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 62
... circumscribed about a circle , when each of its sides is tangent . to the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches each of the sides of the polygon . © о POSTULATE . A circumference can be ...
... circumscribed about a circle , when each of its sides is tangent . to the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches each of the sides of the polygon . © о POSTULATE . A circumference can be ...
Page 91
... 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 with- out the given circle ...
... 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 with- out the given circle ...
Page 143
... circumscribed about any regular polygon ; a circle may also be inscribed in it . 1o . Let ABCF be a regular polygon : then can the cir- cumference 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 cir- cumference of a circle be circumscribed about it . For , through three consecutive ver- tices A , B ...
Page 144
... circumscribed and inscribed circles . 2. The ANGLE AT THE CENTRE is the angle formed by drawing lines from the centre to the extremities of any side . The angle at the centre is equal to four right angles divided by the number of sides ...
... circumscribed and inscribed circles . 2. The ANGLE AT THE CENTRE is the angle formed by drawing lines from the centre to the extremities of any side . The angle at the centre is equal to four right angles divided by the number of sides ...
Page 148
... . The area of any regular inscribed polygon is less than that of a regular inscribed polygon of double the number of sides , because a part is less than the whole . PROPOSITION VII . PROBLEM . To circumscribe , about a 148 GEOMETRY .
... . The area of any regular inscribed polygon is less than that of a regular inscribed polygon of double the number of sides , because a part is less than the whole . PROPOSITION VII . PROBLEM . To circumscribe , about a 148 GEOMETRY .
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Common terms and phrases
AB² AC² altitude angle is equal apothem Applying logarithms axis base and altitude base multiplied bisects centre chord circumference cone consequently convex surface corresponding cosec cosine cotangent cylinder denote diagonals diameter distance divided draw drawn edges equal altitudes equal in volume equilateral feet find the area formula frustum given line given point greater hence homologous hypothenuse included angle inscribed circle inscribed polygon intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROBLEM.-To PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium segment similar sine slant height sphere spherical angle spherical polygon spherical triangle square straight line tangent THEOREM triangle ABC triangular prisms triedral angle 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 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.