Elements of Geometry and Trigonometry: With Notes |
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Page 2
... sides , the simplest of all , is called a triangle ; that of four sides , a quadilateral ; that of five , a pentagon ; that of six , a hexagon ; and so on . Δ Δ Δ XV . An equilateral triangle is one which has its three sides equal ; an ...
... sides , the simplest of all , is called a triangle ; that of four sides , a quadilateral ; that of five , a pentagon ; that of six , a hexagon ; and so on . Δ Δ Δ XV . An equilateral triangle is one which has its three sides equal ; an ...
Page 3
... sides equal , and its angles right . ( See Prop . 28. I. ) The rectangle , which has its angles right , with- out having its sides equal . ( See the same Prop . ) The parallelogram , or rhomboid , which has its opposite sides parallel ...
... sides equal , and its angles right . ( See Prop . 28. I. ) The rectangle , which has its angles right , with- out having its sides equal . ( See the same Prop . ) The parallelogram , or rhomboid , which has its opposite sides parallel ...
Page 8
... sides which contain it in the one , are respectively equal to an angle and the two sides which contain it in the other . Let the angle A be equal to D , the side AC equal to the side DF , the side AB equal to DE ; then will the triangle ...
... sides which contain it in the one , are respectively equal to an angle and the two sides which contain it in the other . Let the angle A be equal to D , the side AC equal to the side DF , the side AB equal to DE ; then will the triangle ...
Page 9
... side BC , the sum of these straight lines will be less than that of the two other sides AB , AC . LET BO be produced till it meet the side AC in D. The line OC ( Prop . 8. ) is shorter than OD + DC : add BO to each , and we have BO + OC ...
... side BC , the sum of these straight lines will be less than that of the two other sides AB , AC . LET BO be produced till it meet the side AC in D. The line OC ( Prop . 8. ) is shorter than OD + DC : add BO to each , and we have BO + OC ...
Page 10
With Notes Adrien Marie Legendre. PROPOSITION X. THEOREM . If the two sides AB , AC , of the triangle ABC , are equal re- spectively to the two sides DE , DF , of the triangle DEF , while , at the same time , the angle BAC contained by ...
With Notes Adrien Marie Legendre. PROPOSITION X. THEOREM . If the two sides AB , AC , of the triangle ABC , are equal re- spectively to the two sides DE , DF , of the triangle DEF , while , at the same time , the angle BAC contained by ...
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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.