Elements of Geometry and Trigonometry |
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Page 48
... figure is a parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then will it be a ... figure is a parallelogram ( D. 28 ) ; which was to be proved . PROPOSITION XXX . THEOREM . If two sides of a ...
... figure is a parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then will it be a ... figure is a parallelogram ( D. 28 ) ; which was to be proved . PROPOSITION XXX . THEOREM . If two sides of a ...
Page 49
... figure is a parallelogram ; which was to be proved . Cor . If two points be taken at equal distances from a line , and on the same side of it , the line joining them will be parallel to the given line . PROPOSITION XXXI . THEOREM . The ...
... figure is a parallelogram ; which was to be proved . Cor . If two points be taken at equal distances from a line , and on the same side of it , the line joining them will be parallel to the given line . PROPOSITION XXXI . THEOREM . The ...
Page 59
... figure , bounded by a curved , line , every point of which is equally distant from a point within , called the centre . The bounding line is called the cir cumference . 2. A RADIUS is a straight line drawn from the centre to any point ...
... figure , bounded by a curved , line , every point of which is equally distant from a point within , called the centre . The bounding line is called the cir cumference . 2. A RADIUS is a straight line drawn from the centre to any point ...
Page 89
... figure is a parallelogram ( D. 28 ) ; also formed with the given sides and given angle . it is PROBLEM XIII . To find the centre of a given circumference . Take any three points A , B , and C , on the circumference or arc , and join ...
... figure is a parallelogram ( D. 28 ) ; also formed with the given sides and given angle . it is PROBLEM XIII . To find the centre of a given circumference . Take any three points A , B , and C , on the circumference or arc , and join ...
Page 93
... which the 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- BOOK IV Proportions of Figures-Measurement of Areas,
... which the 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- BOOK IV Proportions of Figures-Measurement of Areas,
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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...