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 . 76 A α F D B / b For , each interior angle , plus its ex- terior angle , as A + a , is ...
... 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 . 76 A α F D B / b For , each interior angle , plus its ex- terior angle , as A + a , is ...
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 B 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 B 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- ken together , are measured by the half of the ...
... 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- ken together , are measured by the half of the ...
Page 69
... ADF , there will remain the parallelogram ABEF ; and if from the same quadrilateral ABED , we take away the equal triangle CBE , there will remain the parallelogram ABĈD . Hence these two parallelograms ABCD , ABEF , which have BOOK IV .
... ADF , there will remain the parallelogram ABEF ; and if from the same quadrilateral ABED , we take away the equal triangle CBE , there will remain the parallelogram ABĈD . Hence these two parallelograms ABCD , ABEF , which have BOOK IV .
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface Cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.