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 OD which the polygon is supposed to stand . 25. Triangles may be classified with reference either to their sides , or their angles . When ...
... vertices of two angles , not consecutive . 24 . A BASE of a polygon is any one of its sides OD which the polygon is supposed to stand . 25. Triangles may be classified with reference either to their sides , or their angles . When ...
Page 60
... vertices are all in the circum- ference . 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 circum- ference . 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 89
... vertices of a triangle , the circle will be 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 ...
... vertices of a triangle , the circle will be 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 ...
Page 110
... vertices at the same point E , have a common altitude : hence , ( P. VI . , they will D C. ) 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 , have a common altitude : hence , ( P. VI . , they will D C. ) 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 ...
Page 133
... vertices B and G lie in the E same line BG parallel to the base , their altitudes are equal , and consequently , the triangles are equal : hence , the polygon GCDE is equal to the polygon ABCDE . Again , draw CE ; produce AE and draw DF ...
... vertices B and G lie in the E same line BG parallel to the base , their altitudes are equal , and consequently , the triangles are equal : hence , the polygon GCDE is equal to the polygon ABCDE . Again , draw CE ; produce AE and draw DF ...
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Common terms and phrases
ABē ACē 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