Elements of Geometry and Trigonometry: With Notes |
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Page iii
... Mathematics IN THE UNIVERSITY OF EDINBURGH , THIS TRANSLATION OF LEGENDRE'S ELEMENTS OF GEOMETRY IS INSCRIBED , IN TESTIMONY OF THE RESPECT AND ESTEEM OF THE EDITOR . PREFACE OF THE EDITOR . THE “ Elements of Geometry Coralien Lisembre Lex.
... Mathematics IN THE UNIVERSITY OF EDINBURGH , THIS TRANSLATION OF LEGENDRE'S ELEMENTS OF GEOMETRY IS INSCRIBED , IN TESTIMONY OF THE RESPECT AND ESTEEM OF THE EDITOR . PREFACE OF THE EDITOR . THE “ Elements of Geometry Coralien Lisembre Lex.
Page vii
... inscribed Quadrila- teral , the Parallelepipedon , and the Triangular Py- ramid , 246 VI . On the shortest Distance between two straight Lines not situated in the same Plane , ............ . 253 VII . On symmetrical Polyedrons , 254 ...
... inscribed Quadrila- teral , the Parallelepipedon , and the Triangular Py- ramid , 246 VI . On the shortest Distance between two straight Lines not situated in the same Plane , ............ . 253 VII . On symmetrical Polyedrons , 254 ...
Page 25
... inscribed in a circle , when its extremities are in the circumference , as AB . An inscribed angle is one which , like BAC , has its vertex in the circumference , and is formed by two chords . An inscribed triangle is one which , like ...
... inscribed in a circle , when its extremities are in the circumference , as AB . An inscribed angle is one which , like BAC , has its vertex in the circumference , and is formed by two chords . An inscribed triangle is one which , like ...
Page 26
... inscribed in a circle is equal to its diameter . PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points . For , if it could meet it in three , those three points would be equally ...
... inscribed in a circle is equal to its diameter . PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points . For , if it could meet it in three , those three points would be equally ...
Page 35
... the circle , which serve as a measure of the different angles , may also serve as a measure of the different sectors , in the same circle , or equal circles . PROPOSITION XVIII . THEOREM . The inscribed angle BAD is BOOK II . 35.
... the circle , which serve as a measure of the different angles , may also serve as a measure of the different sectors , in the same circle , or equal circles . PROPOSITION XVIII . THEOREM . The inscribed angle BAD is BOOK II . 35.
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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.