Elements of Geometry and Trigonometry |
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Page 59
... radii of the same circle are equal . are also equal , and each is double the radius . 4. An ARC is any part of a circumference . All diameters 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 . are also equal , and each is double the radius . 4. An ARC is any part of a circumference . All diameters 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 A B common ; the triangles are , therefore , 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 A B common ; the triangles are , therefore , 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 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 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
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence