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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 transverse triangle vertex vertical
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.
Page 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.