Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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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 . Ө о POSTULATE . A circumference can be ...
... 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 . Ө о POSTULATE . A circumference can be ...
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 . ין 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 , C ...
... circumscribed about any regular polygon ; a circle may also be inscribed in it . ין 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 , C ...
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
... 2. 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 . To circumscribe , about a 142 GEOMETRY .
... 2. 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 . To circumscribe , about a 142 GEOMETRY .
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence