Elements of Geometry and Trigonometry: With Notes |
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Page vii
... Circumference to the Diameter , and also its Square , are irrational Numbers , 239 V. Containing the Analytical Solution of various Prob- lems concerning the Triangle , the inscribed Quadrila- teral , the Parallelepipedon , and the ...
... Circumference to the Diameter , and also its Square , are irrational Numbers , 239 V. Containing the Analytical Solution of various Prob- lems concerning the Triangle , the inscribed Quadrila- teral , the Parallelepipedon , and the ...
Page 24
... circumference is but a line . II . Every straight line , CA , CE , CD , drawn from the centre to the circumference , is called a radius or semidiameter ; every line which , like AB , passes through the centre , and is termi- nated on ...
... circumference is but a line . II . Every straight line , CA , CE , CD , drawn from the centre to the circumference , is called a radius or semidiameter ; every line which , like AB , passes through the centre , and is termi- nated on ...
Page 25
... circumference , and is formed by two chords . An inscribed triangle is one which , like BAC , has its three angular ... circumference . The circle is said to circumscribe such a figure . VII . A secant is a line which meets the cir ...
... circumference , and is formed by two chords . An inscribed triangle is one which , like BAC , has its three angular ... circumference . The circle is said to circumscribe such a figure . VII . A secant is a line which meets the cir ...
Page 26
... circumference into two equal parts . For , if the figure AEB be applied to AFB , their common base AB retaining its position , the curve line AEB must fall exactly on the curve line AFB , otherwise there would , in A the one or the ...
... circumference into two equal parts . For , if the figure AEB be applied to AFB , their common base AB retaining its position , the curve line AEB must fall exactly on the curve line AFB , otherwise there would , in A the one or the ...
Page 28
... circumference may always be made to pass , and but one . JOIN AB , BC ; and bisect those straight lines by the perpendiculars DE , FG : we assert first , that DE and FG , will meet in some point O. For , they must necessarily cut each ...
... circumference may always be made to pass , and but one . JOIN AB , BC ; and bisect those straight lines by the perpendiculars DE , FG : we assert first , that DE and FG , will meet in some point O. For , they must necessarily cut each ...
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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.