Elements of Geometry and Trigonometry: With Notes |
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Page 24
... radius or semidiameter ; every line which , like AB , passes through the centre , and is termi- nated on both sides by the circumference , is called a diameter . From the definition of a circle , it follows that all the radii are equal ...
... radius or semidiameter ; every line which , like AB , passes through the centre , and is termi- nated on both sides by the circumference , is called a diameter . From the definition of a circle , it follows that all the radii are equal ...
Page 27
... radius CD will fall on the radius OG , and the point D on the point G ; therefore the arc AMD is equal to the arc ENG . PROPOSITION V. THEOREM . In the same circle , or in equal circles , a greater arc is subtended by a greater chord ...
... radius CD will fall on the radius OG , and the point D on the point G ; therefore the arc AMD is equal to the arc ENG . PROPOSITION V. THEOREM . In the same circle , or in equal circles , a greater arc is subtended by a greater chord ...
Page 28
... radius CG , at right angles to the chord AB , divides the arc subtended by that chord into two equal parts at the point G. Scholium . The centre C , the middle point D of the chord AB , and the middle point G of the arc subtended by ...
... radius CG , at right angles to the chord AB , divides the arc subtended by that chord into two equal parts at the point G. Scholium . The centre C , the middle point D of the chord AB , and the middle point G of the arc subtended by ...
Page 29
... 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 straight line : we assert farther , that but one can be ...
... 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 straight line : we assert farther , that but one can be ...
Page 30
... radius CA ; hence , in reference to this new tangent , the radius AC would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be shorter than CA ; hence this supposed tangent would enter the ...
... radius CA ; hence , in reference to this new tangent , the radius AC would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be shorter than CA ; hence this supposed tangent would enter 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.