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 16
... vertices of two angles , not consecutive . 24. A BASE of a polygon is any one of its sides on which the polygon is supposed to stand . 25. Triangles may be classified with reference to either their sides , or their angles . When ...
... vertices of two angles , not consecutive . 24. A BASE of a polygon is any one of its sides on which the polygon is supposed to stand . 25. Triangles may be classified with reference to either their sides , or their angles . When ...
Page 62
... vertices are all in the cir- cumference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11. A TANGENT is a straight line which touches the circumference in one point only . This ...
... vertices are all in the cir- cumference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11. A TANGENT is a straight line which touches the circumference in one point only . This ...
Page 91
... vertices of a triangle , the circle is 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 ...
... vertices of a triangle , the circle is 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 ...
Page 104
... vertices . The area of OBC is equal to B OEX BC ; the area of OAC is equal to OFX AC ; and the area of OAB is equal to OD x AB ; and since OD , OE , and OF , are equal , the area of the triangle ABC ( A. 9 ) , is equal to OD ( AB + BC + ...
... vertices . The area of OBC is equal to B OEX BC ; the area of OAC is equal to OFX AC ; and the area of OAB is equal to OD x AB ; and since OD , OE , and OF , are equal , the area of the triangle ABC ( A. 9 ) , is equal to OD ( AB + BC + ...
Page 114
... vertices at the same point E , they have a common altitude : hence ( P. VI . , C. ) , E AED : DEB :: AD : DB . B The triangles AED and EDC , have their bases in the same line AC , and their vertices at the same point D ; they have ...
... vertices at the same point E , they have a common altitude : hence ( P. VI . , C. ) , E AED : DEB :: AD : DB . B The triangles AED and EDC , have their bases in the same line AC , and their vertices at the same point D ; they have ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence