Elements of Geometry and Trigonometry |
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Page 56
Adrien Marie Legendre Charles Davies. Let AB , CD , be two chords intersecting each other at E : then will the angle AEC , or DEB , be measured by half of AC + DB . Draw AF parallel to DC : then will the arc DF be ... chord 56 GEOMETRY .
Adrien Marie Legendre Charles Davies. Let AB , CD , be two chords intersecting each other at E : then will the angle AEC , or DEB , be measured by half of AC + DB . Draw AF parallel to DC : then will the arc DF be ... chord 56 GEOMETRY .
Page 57
Adrien Marie Legendre Charles Davies. Let BE be the tangent , and AC the chord . From A , the point of contact , draw the diameter AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by o half the semicircumference AMD ...
Adrien Marie Legendre Charles Davies. Let BE be the tangent , and AC the chord . From A , the point of contact , draw the diameter AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by o half the semicircumference AMD ...
Page 59
... chord AB ; hence the line CD bi- sects the chord at right angles ( Book I. Prop . XVI . Cor . ) ; hence , it bisects the arc AB in the point E ( Prop . VI . ) . Secondly . Let it be required to divide the angle ACB into two equal parts ...
... chord AB ; hence the line CD bi- sects the chord at right angles ( Book I. Prop . XVI . Cor . ) ; hence , it bisects the arc AB in the point E ( Prop . VI . ) . Secondly . Let it be required to divide the angle ACB into two equal parts ...
Page 68
... chord is BC , to the seg- ment whose chord is DE . ДД 4. The base of any rectilineal figure , is the side on which the figure is supposed to stand . 5. The altitude of a triangle is the per- pendicular let fall from the vertex of an ...
... chord is BC , to the seg- ment whose chord is DE . ДД 4. The base of any rectilineal figure , is the side on which the figure is supposed to stand . 5. The altitude of a triangle is the per- pendicular let fall from the vertex of an ...
Page 90
... chords AB , AC , be drawn to the extremities of a diameter BC , the triangle BAC will be right angled at A ( Book III ... chord AB is a mean pro- portional between the diameter BC and the adjacent segment BD , or , what is the same ...
... chords AB , AC , be drawn to the extremities of a diameter BC , the triangle BAC will be right angled at A ( Book III ... chord AB is a mean pro- portional between the diameter BC and the adjacent segment BD , or , what is the same ...
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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