Elements of Geometry and Trigonometry |
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Page 46
... described from the centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line : we ...
... described from the centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line : we ...
Page 49
... . ) . And , whenever the triangle CAD can be constructed , it is plain D that the circles described from the centres C and D , will cut each other in A and B. 7 E PROPOSITION XIII . THEOREM . If the distance between the BOOK III . 49.
... . ) . And , whenever the triangle CAD can be constructed , it is plain D that the circles described from the centres C and D , will cut each other in A and B. 7 E PROPOSITION XIII . THEOREM . If the distance between the BOOK III . 49.
Page 52
... described from the vertices of the angles as centres , with equal 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 ...
... described from the vertices of the angles as centres , with equal 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 ...
Page 53
... described with equal 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 ...
... described with equal 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 ...
Page 62
... described from the centre E , with the radius EF - B , will cut the side DF in two points F and G , lying on the same side of D : hence there will be two triangles DEF , DEG , either of which will satisfy the conditions of the pro- blem ...
... described from the centre E , with the radius EF - B , will cut the side DF in two points F and G , lying on the same side of D : hence there will be two triangles DEF , DEG , either of which will satisfy the conditions of the pro- blem ...
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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