Elements of Geometry and Trigonometry: With Notes |
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Page viii
... Formulas relating to 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 ...
... Formulas relating to 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 ...
Page 56
... formula , ( a - b ) 2 — a2 — 2ab + b2 . PROPOSITION X. THEOREM . The rectangle contained by the sum and the difference of two lines , is equal to the difference of the squares of those lines : thus we have ( AB + BC ) × ( AB — BC ) ...
... formula , ( a - b ) 2 — a2 — 2ab + b2 . PROPOSITION X. THEOREM . The rectangle contained by the sum and the difference of two lines , is equal to the difference of the squares of those lines : thus we have ( AB + BC ) × ( AB — BC ) ...
Page 223
... formula already proves , that if two angles of one triangle are equal to two angles of another , the third angle of the former must also be equal to the third of the latter ; and this granted , it is easy to ar- rive at the theorem we ...
... formula already proves , that if two angles of one triangle are equal to two angles of another , the third angle of the former must also be equal to the third of the latter ; and this granted , it is easy to ar- rive at the theorem we ...
Page 229
... formula , cao 1+ agrees completely be 26 COS c ) . From a a this , therefore , no objection against my theory can be drawn , but ra- ther a full and entire confirmation of it . - To shew in a manner , if possible still clearer , that ...
... formula , cao 1+ agrees completely be 26 COS c ) . From a a this , therefore , no objection against my theory can be drawn , but ra- ther a full and entire confirmation of it . - To shew in a manner , if possible still clearer , that ...
Page 238
... formula . Let a be the defective radius , and b the excessive one , their difference being small ; let a ' and b ' be the radii next in order deduced by the What we are in quest of is the formulas b'ab , a ' = √ ( a . ( a . a + b ) . 2 ...
... formula . Let a be the defective radius , and b the excessive one , their difference being small ; let a ' and b ' be the radii next in order deduced by the What we are in quest of is the formulas b'ab , a ' = √ ( a . ( a . a + b ) . 2 ...
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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.