Elements of Geometry and Trigonometry |
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Page 49
... radii , the greater radius being at the same time less than the sum of the smaller and the distance between the centres , the two circumferences will cut each other . For , to make an intersection possible , the triangle CAD must be ...
... radii , the greater radius being at the same time less than the sum of the smaller and the distance between the centres , the two circumferences will cut each other . For , to make an intersection possible , the triangle CAD must be ...
Page 50
... radii . PROPOSITION XIV . THEOREM . If the distance between the centres of two circles is equal to the difference of their radii , the two circles will touch each other internally . Let C and D be the centres at a dis- tance from each ...
... radii . PROPOSITION XIV . THEOREM . If the distance between the centres of two circles is equal to the difference of their radii , the two circles will touch each other internally . Let C and D be the centres at a dis- tance from each ...
Page 51
... radii will also be equal . Let C and C be the centres of equal circles , and the angle ACB = DCE . First . Since the angles ACB , DCE , are equal , they may be placed upon each other ; and since their sides are equal , the point A will ...
... radii will also be equal . Let C and C be the centres of equal circles , and the angle ACB = DCE . First . Since the angles ACB , DCE , are equal , they may be placed upon each other ; and since their sides are equal , the point A will ...
Page 52
... radii . Let ACB be the greater and ACD the less angle . Let the less angle be placed on the greater . If the propo- sition is not true , the angle ACB will be to the angle ACD as the arc AB is to an arc DIOB greater or less than AD ...
... radii . Let ACB be the greater and ACD the less angle . Let the less angle be placed on the greater . If the propo- sition is not true , the angle ACB will be to the angle ACD as the arc AB is to an arc DIOB greater or less than AD ...
Page 53
... radii , as is implied in all the foregoing propositions . Scholium 1. It appears most natural to measure a quantity by a quantity of the same species ; and upon this principle it would be convenient to refer all angles to the right ...
... radii , as is implied in all the foregoing propositions . Scholium 1. It appears most natural to measure a quantity by a quantity of the same species ; and upon this principle it would be convenient to refer all angles to the right ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex