Elements of Geometry and Trigonometry: With Notes |
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Page 31
... radius CH to the point of contact H ; it will be perpen- dicular to the tangent DE ( 9. II . ) , and also to its parallel MP . But , since CH is perpendicular to the chord MP , the point H must be the middle of the arc MHP ; therefore ...
... radius CH to the point of contact H ; it will be perpen- dicular to the tangent DE ( 9. II . ) , and also to its parallel MP . But , since CH is perpendicular to the chord MP , the point H must be the middle of the arc MHP ; therefore ...
Page 32
... radius being at the same time less than the sum of the smaller and the distance between the centres , the two circles will cut each other . For to make an intersection possible , the triangle CAD ( see the preceding figure ) must be ...
... radius being at the same time less than the sum of the smaller and the distance between the centres , the two circles will cut each other . For to make an intersection possible , the triangle CAD ( see the preceding figure ) must be ...
Page 38
... radius greater than the half of AB , de- scribe two arcs cutting each other in B ; the point B will be equally distant from A and B. Find , in like manner , above or beneath the line AB , a second point E , equally dis- tant from the ...
... radius greater than the half of AB , de- scribe two arcs cutting each other in B ; the point B will be equally distant from A and B. Find , in like manner , above or beneath the line AB , a second point E , equally dis- tant from the ...
Page 39
... radius , describe the arc IL , terminating in the two sides of the angle ; from the point A as K a centre , with a distance AB equal OD to KI , describe the indefinite arc BO ; then take a radius equal to the chord LI , with which ...
... radius , describe the arc IL , terminating in the two sides of the angle ; from the point A as K a centre , with a distance AB equal OD to KI , describe the indefinite arc BO ; then take a radius equal to the chord LI , with which ...
Page 40
... radius sufficiently great , describe the indefinite arc EO ; from the point E as a centre , with the same radius , de- scribe the arc AF ; take EO = AF , and draw AD : this will be the pa- rallel required . B For , joining AE , the ...
... radius sufficiently great , describe the indefinite arc EO ; from the point E as a centre , with the same radius , de- scribe the arc AF ; take EO = AF , and draw AD : this will be the pa- rallel required . B For , joining AE , the ...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |
Common terms and phrases
AC² adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cos² cosine cylinder demonstration determined diagonal diameter draw drawn equal angles equation equivalent faces figure formulas frustum greater homologous sides hypotenuse inclination inscribed intersection isosceles join less likewise manner measure multiplied number of sides opposite parallel parallelepipedon parallelogram perpendicular plane MN polyedron prism PROBLEM Prop PROPOSITION quadrilateral quantities radii radius ratio rectangle rectilineal triangle regular polygon right angles right-angled triangle SABC Scholium sector segment shew shewn side BC similar sin² sines solid angle sphere spherical polygon spherical triangle square straight line suppose tang tangent THEOREM third side three angles three plane angles triangle ABC triangular pyramids vertex vertices
Popular passages
Page 152 - AMB be a section, made by a plane, in the sphere, whose centre is C. From the...
Page 24 - THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 62 - Similar triangles are to each other as the squares of their homologous sides.
Page 211 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.
Page 187 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 140 - AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively equivalent, namely, DEF to def, GHI to ghi, &c.
Page 150 - The radius of a sphere is a straight line, drawn from the centre to any point...
Page 168 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 135 - XII.) ; in like manner, the two solids AQ, AK, having the same base, AOLE, are to each other as their altitudes AD, A M.