Elements of Geometry and Trigonometry: With Notes |
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Page vii
... 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 Triangular Py- ramid ...
... 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 Triangular Py- ramid ...
Page 24
... diameter . From the definition of a circle , it follows that all the radii are equal ; that all the diameters are equal also , and each double of the radius . III . A portion of the circumference , such as 5 24 GEOMETRY . The Circle and ...
... diameter . From the definition of a circle , it follows that all the radii are equal ; that all the diameters are equal also , and each double of the radius . III . A portion of the circumference , such as 5 24 GEOMETRY . The Circle and ...
Page 25
... when all its sides are tangents to the circumference ( see the diagram of Prop . 6. IV . ) : in the same case , the circle is said to be inscribed in the polygon . PROPOSITION I. THEOREM . Every diameter AB divides the circle BOOK II 25.
... when all its sides are tangents to the circumference ( see the diagram of Prop . 6. IV . ) : in the same case , the circle is said to be inscribed in the polygon . PROPOSITION I. THEOREM . Every diameter AB divides the circle BOOK II 25.
Page 26
... diameter . I B For , if the radii AC , CD ( see the last figure ) be drawn to the extremities of the chord AD , we shall have the straight line AD AC + CD , or AD AB . Cor . Hence , the greatest line which can be inscribed in a circle ...
... diameter . I B For , if the radii AC , CD ( see the last figure ) be drawn to the extremities of the chord AD , we shall have the straight line AD AC + CD , or AD AB . Cor . Hence , the greatest line which can be inscribed in a circle ...
Page 36
... diameter AE , and the radii CB , CD . E The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( 23.1 ) : but the triangle BAC being isosceles , the angle CAB is equal to ABC ...
... diameter AE , and the radii CB , CD . E The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( 23.1 ) : but the triangle BAC being isosceles , the angle CAB is equal to ABC ...
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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
ACē adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cosē 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 sinē 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.