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 σελίδες
Άλλες εκδόσεις - Προβολή όλων
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ...
Πλήρης προβολή - 1837
ABCD affection altitude angle ABC axis base bisects called centre circle common section cone conjugate consequently contained cord cosine curve cylinder described diameter difference distance divided draw drawn ellipse equal evidently extremities fall figure foci focus fore given given point greater half Hence hyperbola inclination intercepted intersection join less lines drawn manner measure meet namely opposite ordinate parabola parallel parallelogram pass perpendicular perspective plane point of contact pole primitive prism produced projection proportional PROPOSITION proved pyramid quadrant radius ratio reason rectangle right angles segments semi-ordinate sides similar sine small circle solid sphere spherical triangle square straight line surface tangent THEOREM third touch transverse triangle vertex vertical
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.