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
... BASE of a polygon is any one polygon is any one of its sides on which the polygon is supposed to stand . 25. Triangles may be classified with reference either to their sides , or their angles . When classified with reference to their ...
... BASE of a polygon is any one polygon is any one of its sides on which the polygon is supposed to stand . 25. Triangles may be classified with reference either to their sides , or their angles . When classified with reference to their ...
Page 31
... base equal to AC , by hypothesis , common , and BD equal to DC , by construction : hence , the triangles BAD , and ... base , bisects the vertical angle , and is per- pendicular to the base . PROPOSITION XII . THEOREM . If two angles of ...
... base equal to AC , by hypothesis , common , and BD equal to DC , by construction : hence , the triangles BAD , and ... base , bisects the vertical angle , and is per- pendicular to the base . PROPOSITION XII . THEOREM . If two angles of ...
Page 93
... distance is measured , is called the vertex of the triangle , and the opposite side , is called the base of the triangle . 5. The ALTITUDE OF A PARALLELOGRAM , is the perpen- BOOK IV Proportions of Figures-Measurement of Areas,
... distance is measured , is called the vertex of the triangle , and the opposite side , is called the base of the triangle . 5. The ALTITUDE OF A PARALLELOGRAM , is the perpen- BOOK IV Proportions of Figures-Measurement of Areas,
Page 94
... 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 ...
... 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 ...
Page 95
... base A BA of the parallelogram ; B then , because 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 . equal to From A , draw AE parallel to BC ...
... base A BA of the parallelogram ; B then , because 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 . equal to From A , draw AE parallel to BC ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence