Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 either to 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 either to their sides , or their angles . When classified with reference to their sides , there are two ...
Page 31
... base equal to AC , by hypothesis , equal to DC , by construction : hence , the triangles BAD , and DAC , have the ... base , bisects the vertical angle , and is per- pendicular to the base . PROPOSITION XII . THEOREM . If two angles of a ...
... base equal to AC , by hypothesis , equal to DC , by construction : hence , the triangles BAD , and DAC , have the ... base , bisects the vertical angle , and is per- pendicular to the base . PROPOSITION XII . THEOREM . If two angles of a ...
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- Problems relating to the First and Third Books, BOOK IV.
... 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- Problems relating to the First and Third Books, BOOK IV.
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 of the parallelogram ; BA 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 of the parallelogram ; BA 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
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following