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 19
... divided into two solids , which will be to one another as their bases . Let the solid parallelopiped ABCD be cut by the plane EV , which is parallel to the opposite planes AR , HD , and divides the whole into the solids ABFV , EGCD ; as ...
... divided into two solids , which will be to one another as their bases . Let the solid parallelopiped ABCD be cut by the plane EV , which is parallel to the opposite planes AR , HD , and divides the whole into the solids ABFV , EGCD ; as ...
Side 21
... divided into 4 , and HF into 3 , equal parallelopipeds , AS , LT , & c . The figures AS , LT , & c . are parallelopipeds , for their opposite sides are parallel ( II . Def . 5 ) , and hence the opposite sides are equal and similar ...
... divided into 4 , and HF into 3 , equal parallelopipeds , AS , LT , & c . The figures AS , LT , & c . are parallelopipeds , for their opposite sides are parallel ( II . Def . 5 ) , and hence the opposite sides are equal and similar ...
Side 35
... divided , namely , HT , TU , UV , VE , and through the points T , U , and V , let the sections TZW , UZX , V @ Y , be made parallel to the base FGH . The section NQL is equal to the section WZT ( II . 14 ) ; as also ORI to XEU , and PSM ...
... divided , namely , HT , TU , UV , VE , and through the points T , U , and V , let the sections TZW , UZX , V @ Y , be made parallel to the base FGH . The section NQL is equal to the section WZT ( II . 14 ) ; as also ORI to XEU , and PSM ...
Side 36
... divided into three pyramids that have triangular bases , and that are equal to one another . Let there be a prism of which the base is the triangle ABC , and let DEF be the triangle opposite to the base . The prism ABCDEF may be divided ...
... divided into three pyramids that have triangular bases , and that are equal to one another . Let there be a prism of which the base is the triangle ABC , and let DEF be the triangle opposite to the base . The prism ABCDEF may be divided ...
Side 37
... divided into three equal pyramids . COR . 1. From this it is manifest that every pyramid is the third part of a prism which has the same base , and the same altitude with it ; for if the base of the prism be any other figure than a ...
... divided into three equal pyramids . COR . 1. From this it is manifest that every pyramid is the third part of a prism which has the same base , and the same altitude with it ; for if the base of the prism be any other figure than a ...
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...