Elements of Geometry and Trigonometry: With Notes |
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Page viii
... Tangents , & C. ....................................... 279 Theorems and Formulas relating to Sines , Cosines , Tangents , & c.285 On the Construction of Tables of Sines , 304 RECTILINEAL TRIGONOMETRY , ............... 308 Principles ...
... Tangents , & C. ....................................... 279 Theorems and Formulas relating to Sines , Cosines , Tangents , & c.285 On the Construction of Tables of Sines , 304 RECTILINEAL TRIGONOMETRY , ............... 308 Principles ...
Page 25
... tangent is a line which has but one point in common with the circumference . CD is a tangent . The point M is called the point of contact . M IX . In like manner , two circumferences touch each other when they have but one point in ...
... tangent is a line which has but one point in common with the circumference . CD is a tangent . The point M is called the point of contact . M IX . In like manner , two circumferences touch each other when they have but one point in ...
Page 30
... tangent . A E D O Scholium . From a given point A , no more than one tan- gent AD can be drawn to the circumference ; for if another could be drawn , it would not be perpendicular to the radius CA ; hence , in reference to this new tangent ...
... tangent . A E D O Scholium . From a given point A , no more than one tan- gent AD can be drawn to the circumference ; for if another could be drawn , it would not be perpendicular to the radius CA ; hence , in reference to this new tangent ...
Page 31
... tangent DE ( 9. II . ) , and also to its parallel MP . But , since CH is perpendicular to the chord MP , the point H ... tangents , the one at H , the other at K , draw the parallel secant AB ; and , from what has just been shewn , we ...
... tangent DE ( 9. II . ) , and also to its parallel MP . But , since CH is perpendicular to the chord MP , the point H ... tangents , the one at H , the other at K , draw the parallel secant AB ; and , from what has just been shewn , we ...
Page 37
... tangent and a chord , is measured by the half of the arc AMDC , included between its sides . From A , the point of contact , draw the diameter AD . The angle BAD is right ( 9. II . ) and is measured by half the circumference AMD ; the ...
... tangent and a chord , is measured by the half of the arc AMDC , included between its sides . From A , the point of contact , draw the diameter AD . The angle BAD is right ( 9. II . ) and is measured by half the circumference AMD ; 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
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.