Elements of Geometry and Trigonometry: With Notes |
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Page viii
... Sines , Cosines , Tangents , & c.285 On the Construction of Tables of Sines , 304 RECTILINEAL TRIGONOMETRY , ............... 308 Principles for the Solution of Rectilineal Triangles , ~ 308 Solution of Right - angled Rectilineal ...
... Sines , Cosines , Tangents , & c.285 On the Construction of Tables of Sines , 304 RECTILINEAL TRIGONOMETRY , ............... 308 Principles for the Solution of Rectilineal Triangles , ~ 308 Solution of Right - angled Rectilineal ...
Page 253
... sine + he sin2 - 2 fg ( cosy - cost cosα ) cosa cos y ) -2 gh ( cosa cos y cos C -2 fh ( cos 2 COS O COS 26 COS 2 -- y + 2 cosa cos • cos γ } NOTE VI . On the shortest distance between two straight lines not situated in the same plane ...
... sine + he sin2 - 2 fg ( cosy - cost cosα ) cosa cos y ) -2 gh ( cosa cos y cos C -2 fh ( cos 2 COS O COS 26 COS 2 -- y + 2 cosa cos • cos γ } NOTE VI . On the shortest distance between two straight lines not situated in the same plane ...
Page 277
... sines , cosines , tangents , & c . which furnish a very simple mode of expressing the relations that subsist be- tween the sides and angles of triangles . We shall first explain the properties of those lines , and the principal formulas ...
... sines , cosines , tangents , & c . which furnish a very simple mode of expressing the relations that subsist be- tween the sides and angles of triangles . We shall first explain the properties of those lines , and the principal formulas ...
Page 279
... SINES , COSINES , TANGENTS , & c . 1S V. The sine of the arc A M , or of the angle ACM , the perpendicular MP let fall from one extremity of the arc , on the diameter which passes through the other extremity . If at the extremity of the ...
... SINES , COSINES , TANGENTS , & c . 1S V. The sine of the arc A M , or of the angle ACM , the perpendicular MP let fall from one extremity of the arc , on the diameter which passes through the other extremity . If at the extremity of the ...
Page 280
... sine , tangent , and secant of the arc MD , the complement of AM . For the sake of brevity , they are called the cosine , cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , DS = cot AM , or ...
... sine , tangent , and secant of the arc MD , the complement of AM . For the sake of brevity , they are called the cosine , cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , DS = cot AM , or ...
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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.