Elements of Geometry and Trigonometry: With Notes |
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Page v
... pyramid , discovered by M. Queret of St Malo , which is substituted in place of the former demonstration , and forms Prop . XVII . and XVIII . of Book VI . * M. Queret has been anticipated in this demonstration by the late Professor ...
... pyramid , discovered by M. Queret of St Malo , which is substituted in place of the former demonstration , and forms Prop . XVII . and XVIII . of Book VI . * M. Queret has been anticipated in this demonstration by the late Professor ...
Page 130
... pyramid , the point S its vertex ; and the whole of the triangles ASB , BSC , & c . form its convex or lateral surface . XII . The altitude of a pyramid is the perpendicular let fall from the vertex upon the plane of the base , produced ...
... pyramid , the point S its vertex ; and the whole of the triangles ASB , BSC , & c . form its convex or lateral surface . XII . The altitude of a pyramid is the perpendicular let fall from the vertex upon the plane of the base , produced ...
Page 131
With Notes Adrien Marie Legendre. XIII . A pyramid is triangular , quadrangular , & c . according as its base is a triangle , a quadrilateral , & c . XIV . A pyramid is regular , when its base is a regular poly- gon , and when , at the ...
With Notes Adrien Marie Legendre. XIII . A pyramid is triangular , quadrangular , & c . according as its base is a triangle , a quadrilateral , & c . XIV . A pyramid is regular , when its base is a regular poly- gon , and when , at the ...
Page 132
With Notes Adrien Marie Legendre. tices of so many triangular pyramids having the triangle just described for a common base ; and each of those pyramids will determine the position of a solid angle of the polyedron with reference to the ...
With Notes Adrien Marie Legendre. tices of so many triangular pyramids having the triangle just described for a common base ; and each of those pyramids will determine the position of a solid angle of the polyedron with reference to the ...
Page 146
... bases simply ; hence two prisms of the same altitude are to each other as their bases . For a like reason , two prisms of the same base are to each other as their altitudes . PROPOSITION XVI . LEMMA . If a pyramid SABCDE is 146 GEOMETRY .
... bases simply ; hence two prisms of the same altitude are to each other as their bases . For a like reason , two prisms of the same base are to each other as their altitudes . PROPOSITION XVI . LEMMA . If a pyramid SABCDE is 146 GEOMETRY .
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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.