Elements of Geometry and Trigonometry |
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Page 31
... ABCD- FG , be produced , in the same direction ; then will the sum of the exterior angles a + b + c + d + f + g , be equal to four right angles . G A α F B / b For , each interior angle , plus its ex- terior angle , as A + a , is equal ...
... ABCD- FG , be produced , in the same direction ; then will the sum of the exterior angles a + b + c + d + f + g , be equal to four right angles . G A α F B / b For , each interior angle , plus its ex- terior angle , as A + a , is equal ...
Page 32
... ABCD be a parallelogram : then will AB = DC , AD = BC , A = C , and ADC = ABC . For , draw the diagonal BD . The triangles ABD , DBC , have a common side BD ; and since AD , BC , are parallel , they have also the angle ADB DBC , ( Prop ...
... ABCD be a parallelogram : then will AB = DC , AD = BC , A = C , and ADC = ABC . For , draw the diagonal BD . The triangles ABD , DBC , have a common side BD ; and since AD , BC , are parallel , they have also the angle ADB DBC , ( Prop ...
Page 33
... ABCD is a parallelogram . PROPOSITION XXXI . THEOREM . The two diagonals of a parallelogram divide each other into equal parts , or mutually bisect each other . Let ABCD be a parallelogram , AC and DB its diagonals , intersecting at E ...
... ABCD is a parallelogram . PROPOSITION XXXI . THEOREM . The two diagonals of a parallelogram divide each other into equal parts , or mutually bisect each other . Let ABCD be a parallelogram , AC and DB its diagonals , intersecting at E ...
Page 55
... ABCD , are to- gether equal to two right angles : for the an- gle BAD is measured by half the arc BCD , the angle BCD is measured by half the arc BAD ; hence the two angles BAD , BCD , ta- D ken together , are measured by the half of ...
... ABCD , are to- gether equal to two right angles : for the an- gle BAD is measured by half the arc BCD , the angle BCD is measured by half the arc BAD ; hence the two angles BAD , BCD , ta- D ken together , are measured by the half of ...
Page 69
... ABCD , ABEF : and since they are sup- posed to have the same altitude , their upper bases DC , FE , will be both situated in one straight line parallel to AB ... ABCD Hence these two parallelograms ABCD , ABEF , which have BOOK IV . 69.
... ABCD , ABEF : and since they are sup- posed to have the same altitude , their upper bases DC , FE , will be both situated in one straight line parallel to AB ... ABCD Hence these two parallelograms ABCD , ABEF , which have BOOK IV . 69.
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex