Elements of Geometry and Trigonometry |
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Page 82
... PROBLEM II . To erect a perpendicular to a given straight line , at a given point of that line . Let BC be a given line , and let A be a given point on that line . C , as Lay off from A the equal distances AB and AC ; from B and C ...
... PROBLEM II . To erect a perpendicular to a given straight line , at a given point of that line . Let BC be a given line , and let A be a given point on that line . C , as Lay off from A the equal distances AB and AC ; from B and C ...
Page 83
... PROBLEM III . To draw a perpendicular to a given straight line , from ɑ given point without that line . A Let BD be the given line , and A the given point . From A , as a centre , with a ra- dius sufficiently great , describe an arc ...
... PROBLEM III . To draw a perpendicular to a given straight line , from ɑ given point without that line . A Let BD be the given line , and A the given point . From A , as a centre , with a ra- dius sufficiently great , describe an arc ...
Page 84
... PROBLEM V. To bisect a given arc , or a given angle . 1o . Let AEB be a given arc , and C its centre . Draw the chord AB ; through C , draw CD perpendicular to AB ( Prob . III . ) : then will CD bisect the arc AEB ( P. VI . ) . 2o . Let ...
... PROBLEM V. To bisect a given arc , or a given angle . 1o . Let AEB be a given arc , and C its centre . Draw the chord AB ; through C , draw CD perpendicular to AB ( Prob . III . ) : then will CD bisect the arc AEB ( P. VI . ) . 2o . Let ...
Page 85
... PROBLEM VII . Given , two angles of a triangle , to to 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 ...
... PROBLEM VII . Given , two angles of a triangle , to to 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 ...
Page 86
... PROBLEM IX . Given , one side and two angles of a triangle , to construct the triangle . The two angles may be either both adjacent to the given side , or one may be adjacent and the other opposite to it . In the latter case , construct ...
... PROBLEM IX . Given , one side and two angles of a triangle , to construct the triangle . The two angles may be either both adjacent to the given side , or one may be adjacent and the other opposite to it . In the latter case , construct ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
AB² ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
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.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...