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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Resultat 1-5 av 25
Side 2
... reason , the straight line D BC is in the same ; and , by the hypothesis , EB is in it ; * Pl . Ge . refers to the volume on Plane Geometry . therefore the three straight lines EC , CB , BE 2 ELEMENTS OF SOLID GEOMETRY .
... reason , the straight line D BC is in the same ; and , by the hypothesis , EB is in it ; * Pl . Ge . refers to the volume on Plane Geometry . therefore the three straight lines EC , CB , BE 2 ELEMENTS OF SOLID GEOMETRY .
Side 3
... reason , it is in the plane CB ; the straight line BD is therefore common to the planes AB and BC , or it is the common section of these planes . PROPOSITION IV . THEOREM . If a straight line stand at right angles to each of two ...
... reason , it is in the plane CB ; the straight line BD is therefore common to the planes AB and BC , or it is the common section of these planes . PROPOSITION IV . THEOREM . If a straight line stand at right angles to each of two ...
Side 4
... reason , in triangle DPB , DP2 + PB2 = 2 PF2 + 2 FB2 . But since POD is given a right angle , therefore ( Pl . Ge . I. 47 ) PD2 = PO2 + OD2 ; and for a similar reason PB2 PO2 + OB2 . Therefore PD2 + PB2 = 2PO2 + OD2 + OB2 = 2 PO2 + 2 ...
... reason , in triangle DPB , DP2 + PB2 = 2 PF2 + 2 FB2 . But since POD is given a right angle , therefore ( Pl . Ge . I. 47 ) PD2 = PO2 + OD2 ; and for a similar reason PB2 PO2 + OB2 . Therefore PD2 + PB2 = 2PO2 + OD2 + OB2 = 2 PO2 + 2 ...
Side 5
... reason , each of the angles CDB , CDE , is a right angle ; and because AB is equal to DE , and BD common , the two sides AB , BD , are equal to the two ED , DB ; and they contain right angles ; therefore the base AD is equal ( Pl . Ge ...
... reason , each of the angles CDB , CDE , is a right angle ; and because AB is equal to DE , and BD common , the two sides AB , BD , are equal to the two ED , DB ; and they contain right angles ; therefore the base AD is equal ( Pl . Ge ...
Side 6
... reason , CD is likewise at right angles to the plane HGK . Therefore AB , CD , are each of them at right angles to the plane HGK . But if two straight lines are at right angles to the same plane , they are parallel ( I. 6 ) to one ...
... reason , CD is likewise at right angles to the plane HGK . Therefore AB , CD , are each of them at right angles to the plane HGK . But if two straight lines are at right angles to the same plane , they are parallel ( I. 6 ) to 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...