The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Σελίδα 139
... curves and curve surfaces by means of their genesis . We are not , however , imperatively tied down to this arrangement ; but whatever method we employ , the description must be adequate , complete , and devoid of superfluous con ...
... curves and curve surfaces by means of their genesis . We are not , however , imperatively tied down to this arrangement ; but whatever method we employ , the description must be adequate , complete , and devoid of superfluous con ...
Σελίδα 208
... curve A'EB ' is also a semicircle . * This secondary series of circles are called sub - contrary or antiparallel to the former : the former name is most frequently used , -the latter the more convenient . CHAPTER VIII . GEOMETRY OF THE ...
... curve A'EB ' is also a semicircle . * This secondary series of circles are called sub - contrary or antiparallel to the former : the former name is most frequently used , -the latter the more convenient . CHAPTER VIII . GEOMETRY OF THE ...
Σελίδα 221
... curves , and the equations of their tangents , normals , and diameters . In establishing that method , however , a ... curve . When the directing plane cuts one sheet only of the complete cone , the figure is called the ellipse . † 4 ...
... curves , and the equations of their tangents , normals , and diameters . In establishing that method , however , a ... curve . When the directing plane cuts one sheet only of the complete cone , the figure is called the ellipse . † 4 ...
Σελίδα 222
... curve is called the principal diameter or axis of the parabola . 6. The middle of the transverse diameter of the ellipse or hyperbola is called the centre of the curve , and a line drawn through the centre at right angles to that ...
... curve is called the principal diameter or axis of the parabola . 6. The middle of the transverse diameter of the ellipse or hyperbola is called the centre of the curve , and a line drawn through the centre at right angles to that ...
Σελίδα 223
... curve , the property is consequently established . COR . 1. Let B and P be any two points in the parabola PAP ' , and BF , PM their semi - ordinates ; then by the proposition , AF : AM :: BF2 : PM2 , or AF : BF2 :: AM : PM2 . Hence , if ...
... curve , the property is consequently established . COR . 1. Let B and P be any two points in the parabola PAP ' , and BF , PM their semi - ordinates ; then by the proposition , AF : AM :: BF2 : PM2 , or AF : BF2 :: AM : PM2 . Hence , if ...
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ABC is equal ABCD adjacent angles angle ABC angle BAC axis bisected centre circle ABC circumference coincide cone construction coordinate planes described Descriptive Geometry diameter dicular dihedral angles draw edges ellipse equal angles equiangular equimultiples given line given point given straight line greater hence horizontal hyperbola inclination intersection join less Let ABC Let the plane line BC lines drawn magnitudes meet multiple orthograph parabola parallel planes parallelogram parallelopiped perpen perpendicular perpendicular to MN plane MN plane of projection plane parallel plane PQ prisms profile angles profile plane projecting plane Prop Q. E. D. PROPOSITION ratio rectangle rectangle contained rectilineal figure remaining angle respectively right angles SCHOLIUM segment sides six right sphere spherical angle tangent THEOR trace triangle ABC trihedral vertex Whence Wherefore