Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 7
... Parallelogram ,. The Area of a Triangle , ..... Formula for the Sine of Half an Angle ,. Area of a Trapezoid , Area of a Quadrilateral , Area of a Polygon , 105 106 106 108 112 112 113 114 . Area of a Regular Polygon , To find the ...
... Parallelogram ,. The Area of a Triangle , ..... Formula for the Sine of Half an Angle ,. Area of a Trapezoid , Area of a Quadrilateral , Area of a Polygon , 105 106 106 108 112 112 113 114 . Area of a Regular Polygon , To find the ...
Page 17
... PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A ...
... PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A ...
Page 43
... HMB is equal to its alternate angle MBC ( P. XX . , C. 2 ) : hence , GHK is equal to ABC ; which was to be proved . Cor . The opposite angles of a parallelogram are equal . PROPOSITION XXV . THEOREM . In any triangle , the BOOK I. 43.
... HMB is equal to its alternate angle MBC ( P. XX . , C. 2 ) : hence , GHK is equal to ABC ; which was to be proved . Cor . The opposite angles of a parallelogram are equal . PROPOSITION XXV . THEOREM . In any triangle , the BOOK I. 43.
Page 47
... parallelogram , the opposite sides are equal , each to each .. Let ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . D C For , draw the diagonal BD . Then , because AB and DC are parallel , the A angle DBA is equal ...
... parallelogram , the opposite sides are equal , each to each .. Let ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . D C For , draw the diagonal BD . Then , because AB and DC are parallel , the A angle DBA is equal ...
Page 48
... parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Draw the diagonal DB . Then , the triangles ADB and CBD , will have A D the sides of the one equal to the sides of the ...
... parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Draw the diagonal DB . Then , the triangles ADB and CBD , will have A D the sides of the one equal to the sides of the ...
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Common terms and phrases
ABē ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following