Page:Philosophical Transactions - Volume 003.djvu/62



Numb. 30., We gave an account of a small Tract, entitul'd Quadratura Circuli & Hyperboæ in Propria sua Proportionis specie inventa & demonstrata, á Jac. Gregorio Scoto; and intimated, that it would be reprinted here, and accordingly the Impression was begun; but since then, the Author writing to a member of the 'R. Society, signifies, that it is now reprinting at Venice (and possibly not without some enlargement;) which hath caused the design to be laid aside here. Mean time, the same Author hath sent over his other Book of his own composure also: in the Preface whereof he observes, That the defect of Algebra (which is most manifest in the Mensuration of Curved quantities) may in some manner be supplyed, if out of some essential property of any Figure  be given a method of changing it into another Figure (equal thereto) that hath known properties, and of that into another add so forward, until at last you change it into some known quantity: And he modestly faith, that his own Treatise hath so far pursued this Method, that it refuseth no particular figure yet consider'd by Geometry.

After this, he answers such objections, as either have been, or such as himself could conceive might be made against: his former Book of the Quadrature of the Circle and Hyperbola.

For such, as would square a Circle organically, or divide an Angle in a given ratio, he supposeth, that there is no easier way of doing it, then by the common Linea Quadratrix, (the properties whereof are largely handled in Leotandi Cyclomathia, Lugduni, 1663. in quarto.)

Then he discourseth, that all things concerning Logarithmes and the Composition of Ratio's may be perform'd by help of a Curved Line, drawn through the Tops of a Rank of Lines in continual Proportion, (landing as Perpendiculars on a right line and at equal distance; that the Operations perform'd thereby are not to Rh