Elements of Geometry and Trigonometry: With Notes |
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Page viii
... Cosines , Tangents , & C. ....................................... 279 Theorems and Formulas relating to Sines , Cosines , Tangents , & c.285 On the Construction of Tables of Sines , 304 RECTILINEAL TRIGONOMETRY , ............... 308 ...
... Cosines , Tangents , & C. ....................................... 279 Theorems and Formulas relating to Sines , Cosines , Tangents , & c.285 On the Construction of Tables of Sines , 304 RECTILINEAL TRIGONOMETRY , ............... 308 ...
Page 234
... cosine of the arc which corresponds to that angle , it follows , that just as we have the ge- neral relation Angle = so also we have a certain cosine ( and every cosine must be an abstract number ) equal to a certain algebraical ...
... cosine of the arc which corresponds to that angle , it follows , that just as we have the ge- neral relation Angle = so also we have a certain cosine ( and every cosine must be an abstract number ) equal to a certain algebraical ...
Page 250
... cosine of the angle CSP , or of the arc FH : and here , in the spherical triangle EFH , we have cos FH cos EH + sin EF sin EH cos E ; substituting the values EF COSC - COS & COS Y sina sin y = cos EF a and sin EH sin y cos E = we obtain ...
... cosine of the angle CSP , or of the arc FH : and here , in the spherical triangle EFH , we have cos FH cos EH + sin EF sin EH cos E ; substituting the values EF COSC - COS & COS Y sina sin y = cos EF a and sin EH sin y cos E = we obtain ...
Page 277
... 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 derived ...
... 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 derived ...
Page 279
... 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 radius ...
... 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 radius ...
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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.