common ; the triangles are , therefore , A G B equal in all their parts : hence , AD is equal to DB . Again ...
Page 71
... radii . Let the circumferences , whose centres are C and D , intersect at A : then will CD be less than the sum , and greater than the difference of the radii of the two circles . For , draw AC and AD , forming the triangle ACD . Then ...
... radii . Let the circumferences , whose centres are C and D , intersect at A : then will CD be less than the sum , and greater than the difference of the radii of the two circles . For , draw AC and AD , forming the triangle ACD . Then ...
Page 72
... radii , one will be tangent to the other internally . Let C and D be the centres of two circles , and let the distance between these centres be equal to the difference of the radii : then will the one be tangent to the other in ...
... radii , one will be tangent to the other internally . Let C and D be the centres of two circles , and let the distance between these centres be equal to the difference of the radii : then will the one be tangent to the other in ...
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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