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
... proposition , the eighteenth , has been added . The Spherical Trigonometry has been improved by inserting the ... proposition of the second book of Solid Geometry , depending on the principle established in the twenty - seventh ...
... proposition , the eighteenth , has been added . The Spherical Trigonometry has been improved by inserting the ... proposition of the second book of Solid Geometry , depending on the principle established in the twenty - seventh ...
Side
... propositions through the whole of the Elements , namely , that in the demonstration of a theorem he never supposes any ... proposition that may not improperly be considered as terminating the elementary part of Geometry . " This volume ...
... propositions through the whole of the Elements , namely , that in the demonstration of a theorem he never supposes any ... proposition that may not improperly be considered as terminating the elementary part of Geometry . " This volume ...
Side 2
... PROPOSITION I. THEOREM . One part of a straight line cannot be in a plane , and an- other part above it . If it be possible , let AB , part of the straight line ABC , be in the plane , and the part BC above it ; and since the straight ...
... PROPOSITION I. THEOREM . One part of a straight line cannot be in a plane , and an- other part above it . If it be possible , let AB , part of the straight line ABC , be in the plane , and the part BC above it ; and since the straight ...
Side 3
... PROPOSITION III . THEOREM . If two planes cut one another , their common section is a straight line . B Let two planes AB , BC , cut one another , and let B and D be two points in the line of their com- mon section . From B to D draw ...
... PROPOSITION III . THEOREM . If two planes cut one another , their common section is a straight line . B Let two planes AB , BC , cut one another , and let B and D be two points in the line of their com- mon section . From B to D draw ...
Side 4
... PROPOSITION V. THEOREM . If three straight lines meet all in one point , and a straight line stand at right angles to each of them in that point , these three straight lines are in one and the same plane . Let the straight line AB stand ...
... PROPOSITION V. THEOREM . If three straight lines meet all in one point , and a straight line stand at right angles to each of them in that point , these three straight lines are in one and the same plane . Let the straight line AB stand ...
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...