VOL. IV.] PHILOSOPHICAL TRANSACTIONS. 341 



figures being produced meet above the vertex. Here the problem is deter- 

 mined by the intersections of two conic sections, of which a circle cannot 

 be one, unless its centre be in the axis of the other figure. And in this second 

 case, these points of intersection fall in the same right line or projected meri- 

 dian, as they did before, but at a more remote distance from the pole, viz. in 

 the former supposition the solar distance was measured by a right line, that was 

 the double tangent of half the arch; here it is the tangent of the whole arch. 

 Hence it is evident how one projection may produce another, yea infinite others, 

 by altering the scale; and how the lesser circles in the stereographic projection 

 help to describe the conic sections in the gnomonic projection; but to reduce 

 the matter to one common radius, if we suppose two spheres equal, and so 

 placed about the same axis, that the pole of the one shall pass through the cen- 

 tre of the other, and the tangent plane to pass through the said centre or pole, 

 and that a lesser circle has the same position in the one as in the other; then, if 

 the eye be at the south pole of the one, it is at the centre of the other; and 

 any projected meridian drawn from the projected pole, to pass through both the 

 projections of these lesser circles, the distances of the paints of intersection are 

 the tangents of the half and the whole arch of the meridian so intersected. But 

 as to the points of intersection, which determine the problem proposed, they 

 may be found without the aid of the former way, from a gnomonic and stereo- 

 graphic method of measuring and setting off the sides and angles of spherical 

 triangles in those projections, which is necessary in what follows. 



3. If the problem is to be performed by mixed geometry, as by a circle and 

 either a parabola, hyperbola, or ellipsis, the circle may be conceived to be the 

 sub-contrary section of a cone projected by the eye at the south-pole, and any 

 of the rest of the sections by the eye at the centre of the sphere. 



4. If by any of the conic sections however situated, the projecting plain may 

 remain the same, but the eye must be in some other part of the surface of the 

 sphere, and not in the axis. 



An Account of Boohs, N° 46, p. 934. 



I. Praeludia Botanica Roberti Morison * Scoti Aberdonensis. Londini. 

 1669, 8vo. 



* Robert Morison, one of the most celebrated botanists of the I7th century, was a native of 

 Aberdeen in Scotland, where he was born in the year l620. In this university he took his degree 

 of master of arts. Having a strong inclination for tlie study of physic, and more particularly for that 

 of botany, he went to Paris, where he obtained the degree of doctor of physic. His reputation as a 

 botanist induced Gaston Duke of Orleans, an admirer of that study, to give him the direction of the 

 Royal Garden at Blois. After the death of the Duke of Orleans he came into England, in the year 



