Elements of Geometry and Trigonometry: With Notes |
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Page 15
... join AG . The triangle ABG is equal to DEF ; for the right angles B and E are equal , the side ABD E , and BG = EF ; hence these triangles are equal ( Prop . 6. ) , and conse- quently AG = DF . Now ( Hyp . ) we have DF - AC ; and there ...
... join AG . The triangle ABG is equal to DEF ; for the right angles B and E are equal , the side ABD E , and BG = EF ; hence these triangles are equal ( Prop . 6. ) , and conse- quently AG = DF . Now ( Hyp . ) we have DF - AC ; and there ...
Page 25
... 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 to two arcs , FHG , FEG , and consequently also to two ...
... 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 to two arcs , FHG , FEG , and consequently also to two ...
Page 28
... 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 other , if they are not parallel . Now , suppose they were ...
... 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 other , if they are not parallel . Now , suppose they were ...
Page 31
... joins the points of intersection , and will divide it into two equal parts . For the line AB , which joins the points of intersection , is a chord common to the two circles . And if a perpendicular be " 3 erected from the middle of this ...
... joins the points of intersection , and will divide it into two equal parts . For the line AB , which joins the points of intersection , is a chord common to the two circles . And if a perpendicular be " 3 erected from the middle of this ...
Page 34
... join CI . The arcs AB , AI will be to each other as two whole numbers , and by the preceding theorem , we shall have the angle ACB : angle ACI :: arc AB : arc AI . Comparing these two proportions with each other , and observing that the ...
... join CI . The arcs AB , AI will be to each other as two whole numbers , and by the preceding theorem , we shall have the angle ACB : angle ACI :: arc AB : arc AI . Comparing these two proportions with each other , and observing that 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.