Elements of Geometry and Trigonometry: With Notes |
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Page 7
... draw the line CF , mak- ing with CA the right angle ACF . Now since ACD is a straight line , the angle FCD will be right ( Prop . 2. cor . 1. ) ; and since ACE is a straight line , the angle FCE will likewise be right . But the part FCE ...
... draw the line CF , mak- ing with CA the right angle ACF . Now since ACD is a straight line , the angle FCD will be right ( Prop . 2. cor . 1. ) ; and since ACE is a straight line , the angle FCE will likewise be right . But the part FCE ...
Page 13
... drawn to that line . FOR , suppose we can draw two , AB and AC . Produce one of them AB , till BF is equal to AB , and join FC . Q A B E The triangle CBF is equal ABC ; for the angles CBF and CBA are right , the D side CB is common ...
... drawn to that line . FOR , suppose we can draw two , AB and AC . Produce one of them AB , till BF is equal to AB , and join FC . Q A B E The triangle CBF is equal ABC ; for the angles CBF and CBA are right , the D side CB is common ...
Page 14
... drawn to several points in the same line . First , The perpendicular AB will be shorter than any oblique line . Secondly , The two oblique lines , AC , AE drawn on different sides of the perpendicular , at equal distances BC , BE , will ...
... drawn to several points in the same line . First , The perpendicular AB will be shorter than any oblique line . Secondly , The two oblique lines , AC , AE drawn on different sides of the perpendicular , at equal distances BC , BE , will ...
Page 16
... drawn perpendicular to AB . The point G cannot fall on A , for the angle FAB is less than a right angle ; it can still less fall on H in the production of BA , for then there would be two perpendiculars KA , KH , drawn from the same ...
... drawn perpendicular to AB . The point G cannot fall on A , for the angle FAB is less than a right angle ; it can still less fall on H in the production of BA , for then there would be two perpendiculars KA , KH , drawn from the same ...
Page 17
... draw the straight line EGF per- pendicular to AC . It will also be perpendicular to BD . For the sum GAE + GBD is ( Hyp . ) equal to two right angles ; the sum GBF + GBD is ( Prop . 2. ) likewise equal to two right angles ; and taking ...
... draw the straight line EGF per- pendicular to AC . It will also be perpendicular to BD . For the sum GAE + GBD is ( Hyp . ) equal to two right angles ; the sum GBF + GBD is ( Prop . 2. ) likewise equal to two right angles ; and taking ...
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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.