Elements of Geometry and Trigonometry: With Notes |
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Page 3
... adjacent to each other . AC , in the diagram of Prop . 28 , is a diagonal . XIX . An equilateral polygon is one which has all its sides equal ; an equiangular polygon , one which has all its angles equal . XX . Two polygons are mutually ...
... adjacent to each other . AC , in the diagram of Prop . 28 , is a diagonal . XIX . An equilateral polygon is one which has all its sides equal ; an equiangular polygon , one which has all its angles equal . XX . Two polygons are mutually ...
Page 6
... adjacent one DCB , and both of them must be right . But since ACD is a right angle , its adjacent K B one ACE must also be right : hence the angle ACE = ACD ; hence AB is perpendicular to DE . Cor . 3. All the consecutive angles BAC ...
... adjacent one DCB , and both of them must be right . But since ACD is a right angle , its adjacent K B one ACE must also be right : hence the angle ACE = ACD ; hence AB is perpendicular to DE . Cor . 3. All the consecutive angles BAC ...
Page 7
... adjacent angles , ACD , DCB , are together equal to two right angles , the two exterior sides , AC , CB , will lie in the same straight line . FOR if CB is not the production of AC , let CE be that production : then the line ACE being ...
... adjacent angles , ACD , DCB , are together equal to two right angles , the two exterior sides , AC , CB , will lie in the same straight line . FOR if CB is not the production of AC , let CE be that production : then the line ACE being ...
Page 13
... adjacent angles BCA , BCF are together equal to two right angles , the line ACF must ( Prop . 4. ) be straight ; from whence it follows , that between the same two points A and F , two straight lines can be drawn ; which is im- possible ...
... adjacent angles BCA , BCF are together equal to two right angles , the line ACF must ( Prop . 4. ) be straight ; from whence it follows , that between the same two points A and F , two straight lines can be drawn ; which is im- possible ...
Page 17
... adjacent angles equal ; therefore ( Prop . 7. ) they are themselves equal , and the angle BFG is equal to AEG : but AEG is a right angle by construction ; therefore the line AC , BD , being perpendicular to the same straight line EF ...
... adjacent angles equal ; therefore ( Prop . 7. ) they are themselves equal , and the angle BFG is equal to AEG : but AEG is a right angle by construction ; therefore the line AC , BD , being perpendicular to the same straight line EF ...
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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.