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 19
... divided into two equal parts . 5. An angle may be bisected . 6. A perpendicular may be drawn to a given straight line , either from a point without , or from a point on the line . 7. A straight line may be drawn , making with a given ...
... divided into two equal parts . 5. An angle may be bisected . 6. A perpendicular may be drawn to a given straight line , either from a point without , or from a point on the line . 7. A straight line may be drawn , making with a given ...
Page 45
... divided into as many triangles , less two , as it has sides , having the point A for a common vertex , and for bases , the sides of the polygon , except the two which form the angle A. It is evident , also , that the sum of the angles ...
... divided into as many triangles , less two , as it has sides , having the point A for a common vertex , and for bases , the sides of the polygon , except the two which form the angle A. It is evident , also , that the sum of the angles ...
Page 46
... divided by the number of angles . PROPOSITION XXVII . THEOREM . The sum of the exterior angles of a polygon is equal to four right angles . Let the sides of the polygon ABCDE be prolonged , in the same order , forming he exterior angles ...
... divided by the number of angles . PROPOSITION XXVII . THEOREM . The sum of the exterior angles of a polygon is equal to four right angles . Let the sides of the polygon ABCDE be prolonged , in the same order , forming he exterior angles ...
Page 74
... divided into 7 angles , by the radii in the angle Then , suppose Cm , Cn , Cp , & c .; and DOE into 4 angles , by the radii Ox , Oy , and Oz , each equal to the unit M. From the last proposition , the arcs Am , mn 74 GEOMETRY .
... divided into 7 angles , by the radii in the angle Then , suppose Cm , Cn , Cp , & c .; and DOE into 4 angles , by the radii Ox , Oy , and Oz , each equal to the unit M. From the last proposition , the arcs Am , mn 74 GEOMETRY .
Page 76
... divided into equal parts , each less than DO : there will be at least one point of division between D and 0 ; let I be that point ; and draw CI . Then the arcs AB , AI , will be commensura- ble , and we shall have ( P. XVI . ) , angle ...
... divided into equal parts , each less than DO : there will be at least one point of division between D and 0 ; let I be that point ; and draw CI . Then the arcs AB , AI , will be commensura- ble , and we shall have ( P. XVI . ) , angle ...
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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