Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 32
Page 73
... radii , they are tangent , externally : 3. When this distance is less than the sum , and greater than the difference of the radii , they intersect each other in two points : 4. When this distance is equal to the difference of their radii ...
... radii , they are tangent , externally : 3. When this distance is less than the sum , and greater than the difference of the radii , they intersect each other in two points : 4. When this distance is equal to the difference of their radii ...
Page 74
... radii Cm , Cn , Cp , & c .; and DOE into 4 angles , by the radii Ox , Oy , and Oz , each equal to the unit M. From the last proposition , the arcs Am , mn 74 GEOMETRY .
... radii Cm , Cn , Cp , & c .; and DOE into 4 angles , by the radii Ox , Oy , and Oz , each equal to the unit M. From the last proposition , the arcs Am , mn 74 GEOMETRY .
Page 84
... radii and equal : chords hence , they are equal ( P. IV . ) ; therefore , the angles BAD , IKL , measured by them , are also equal ( P. XV . ) . PROBLEM V. To bisect a given arc , or a given angle . 1o . Let AEB be a given arc , and C ...
... radii and equal : chords hence , they are equal ( P. IV . ) ; therefore , the angles BAD , IKL , measured by them , are also equal ( P. XV . ) . PROBLEM V. To bisect a given arc , or a given angle . 1o . Let AEB be a given arc , and C ...
Page 139
... radii OA and OB . Then will the angle AOB be equal to one - sixth of four right angles , or to two - thirds of one right angle , because it is an gle at the centre ( P. II . , D. 2 ) . The sum of the two angles OAB an- and OBA is ...
... radii OA and OB . Then will the angle AOB be equal to one - sixth of four right angles , or to two - thirds of one right angle , because it is an gle at the centre ( P. II . , D. 2 ) . The sum of the two angles OAB an- and OBA is ...
Page 140
... radii OA and OC , the figure AOCB will be a rhombus , because its sides are equal : hence ( B. IV . , P. IV . , C. ) , we have , AB2 + BC2 + OA2 + OC2 = AC2 + OB2 ; or , taking away from the first member the quantity ÕÃ3 , and from the ...
... radii OA and OC , the figure AOCB will be a rhombus , because its sides are equal : hence ( B. IV . , P. IV . , C. ) , we have , AB2 + BC2 + OA2 + OC2 = AC2 + OB2 ; or , taking away from the first member the quantity ÕÃ3 , and from the ...
Other editions - View all
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...