Elements of Geometry and Trigonometry |
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Page 60
... circumscribed about a circle , when all of its sides are tangent o the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches all of the sides of the polygon . O POSTULATE . A circumference can be ...
... circumscribed about a circle , when all of its sides are tangent o the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches all of the sides of the polygon . O 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 within 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 ...
... circumscribed about any regular polygon ; a circle may also be inscribed within 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 ...
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 . Tɩ 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 . Tɩ circumscribe a polygon about 142 GEOMETRY .
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
AB² ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...