Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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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 . The triangles ACD 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 ...
... radii CD and OG . The triangles ACD 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 ...
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 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 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
ABĀ² ABCD adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed cone consequently convex surface cosec Cosine Cosine D Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area following RULE Formula frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC log cot log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle principle demonstrated prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar slant height solution sphere spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prism triedral angle upper base vertex volume whence write the following