Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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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- 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- 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 FEII 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 FEII 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 ...
... 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 ...
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
ABē ABCD ACē adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - 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 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
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 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.