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 83
... construct an angle equal to a given angle . Let A be the given point , AB the given line , and IKL the given angle . From the vertex K as a centre , with any radius KI , describe the arc IL , terminat- K ing in the sides of the angle ...
... construct an angle equal to a given angle . Let A be the given point , AB the given line , and IKL the given angle . From the vertex K as a centre , with any radius KI , describe the arc IL , terminat- K ing in the sides of the angle ...
Page 85
... construct the third angle . Let A and B be given angles of a triangle . Draw a line DF , and at some point of it , as E , construct the an- · gle FEH equal to A , and HEC equal to B. Then , will CED be D equal to the required angle . H ...
... construct the third angle . Let A and B be given angles of a triangle . Draw a line DF , and at some point of it , as E , construct the an- · gle FEH equal to A , and HEC equal to B. Then , will CED be D equal to the required angle . H ...
Page 86
... construct the triangle . Let B and C denote the given sides , and A the given angle . Draw the indefinite line DF , and at D construct an angle FDE , equal to the angle A ; on DF , lay off DH equal to the side C , and on DE , lay off DG ...
... construct the triangle . Let B and C denote the given sides , and A the given angle . Draw the indefinite line DF , and at D construct an angle FDE , equal to the angle A ; on DF , lay off DH equal to the side C , and on DE , lay off DG ...
Page 87
... construct the triangle . Let A and B be the given sides , and C the given angle . Draw an indefinite line DG , and at some point of it , as D , construct an angle GDE equal to the given angle ; on one side of this angle lay off the ...
... construct the triangle . Let A and B be the given sides , and C the given angle . Draw an indefinite line DG , and at some point of it , as D , construct an angle GDE equal to the given angle ; on one side of this angle lay off the ...
Page 88
... construct the parallelogram . Let A and B be the given sides , and C the given angle . Draw the line DH , and at some point as D , construct the angle HDF equal to the angle C. Lay off DE equal to the side A , and DF equal to the side B ...
... construct the parallelogram . Let A and B be the given sides , and C the given angle . Draw the line DH , and at some point as D , construct the angle HDF equal to the angle C. Lay off DE equal to the side A , and DF equal to the side B ...
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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