Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 91
Page 16
... 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 classified with reference to their sides , there are two ...
... 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 classified with reference to their sides , there are two ...
Page 31
... base BC . Then , AB is equal to AC , by hypothesis , AD com- mon , and BD equal to DC , by con- struction : hence ... base , bisects the angle at the vertex , and is perpendicular to the base . PROPOSITION XII . THEOREM . If two angles ...
... base BC . Then , AB is equal to AC , by hypothesis , AD com- mon , and BD equal to DC , by con- struction : hence ... base , bisects the angle at the vertex , and is perpendicular to the base . PROPOSITION XII . THEOREM . If two angles ...
Page 95
... base and a given vertical angle . 13. At a point on a given straight line , construct an angle of 45 ° 14. Construct an isosceles triangle so so that the base BOOK III . 95 Exercises,
... base and a given vertical angle . 13. At a point on a given straight line , construct an angle of 45 ° 14. Construct an isosceles triangle so so that the base BOOK III . 95 Exercises,
Page 98
... base . 6. The ALTITUDE OF A TRAPEZOID is the perpendicular distance between its parallel sides . These sides are called bases ; one the upper , and the other , the lower base . 7. The AREA OF A SURFACE is its numerical value expressed ...
... base . 6. The ALTITUDE OF A TRAPEZOID is the perpendicular distance between its parallel sides . These sides are called bases ; one the upper , and the other , the lower base . 7. The AREA OF A SURFACE is its numerical value expressed ...
Page 99
... base of the parallelogram ; then , be- D E F B cause they have equal altitudes , the vertex of the triangle will lie in the upper base of the parallelogram , or in the prolongation of that base . From A , draw AE parallel to BC ...
... base of the parallelogram ; then , be- D E F B cause they have equal altitudes , the vertex of the triangle will lie in the upper base of the parallelogram , or in the prolongation of that base . From A , draw AE parallel to BC ...
Other editions - View all
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