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 113
... focus , and another perpendicular to the directrix from the point of contact ; it also bisects , and is perpendicular to the line that subtends that angle ( Cor . 2 , and I. 3 ) . COR . 4. - If a straight line from the focus be perpendi ...
... focus , and another perpendicular to the directrix from the point of contact ; it also bisects , and is perpendicular to the line that subtends that angle ( Cor . 2 , and I. 3 ) . COR . 4. - If a straight line from the focus be perpendi ...
Side 116
... focus , is equal to its parameter . Let GE be any diameter , and RE the semi - ordinate to it , which passes through the focus ; then 2RE = 4GD ( figure to proposition VII ) . For RE2 = 4GD · GE ( I. 7 ) ; but GE = FM = GD ( I. 8 , Cor ...
... focus , is equal to its parameter . Let GE be any diameter , and RE the semi - ordinate to it , which passes through the focus ; then 2RE = 4GD ( figure to proposition VII ) . For RE2 = 4GD · GE ( I. 7 ) ; but GE = FM = GD ( I. 8 , Cor ...
Side 118
... focus of a parabola , are to one another directly as the rectangles under their segments . Let the cords GH and PQ intersect one another in the focus F , then GH : PQ = · GF FH : PF · FQ . For , since GH and PQ are equal to the ...
... focus of a parabola , are to one another directly as the rectangles under their segments . Let the cords GH and PQ intersect one another in the focus F , then GH : PQ = · GF FH : PF · FQ . For , since GH and PQ are equal to the ...
Side 119
... focus of a parabola to a point in the directrix , is a mean proportional between half the parameters of the diameters which pass through its extremities . 2. If from any point in the parabola , a tangent , semi- ordinate , and ...
... focus of a parabola to a point in the directrix , is a mean proportional between half the parameters of the diameters which pass through its extremities . 2. If from any point in the parabola , a tangent , semi- ordinate , and ...
Side 120
... focus of a parabola a semi - ordinate be applied to the axis , and from its extremity a tangent be drawn to meet another semi - ordinate produced ; then shall the produced semi - ordinate be equal to the line joining its extremity in ...
... focus of a parabola a semi - ordinate be applied to the axis , and from its extremity a tangent be drawn to meet another semi - ordinate produced ; then shall the produced semi - ordinate be equal to the line joining its extremity in ...
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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...