Elements of Geometry and Trigonometry: With Notes |
From inside the book
Results 6-10 of 69
Page 29
... circumference de- scribed from the centre O , with the radius OB , will pass through the three given points A , B , C. We have now shewn that one circumference can always be made to pass through three given points , not in the same ...
... circumference de- scribed from the centre O , with the radius OB , will pass through the three given points A , B , C. We have now shewn that one circumference can always be made to pass through three given points , not in the same ...
Page 30
... circumference . FOR ( 16. I. ) every oblique line B CE , is longer than the perpendicu- lar CA ; hence the point E is with- out the circle ; hence BD has no point but A common to it with the circumference ; hence BD ( Def . 8. II . ) is ...
... circumference . FOR ( 16. I. ) every oblique line B CE , is longer than the perpendicu- lar CA ; hence the point E is with- out the circle ; hence BD has no point but A common to it with the circumference ; hence BD ( Def . 8. II . ) is ...
Page 33
... circumference : and conversely , if the arcs AB , DE are equal , the angles ACB , DCE will also be equal . First . Since the angles ACB , DCE are equal , they may be placed upon each other ; and since their sides are equal , the point A ...
... circumference : and conversely , if the arcs AB , DE are equal , the angles ACB , DCE will also be equal . First . Since the angles ACB , DCE are equal , they may be placed upon each other ; and since their sides are equal , the point A ...
Page 35
... circumference , we find the ratio of the given angle to a right angle , which is the absolute measure . Scholium 2. All that has been demonstrated in the last three propositions , concerning the comparison of angles with arcs , holds ...
... circumference , we find the ratio of the given angle to a right angle , which is the absolute measure . Scholium 2. All that has been demonstrated in the last three propositions , concerning the comparison of angles with arcs , holds ...
Page 37
... circumference . And every angle BOC , inscribed in a segment less than a semicircle , is an obtuse angle ; for it is measured by the half of the arc BAC , greater than a semicircumference . Cor . 4. The opposite angles A and C , of an ...
... circumference . And every angle BOC , inscribed in a segment less than a semicircle , is an obtuse angle ; for it is measured by the half of the arc BAC , greater than a semicircumference . Cor . 4. The opposite angles A and C , of an ...
Other editions - View all
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.