Elements of Geometry and Trigonometry |
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Page 55
... angles . PROPOSITION XIX . THEOREM . The angle formed by two chords , which intersect each other , is measured by half the sum of the arcs included between its sides . Let AB , CD , be two chords intersecting each BOOK III . 55.
... angles . PROPOSITION XIX . THEOREM . The angle formed by two chords , which intersect each other , is measured by half the sum of the arcs included between its sides . Let AB , CD , be two chords intersecting each BOOK III . 55.
Page 61
... sum of the other two , the arcs would not intersect each other : but the solution will always be possible , when the sum of two sides , any how taken , is greater than the third . F PROBLEM XI . Two sides of a triangle , and BOOK III . 61.
... sum of the other two , the arcs would not intersect each other : but the solution will always be possible , when the sum of two sides , any how taken , is greater than the third . F PROBLEM XI . Two sides of a triangle , and BOOK III . 61.
Page 63
... intersect B each other , draw FG , EG ; DEGF will be the parallelogram required . E For , the opposite sides are equal , by construction ; hence the figure is a parallelogram ( Book I. Prop . XXIX . ) : and it is formed with the given ...
... intersect B each other , draw FG , EG ; DEGF will be the parallelogram required . E For , the opposite sides are equal , by construction ; hence the figure is a parallelogram ( Book I. Prop . XXIX . ) : and it is formed with the given ...
Page 93
... intersect each other in a circle , are reciprocally proportional . Let the chords AB and CD intersect at O : BOOK IV . 93.
... intersect each other in a circle , are reciprocally proportional . Let the chords AB and CD intersect at O : BOOK IV . 93.
Page 94
Adrien Marie Legendre Charles Davies. Let the chords AB and CD intersect at O : then will AO DO : OC : OB . Draw AC and BD . In the triangles ACO , BOD , the angles at O are equal , being verti- cal ; the angle A is equal to the angle D ...
Adrien Marie Legendre Charles Davies. Let the chords AB and CD intersect at O : then will AO DO : OC : OB . Draw AC and BD . In the triangles ACO , BOD , the angles at O are equal , being verti- cal ; the angle A is equal to the angle D ...
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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