Elements of Geometry and Trigonometry |
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Page 61
Adrien Marie Legendre Charles Davies. PROPOSITION I. THEOREM . Any diameter divides the circle , and also its circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle and its ...
Adrien Marie Legendre Charles Davies. PROPOSITION I. THEOREM . Any diameter divides the circle , and also its circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle and its ...
Page 62
... circles , equal arcs are subtended by equal chords ; and conversely , equal chords subtend equal arcs . 1o . In the ... circle EGF , it will coincide with it , and the semi - circumference ADB will coincide with the semi - circumference ...
... circles , equal arcs are subtended by equal chords ; and conversely , equal chords subtend equal arcs . 1o . In the ... circle EGF , it will coincide with it , and the semi - circumference ADB will coincide with the semi - circumference ...
Page 63
... circles ADL and EGK , let the arc EGP be greater than the arc AMD then will : the chord EP be greater than the chord AD . D H P M G E K upon For , place the circle EGK upon AHL , so that the cen- tre shall fall upon the centre C , and ...
... circles ADL and EGK , let the arc EGP be greater than the arc AMD then will : the chord EP be greater than the chord AD . D H P M G E K upon For , place the circle EGK upon AHL , so that the cen- tre shall fall upon the centre C , and ...
Page 65
... circle . Scholium . The centre C , the middle point D of the chord AB , and the middle point G of the subtended arc , are points of the radius perpendicular to the chord . But two points determine the position of a straight line ( A. 11 ) ...
... circle . Scholium . The centre C , the middle point D of the chord AB , and the middle point G of the subtended arc , are points of the radius perpendicular to the chord . But two points determine the position of a straight line ( A. 11 ) ...
Page 66
... less is at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal : then will they be equally distant from the centres . For , let the circle KLG be placed upon ACH 66 GEOMETRY .
... less is at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal : then will they be equally distant from the centres . For , let the circle KLG be placed upon ACH 66 GEOMETRY .
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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...