Elements of Geometry and Trigonometry |
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Page 79
... segment here denotes that part of the hypothenuse , which is cut off by the perpen- dicular let fall from the right angle : thus BD is the segment adjacent to the side AB ; and DC is the segment adjacent to the side AC . We might have ...
... segment here denotes that part of the hypothenuse , which is cut off by the perpen- dicular let fall from the right angle : thus BD is the segment adjacent to the side AB ; and DC is the segment adjacent to the side AC . We might have ...
Page 83
... segments , which are proportional to the adjacent sides . In the triangle ACB , let AD be drawn , bisecting the angle CAB ; then will BD CD : AB : AC . Through the point C , draw CE E parallel to AD till it meets BA produced . In the ...
... segments , which are proportional to the adjacent sides . In the triangle ACB , let AD be drawn , bisecting the angle CAB ; then will BD CD : AB : AC . Through the point C , draw CE E parallel to AD till it meets BA produced . In the ...
Page 88
... segment . 3d . The perpendicular will be a mean proportional between the two segments of the hypothenuse . Let BAC be a right angled triangle , and AD perpendicular to the hypothenuse BC . First . The triangles BAD and BAC have the ...
... segment . 3d . The perpendicular will be a mean proportional between the two segments of the hypothenuse . Let BAC be a right angled triangle , and AD perpendicular to the hypothenuse BC . First . The triangles BAD and BAC have the ...
Page 89
... segment adjacent to that side . Thirdly . Since the triangles ABD , ADC , are similar , by comparing their homologous sides , we have BD : AD : : AĎ : DC ; hence , the perpendicular AD is a mean proportional between the segments BD , DC ...
... segment adjacent to that side . Thirdly . Since the triangles ABD , ADC , are similar , by comparing their homologous sides , we have BD : AD : : AĎ : DC ; hence , the perpendicular AD is a mean proportional between the segments BD , DC ...
Page 90
... segments BD , DC , of the diameter , or what is the same , AD - BD.DC . Hence also , in the second place , the chord AB is a mean pro- portional between the diameter BC and the adjacent segment BD , or , what is the same , AB2 = BD.BC ...
... segments BD , DC , of the diameter , or what is the same , AD - BD.DC . Hence also , in the second place , the chord AB is a mean pro- portional between the diameter BC and the adjacent segment BD , or , what is the same , AB2 = BD.BC ...
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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 convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines 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 sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex