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
Resultat 1-5 av 16
Side 108
... PARABOLA . DEFINITIONS . 1. If a straight line and a point be given in position , the locus of a point which is equally distant from them , is a curve called a parabola . 2. The given line is named the directrix , and the given point ...
... PARABOLA . DEFINITIONS . 1. If a straight line and a point be given in position , the locus of a point which is equally distant from them , is a curve called a parabola . 2. The given line is named the directrix , and the given point ...
Side 109
... parabola , whose directrix is AB , vertex V , and focus F ; and let PAQ be a point without the curve , that is , on the same side of the curve with the directrix : then , if PF be joined , and PQ be drawn perpendicular to AB , PF will ...
... parabola , whose directrix is AB , vertex V , and focus F ; and let PAQ be a point without the curve , that is , on the same side of the curve with the directrix : then , if PF be joined , and PQ be drawn perpendicular to AB , PF will ...
Side 110
... parabola . For HIVC = VF , and VF FH , therefore HI FH ; and hence ( Cor . 1 ) H is without the curve . In a similar manner , every other point of VH may be shown to be without the curve ; therefore VH is a tangent . PROPOSITION II ...
... parabola . For HIVC = VF , and VF FH , therefore HI FH ; and hence ( Cor . 1 ) H is without the curve . In a similar manner , every other point of VH may be shown to be without the curve ; therefore VH is a tangent . PROPOSITION II ...
Side 111
... parabola ; also , every perpen- dicular to it , which cuts the curve , will be nearer to the focus than to the point in the directrix . COR . 3. The parabola is concave towards the axis . For ( Cor . 2 ) the tangent lies between the ...
... parabola ; also , every perpen- dicular to it , which cuts the curve , will be nearer to the focus than to the point in the directrix . COR . 3. The parabola is concave towards the axis . For ( Cor . 2 ) the tangent lies between the ...
Side 112
... parabola , a straight line be drawn , not parallel to a diameter , nor bisecting the angle formed by two lines drawn from that point , the one to the focus , and the other perpendicular to the directrix , it will meet the curve in one ...
... parabola , a straight line be drawn , not parallel to a diameter , nor bisecting the angle formed by two lines drawn from that point , the one to the focus , and the other perpendicular to the directrix , it will meet the curve in one ...
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...