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 |
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Side 98
... ordinate planes . 4. When the two co - ordinate planes are a horizontal and a vertical plane , the projections on them are respectively called the horizontal and vertical projection . 5. In the case of an object of a regular figure ...
... ordinate planes . 4. When the two co - ordinate planes are a horizontal and a vertical plane , the projections on them are respectively called the horizontal and vertical projection . 5. In the case of an object of a regular figure ...
Side 109
... ordinate to a diameter is a straight line , terminated on both sides by the curve , and bisected by that diameter the part of the diameter which it cuts off , is called an absciss . 6. The parameter of a diameter is four times the ...
... ordinate to a diameter is a straight line , terminated on both sides by the curve , and bisected by that diameter the part of the diameter which it cuts off , is called an absciss . 6. The parameter of a diameter is four times the ...
Side 113
... ordinate to the diameter that passes through the point of contact . The cord GH , parallel to the tangent MQ , will be bi- sected by the diameter MN . For , let GA , HE , be per- pendicular to AB , and let FD be perpendicular to and ...
... ordinate to the diameter that passes through the point of contact . The cord GH , parallel to the tangent MQ , will be bi- sected by the diameter MN . For , let GA , HE , be per- pendicular to AB , and let FD be perpendicular to and ...
Side 114
... 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 . For , GN2 GF2 - FN ?: but GF GD CN ; there ...
... 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 . For , GN2 GF2 - FN ?: but GF GD CN ; there ...
Side 115
... ordinate from the same point . For it was proved that GK2 = 4CV · MN . • COR . 2. - If there be two diameters , and from the vertex of each a semi - ordinate be applied to the other , the ab- scisses will be equal . For , let DK , and ...
... ordinate from the same point . For it was proved that GK2 = 4CV · MN . • COR . 2. - If there be two diameters , and from the vertex of each a semi - ordinate be applied to the other , the ab- scisses will be equal . For , let DK , and ...
Andre utgaver - Vis alle
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 segments semi-ordinate semicircle sides similar triangles sine small circle solid angle solid KQ solid less solid parallelopipeds sphere spherical angle spherical triangle square straight lines drawn subcontrary surface tangent THEOREM transverse axis vertex vertical wherefore
Populære avsnitt
Side 50 - 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 15 - DAB : any two of them shall be greater than the third. If the angles BAC, CAD, DAB be all equal, it is evident that any two of them are greater than the third: but if they are not, let BAC be that angle which is not less than either of the other two, and is greater than one of them DAB; and at the point A, in the straight line AB, make, in the plane * 23.
Side 15 - 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 25 - 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 16 - EC : (i. ax. 5.) and because DA is equal to AE, and AC common, but the base DC greater than the base EC; therefore the angle DAC is greater than the angle EAC ; (i.
Side 17 - 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 11 - THEOH.—If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B; C, F...
Side 11 - FD. Join AC, BD, AD, and let AD meet the plane KL in the point X ; and join EX, XF : because the two parallel planes KL, MN are cut by the plane EBDX, the common sections EX, BD are parallel a.
Side 27 - 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 1 - 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...