Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 60
... circumscribed about a circle , when all of its sides are tangent to the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches all of the sides of the polygon . OOD хо о POSTULATE . A circumference can ...
... circumscribed about a circle , when all of its sides are tangent to the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches all of the sides of the polygon . OOD хо о POSTULATE . A circumference can ...
Page 89
... circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle . There may be two cases : the given point may lie on the circumference of the given circle , or it may lie without the given circle . 1o ...
... circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle . There may be two cases : the given point may lie on the circumference of the given circle , or it may lie without the given circle . 1o ...
Page 137
... circumscribed about any regular polygon ; a circle may also be inscribed in it . 1o . Let ABCF be a regular polygon : then can the circumference of a circle be circumscribed about it . For , through three consecutive ver- tices A , B ...
... circumscribed about any regular polygon ; a circle may also be inscribed in it . 1o . Let ABCF be a regular polygon : then can the circumference of a circle be circumscribed about it . For , through three consecutive ver- tices A , B ...
Page 138
... circumscribed and inscribed circles . 2. The ANGLE AT THE CENTRE , is the angle formed by drawing lines from the centre to the extremities of either side . The angle at the centre is equal to four right angles divided by the number of ...
... circumscribed and inscribed circles . 2. The ANGLE AT THE CENTRE , is the angle formed by drawing lines from the centre to the extremities of either side . The angle at the centre is equal to four right angles divided by the number of ...
Page 142
... The area of any regular inscribed polygon . is less than that of a regular inscribed pclygon of double the number of sides , because a part is less than the whole . PROPOSITION VII . PROBLEM . Tu circumscribe a polygon about 142 GEOMETRY .
... The area of any regular inscribed polygon . is less than that of a regular inscribed pclygon of double the number of sides , because a part is less than the whole . PROPOSITION VII . PROBLEM . Tu circumscribe a polygon about 142 GEOMETRY .
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Common terms and phrases
AB² 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