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 98
... upper , and the other , the lower 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 ...
... upper , and the other , the lower 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 ...
Page 99
... base and an equal altitude . Let the triangle ABC , and the parallelogram ABFD , have equal bases and equal ... upper base of the parallelogram , or in the prolongation of that base . From A , draw AE parallel to BC , forming the ...
... base and an equal altitude . Let the triangle ABC , and the parallelogram ABFD , have equal bases and equal ... upper base of the parallelogram , or in the prolongation of that base . From A , draw AE parallel to BC , forming the ...
Page 189
... bases of the prism ; one the upper , and the other the lower base ; the parallelograms taken together make up the lateral or convex surface of the prism ; the lines in which the lateral faces meet , are called lateral edges , and the ...
... bases of the prism ; one the upper , and the other the lower base ; the parallelograms taken together make up the lateral or convex surface of the prism ; the lines in which the lateral faces meet , are called lateral edges , and the ...
Page 191
... base is a regular polygon , and in which the perpendicular , drawn from the vertex to the plane of the base , passes ... upper base of the frustum ; the base of the pyramid is called the lower base of the frustum . 14. The ALTITUDE of a ...
... base is a regular polygon , and in which the perpendicular , drawn from the vertex to the plane of the base , passes ... upper base of the frustum ; the base of the pyramid is called the lower base of the frustum . 14. The ALTITUDE of a ...
Page 196
... base ( D. 11 ) : hence , the lateral edges , SA , SB , & c . , are all equal ( B. VI . , P. V. ) ; but the sides of ... upper and lower bases , multiplied by the slant height . S a Let ABCDE - e be a frustum of a right pyramid , whose vertex ...
... base ( D. 11 ) : hence , the lateral edges , SA , SB , & c . , are all equal ( B. VI . , P. V. ) ; but the sides of ... upper and lower bases , multiplied by the slant height . S a Let ABCDE - e be a frustum of a right pyramid , whose vertex ...
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Common terms and phrases
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.