Solid and Spherical Geometry and Conic Sections: Being a Treatise on the Higher Branches of Synthetical Geometry, Containing the Solid and Spherical Geometry of Playfair ...William and Robert Chambers and sold by all booksellers, 1837 - 164 sider |
Inni boken
Side 114
... semi - ordinate , to any diameter , is equal to the rectangle under the parameter of that diameter , and the corresponding absciss . Case 1. Let GNH be an ordinate to the axis ; then GN2 = 4CV.VN . - FN2 = = - M D VR For , GN2GF2 . -FN2 ...
... semi - ordinate , to any diameter , is equal to the rectangle under the parameter of that diameter , and the corresponding absciss . Case 1. Let GNH be an ordinate to the axis ; then GN2 = 4CV.VN . - FN2 = = - M D VR For , GN2GF2 . -FN2 ...
Side 115
... semi - ordinate be applied to the other , the ab- scisses will be equal . For , let DK , and EH , produced ( figure to proposition VI . ) be the diameters ; then GH is an ordinate to DK , and one from M applied to EH will be the other ...
... semi - ordinate be applied to the other , the ab- scisses will be equal . For , let DK , and EH , produced ( figure to proposition VI . ) be the diameters ; then GH is an ordinate to DK , and one from M applied to EH will be the other ...
Side 116
... ordinate to it , from the point of contact , the subtangent MN is bisected in V ( figure to proposition VII . ) For , let the diameter GL , and its semi - ordinate VL , be drawn , then is ... semi - ordinate HK be drawn 116 CONIC SECTIONS .
... ordinate to it , from the point of contact , the subtangent MN is bisected in V ( figure to proposition VII . ) For , let the diameter GL , and its semi - ordinate VL , be drawn , then is ... semi - ordinate HK be drawn 116 CONIC SECTIONS .
Side 117
... semi - ordinate HK be drawn ; then GN2 = P.VN ( I. 7 ) , and HK2 = P.VK ( Pl . Ge . II . 5 , Cor . ) ; therefore GN2 HK2 P. KN , or ( GN + HK ) · ( GN HK ) P. HE ; that is , = - P HEGE . EQ . • • COR . 1. The parameter of any diameter ...
... semi - ordinate HK be drawn ; then GN2 = P.VN ( I. 7 ) , and HK2 = P.VK ( Pl . Ge . II . 5 , Cor . ) ; therefore GN2 HK2 P. KN , or ( GN + HK ) · ( GN HK ) P. HE ; that is , = - P HEGE . EQ . • • COR . 1. The parameter of any diameter ...
Side 118
... semi - ordinates GN , HK , be drawn ; then VN : VO VO : VK see also figure to proposition X ) . For VN VK = GN2 : HK2 ( I. 7 , Cor . 4 ) = GO2 : HO2 = ON2 : OK2 ; and VN is divided in O and K , so that = - V H K HO N VN , VO , and VK ...
... semi - ordinates GN , HK , be drawn ; then VN : VO VO : VK see also figure to proposition X ) . For VN VK = GN2 : HK2 ( I. 7 , Cor . 4 ) = GO2 : HO2 = ON2 : OK2 ; and VN is divided in O and K , so that = - V H K HO N VN , VO , and VK ...
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Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... A. Bell Uten tilgangsbegrensning - 1837 |
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... William Chambers,Robert Chambers,A Bell Ingen forhåndsvisning tilgjengelig - 2018 |
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... William Chambers,Robert Chambers,A Bell Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
absciss altitude angle ABC assymptotes base centre CG² circumference common section cone Conic Sections conic surface conjugate axis conjugate diameters cord cosine cotangent dicular directrix distance draw EK KF ellipse equal Pl foci focus given angle given point greater Hence hyperbola hypotenuse inclination intercepted intersection Let ABC line be drawn line of common ordinate parabola parallel planes parallelogram pendicular perpen perpendicular perspective plane passing point of contact pole primitive prism projection pyramid ABCD quadrant radius ratio rectangle right angles right-angled spherical triangles segments semi-ordinate semicircle sides similar triangles sine small circle solid angle solid KQ solid less solid parallelopipeds sphere spherical angle spherical triangle square subcontrary surface tangent THEOREM transverse axis vertex vertical wherefore
Populære avsnitt
Side 52 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 17 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Side 27 - LR, the base of which is the parallelogram LQ, and of which LM is one of its insisting straight lines : therefore, because the parallelogram AB is equal to CD, as the base AB is to the base LQ, so is (7.
Side 19 - DAB, which contain the solid angle at A, are less than four right angles. Next, let the solid angle at A be contained by any number of plane angles BAC, CAD, DAE, EAF, FAB. These shall together be less than four right angles.
Side 29 - FC, as the solid HD to the solid DC. But the base HF is equal to the base AE, and the solid GK to the solid AB ; therefore, as the base AE to the base CF, so is the solid AB to the solid CD.
Side 55 - EM (2.) are ^quadrants, and FL, EM together, that is, FE and ML together, are equal to a semicircle. But since A is the pole of ML, ML is the measure of the angle BAC (3.), consequently FE is the supplement of the measure of the angle BAC.
Side 21 - And AB is parallel to CD ; therefore AC is a parallelogram. In like manner, it may be proved, that each of the figures CE, FG, GB, BF, AE is a parallelogram: Join AH, DF; and...
Side 7 - If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane.
Side 11 - CA is at right angles to the given plane, it makes right angles with every straight line meeting it in that plane. But DAE, which is in that plane, meets CA : therefore CAE is a right angle. For the same reason BAE is a right angle. Wherefore the angle CAE is equal to the angle BAE ; and they are in one plane, which is impossible. Also, from a point above a plane, there can be but one perpendicular to that plane ; for if there could be two, they would be parallel (6.
Side 3 - The inclination of a straight line to a plane is the acute angle contained by that straight line, and another drawn from the point in which the first line meets the plane, to the point in which...