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 26
Side 10
... third plane , they have the same inclination to that plane . Let AB and CD be two parallel planes , and EH a third plane cutting them . The planes AB and CD are equally inclined to EH . Let the straight lines EF and GH be the common ...
... third plane , they have the same inclination to that plane . Let AB and CD be two parallel planes , and EH a third plane cutting them . The planes AB and CD are equally inclined to EH . Let the straight lines EF and GH be the common ...
Side 11
... third plane , the interior angle NKM is equal to the exterior angle OLM ; that is , the in- clination of the plane AB to the plane EH , is equal to the inclination of the plane CD to the same plane EH . PROPOSITION XVI . THEOREM . If ...
... third plane , the interior angle NKM is equal to the exterior angle OLM ; that is , the in- clination of the plane AB to the plane EH , is equal to the inclination of the plane CD to the same plane EH . PROPOSITION XVI . THEOREM . If ...
Side 12
... third plane , their common section shall be perpendicular to the same plane . Let the two planes AB , BC , be each of them perpendi- cular to a third plane , and let BD be the common section of the first two ; BD is perpendicular to the ...
... third plane , their common section shall be perpendicular to the same plane . Let the two planes AB , BC , be each of them perpendi- cular to a third plane , and let BD be the common section of the first two ; BD is perpendicular to the ...
Side 14
... third by equilateral triangles ; the fourth by pentagons ; and the fifth by equilateral tri- angles . 10. A sphere is a solid described by the revolution of a semicircle about its diameter , which remains fixed . The axis of the sphere ...
... third by equilateral triangles ; the fourth by pentagons ; and the fifth by equilateral tri- angles . 10. A sphere is a solid described by the revolution of a semicircle about its diameter , which remains fixed . The axis of the sphere ...
Side 15
... third . Let the solid angle at A be contained by the three plane angles BAC , CAD , DAB . Any two of them are greater than the third . D If the angles BAC , CAD , DAB , be all equal , it is evi- dent that any two of them are greater ...
... third . Let the solid angle at A be contained by the three plane angles BAC , CAD , DAB . Any two of them are greater than the third . D If the angles BAC , CAD , DAB , be all equal , it is evi- dent that any two of them are greater ...
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 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...