of Mathematical Learning. 



Geometry, and efpecially Algebra, are the 

 Keys of all the Inquiries, that can be made con- 

 cerning Magnitude. Thefe Sciences which are 

 only converfent about abftruie Relations, and 

 fimple Ideas, may /eem dry and barren , whilft 

 they keep within the Verge of the Intellectual 

 World j but mixt Mathematicks, which (loop to 

 Matter, and confider the Motion of the Stars, 

 the Augmentation of moving Forces, the diffe* 

 rent PafTages of the Rays of Light through 

 different Mediums ;the different Effects of Sound 

 by the Vibration of Things ; to conclude all thole 

 Sciences, which difcover the particular Relations 

 of Senfible Magnitudes go on farther and more 

 fecurely, when the Art pf difcovering Relations 

 in General is more perfect. The Univerfal In- 

 ftrument cannot be too extenfive, too handy, or 

 too eafily apply'd : It is ufeful to all the Sciences, 

 and they cannot be without it : And therefore a- 

 mong the Mathematicians of the Academy, who 

 are defign'd to be ufeful to the Publick, the Geo- 

 metricians and Algebrifts make a Clafs, as well as 

 the Aftronomers and Mechanicks. 



However, it is certain, that Speculations pure- 

 ly of Geometry, or of Algebra, are not about 

 ufeful things But it is certain too, that thofe 

 that are not, either lead or belong to thofe that 

 are. It is in it felf a very barren thing to know, 

 that in a Parabola a Subtengant is double the 

 correfponding Abfciffce ; but yet it is a Degree of 

 Knowledge neceffa ry to the Art of throwing 

 Bombs, (6 exactly as they can do now. There 

 are not by far fo many evident Ufes as Proporti- 

 ons or Truths in the Mathematicks : Yet it is 

 enough if the Concourfe of feveral Truths is ge- 

 nerally of fome ufe. 



a 3 Farther 



