Elements of Geometry and Trigonometry: With Notes |
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Page 23
... ABCD is a parallelogram . PROPOSITION XXXI . THEOREM . If two opposite sides AB , CD of a quadrilateral are equal and parallel , the remaining sides will also be equal and parallel , and the figure ABCD will be a parallelogram . Draw ...
... ABCD is a parallelogram . PROPOSITION XXXI . THEOREM . If two opposite sides AB , CD of a quadrilateral are equal and parallel , the remaining sides will also be equal and parallel , and the figure ABCD will be a parallelogram . Draw ...
Page 37
... ABCD , are to- gether equal to two right angles : for the angles BAD is measured by half the arc BCD , the angle BCD is measured by half the arc BAD ; hence the two angles BAD , BCD , taken together , are measured by the half of the ...
... ABCD , are to- gether equal to two right angles : for the angles BAD is measured by half the arc BCD , the angle BCD is measured by half the arc BAD ; hence the two angles BAD , BCD , taken together , are measured by the half of the ...
Page 50
... ABCD . Hence these two parallelograms ABCD , ABEF , which have the same base and altitude , are equivalent . Cor . Every parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II ...
... ABCD . Hence these two parallelograms ABCD , ABEF , which have the same base and altitude , are equivalent . Cor . Every parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II ...
Page 51
... ABCD , AEFD be two rect- angles having the common altitude AD : they are to each other as their bases AB , AE ... ABCD will contain seven partial rectangles , while AEFD will contain four : hence the rectangle ABCD is to AEFD as 7 is to ...
... ABCD , AEFD be two rect- angles having the common altitude AD : they are to each other as their bases AB , AE ... ABCD will contain seven partial rectangles , while AEFD will contain four : hence the rectangle ABCD is to AEFD as 7 is to ...
Page 52
... ABCD cannot be to AEFD as AB is to a line greater than AE . Exactly in the same manner , it may be shewn that the ... ABCD , AEFD , of the same altitude , are to each other as their bases AB , AE . PROPOSITION IV . THEOREM . Any two ...
... ABCD cannot be to AEFD as AB is to a line greater than AE . Exactly in the same manner , it may be shewn that the ... ABCD , AEFD , of the same altitude , are to each other as their bases AB , AE . PROPOSITION IV . THEOREM . Any two ...
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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.