Elements of Geometry and Trigonometry: With Notes |
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Page 25
... chord or subtense of an arc is the straight line FG , which joins its two extremities . IV . A segment is the surface , or portion of a circle , includ- ed between an arc and its chord . Note . In all cases , the same chord FG belongs ...
... chord or subtense of an arc is the straight line FG , which joins its two extremities . IV . A segment is the surface , or portion of a circle , includ- ed between an arc and its chord . Note . In all cases , the same chord FG belongs ...
Page 26
... chords ; and , conversely , equal chords subtend equal arcs . If the radii AC , EO are equal , and the arcs AMD , ENG ; then the chord AD will be equal to the chord A EG . For , since the diameters AB , EF are equal , the semi- circle ...
... chords ; and , conversely , equal chords subtend equal arcs . If the radii AC , EO are equal , and the arcs AMD , ENG ; then the chord AD will be equal to the chord A EG . For , since the diameters AB , EF are equal , the semi- circle ...
Page 27
... chord AD is equal to the chord EG . Conversely , supposing again the radii AC , EO to be equal , if the chord AD is equal to the chord EG , the arcs AMD , ENG will be equal . For , if the radii CD , OG be drawn , the triangles ACD , EOG ...
... chord AD is equal to the chord EG . Conversely , supposing again the radii AC , EO to be equal , if the chord AD is equal to the chord EG , the arcs AMD , ENG will be equal . For , if the radii CD , OG be drawn , the triangles ACD , EOG ...
Page 28
... chord AB , divides it , and the subtended arc AGB , each into two equal parts . DRAW the radii CA , CB . These radii ... chord AG is equal to the chord GB , the arc AG will be equal to the arc GB ; hence , the radius CG , at right angles ...
... chord AB , divides it , and the subtended arc AGB , each into two equal parts . DRAW the radii CA , CB . These radii ... chord AG is equal to the chord GB , the arc AG will be equal to the arc GB ; hence , the radius CG , at right angles ...
Page 29
... chords are equally distant from the centre ; and two unequal chords , the less is farther from the centre . First . Suppose the chord AB - DE . Bisect those chords by the perpendicu- lars CF , CG , and draw the radii CA , CD . In the ...
... chords are equally distant from the centre ; and two unequal chords , the less is farther from the centre . First . Suppose the chord AB - DE . Bisect those chords by the perpendicu- lars CF , CG , and draw the radii CA , CD . In 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
ACē adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cosē 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 sinē 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.