given cause for the first term, and the component parts of the given effect for the second; then taking the component parts of any other cause producing similar effects for the third term, and the effect performed by these for the fourth, all operations in proportion will be reduced to the form of four terms; and if all the terms are complete, the product of the two extremes will always be equal to the product of the two means. The best method of computing vulgar, decimal, and duodecimal fractions, and of extracting the square and cube roots, in order to facilitate the knowledge of Mensuration, concludes this part. MENSURATION itself is then explained. This, showing the proportion one magnitude bears to another of the same kind, is necessary to enable the architect b 2 architect to proportion the scantlings of his timber, and to give strength and stability to his design. I have therefore given rules for measuring all the most useful kinds of figures, in the shortest way, as applied to lines, superficies, and solids. The customary methods of measuring the several Artificers Works, are then pointed out in a plain and familiar manner, with examples at full length, for the assistance of workmen in general, that they may be enabled to detect the impositions of fraudulent men, who too often find their way into every profession, and the mistakes that others may inadvertently make. The method of measuring groins upon any rectangular plan, is afterwards subjoined. P. NICHOLSON. October 6, 1808. II. From a given point, in a given right line, to erect 8 XIII. Given three points not in a straight line, to find any number of points laying between them, so that they shall be all in the circumference XIV. Given three points, not in a straight line, to find a fourth point, laying on the outside of these points, so that all the four points shall be in XVI To describe the segment of a circle to any length XVII. To describe the segment of a circle, by means XIX. In a given square to inscribe a regular octagon XX. In a given circle to inscribe an equilateral tri- angle, an hexagon, or a dodecagon XXVII. To make a triangle equal to three given straight lines, if any two of them, however taken, are greater than the third XXXI. To reduce a triangle to a rectangle XXXII. To make a rectangle, having a side equal |