Page:Philosophical Transactions - Volume 003.djvu/163

 ever in useless Notions and insignificant Generals, but to search after the Knowledge of those things which really enoble and enrich the Mind, and are beneficial to the Life of man, But, this by the by: The Book it self contains 25, considerable Propofitions, to touch some of which, we shall take notice, that

The 1. is to find the solidity of Pyramids and Cones, or frustum Pyramids and Cones, applicable to the Measuring of all Solids or Vessels of that form; whether whole or in part, or gradually, i.e. foot by foot, or inch by inch.

The 2d and 3d, may be apply'd to the measuring of irregular Solids, and useful for the exact measuring of all sorts of Stone and Timber; also of all sorts of Elliptick, Parabolick and Hyperbolick irregular Solids, or Vessels made of that Form; seeing that such Solids may be cut into Parallelepipedons, Prismes and Pyramids, and then reduced to their own nature by the proportion of the Parallelogram, adscribed about those Figures, to the Figures themselves.

The 4th shews the measuring of frustum Pyramides, when their Bases are not parallel.

The 5th is about the relation of the Sphere and Spheroide, to the Cylinders of their bases and altitudes, as well of the parts as the whole.

The 6th hath the measuring of the midle Zone of a Sphere and Spheroide: And in regard that the midle Zone of a Spheroide hath been generally taken for the Figure representing a Cask, the one being measured, the other will be so also.

To pass, with the Author (in the Application of his Book) to the 12th Propos. there is the measuring of a portion of a Sphere, which is applicable to the measuring of the inverted Crown of Brewers Coppers, or several other uses.

The 13th gives the measuring of Parabolick Conoides, which may be taken for a Brewers Copper, the Crown inverted.

The 14th measureth the Hyperbolick Conoid, which may be taken for a Brewers Copper.

The 15th, 16th, 17th, and 18th give the measuring of a Sphere, Spheroid, Parabolick Conoid and Hyperbolick Conoid, as well the whole as their parts.

The 20th measureth Circular and Elliptick Spindles. Rh