Elements of Geometry and Trigonometry |
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Page 84
... equal to the chord LI , from B as a centre , describe an arc cutting the arc BO ... measured by them , are also equal ( P. XV . ) . PROBLEM V. To bisect a given ... half of an arc or angle be bisected , the original arc or angle will be ...
... equal to the chord LI , from B as a centre , describe an arc cutting the arc BO ... measured by them , are also equal ( P. XV . ) . PROBLEM V. To bisect a given ... half of an arc or angle be bisected , the original arc or angle will be ...
Page 92
... measured by and the inscribed angle For , the angle ABF , equal to half of the arc AKB ( P. XXI . ) ; AMB is measured by half of the same arc : angle AMB is equal to the angle EBD , quently , to the given angle . hence , the and conse ...
... measured by and the inscribed angle For , the angle ABF , equal to half of the arc AKB ( P. XXI . ) ; AMB is measured by half of the same arc : angle AMB is equal to the angle EBD , quently , to the given angle . hence , the and conse ...
Page 127
... measured by half of the arc CB ( B. III . , P. XVIII . ) . The angles OBD and OCA , will also be equal , because each is measured by B half of the arc AD : hence , the triangles OBD and OCA are similar ( P. XIX . , C. ) , and ...
... measured by half of the arc CB ( B. III . , P. XVIII . ) . The angles OBD and OCA , will also be equal , because each is measured by B half of the arc AD : hence , the triangles OBD and OCA are similar ( P. XIX . , C. ) , and ...
Page 128
... equal , because each is measured by half of the arc AD : hence , they are similar , and consequently , their homologous sides are proportional ; whence , OB : OC :: : OD : OA ; which was to be proved . Cor . From the above proportion ...
... equal , because each is measured by half of the arc AD : hence , they are similar , and consequently , their homologous sides are proportional ; whence , OB : OC :: : OD : OA ; which was to be proved . Cor . From the above proportion ...
Page 219
... equal to the half sum of AO and DC . Now , if the line AD be revolved about OC , as an axis , it will generate the surface of a frustum of a cone whose slant height is AD ; the point will generate a circumference which is equal to half ...
... equal to the half sum of AO and DC . Now , if the line AD be revolved about OC , as an axis , it will generate the surface of a frustum of a cone whose slant height is AD ; the point will generate a circumference which is equal to half ...
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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...