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 . an 4. An ARC is any part of a circumference . 5. A CHORD is a straight line joining the extremities of arc . Any chord belongs to two ...
... radii of the same circle are equal . All diameters are also equal , and each is double the radius . an 4. An ARC is any part of a circumference . 5. A CHORD is a straight line joining the extremities of 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 párts : 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 párts : 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 D 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 D 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- ternally ...
... 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- ternally ...
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Common terms and phrases
AB˛ ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following