Page:Philosophical Transactions - Volume 004.djvu/46

 Circles, the distances of the Points 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 GnoomnickGnomonick [sic] and Stereographick 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 perform'd by Mixt Geometry, as by Circle and either a Parabola, Hyperbola, or Ellipsis, the Circle may be conceived to be the Sun-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 Center of the Sphere.

4. It by any of the Conick Sections however posited; 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.

These things were mention’d to invite the Learned to their Consideration: I shall only further adde, that we cannot say, what may be expected from the labours and endeavors of divers Learned men of this Nation, particularly from Dr. Wallis, who hath so excellently resolved and constructed all Cubick Æquations at the end of the first Treatise of his Opera Mathematica by aide of a Cubick Parabolaster, mentioning, that by such Curves the Roots of all Equations may be found: And who hath promised a Treatise of Algebra and Angular Sections, wherein the Reader need not doubt to meet with satisfaction in these Mysteries. Nor ought we to omit the mentioning of the Modest and Learned Mr. Barrow, who (among many other excellent Subjects, and particularly his Opticks now, at the Press) hath perform'd, what the famous Italian Geometer Mich. A. Ricci hath promis'd in ''Exercitat. Geometrica (printed at Rome 1666. and lately reprinted here) about Curves of several degrees, that serve to determine and resolve all Æquations:'' which hath likewise been done by other Learn'd men of this Nation.

This Prelude of this Excellent Botanist hath two parts; The first gives us an Alphabetical Catalogue of all the Plants in the Rh