Page:Philosophical Transactions - Volume 004.djvu/20

 which the least lines are to be drawn; which he hath extended, and applyed to those infinite sorts of other Parabola's.

Chap. 7. Treats De Firurarum dimensione ex data Centro Æquilibrii: This he saith is accurately handled by the Learned already; Aliquot tamen modos adscribit, ut non difficules, uta nec inutiles ad investiganda Æquilibrii Centra: which may be applyed to good use; for, in any Curve, if there be Ordinates enough given, standing erect at an equal parallel distance, you may approach the Area, and if by ayd thereof, you find the Center of Gravity, then do you obtain the measure either of the Round Solid, or Spindle made by the Rotation of the given Figure, or of Hoofes raised upon it as a Base.

Chap. 8. The Author sheweth an easie way of finding the Center of Gravity of an Hyberbolical Conoid, and that in order to the resolution of this Probleme; Locum invenire, ad quem sunt omnia Centra Conoidum Hyperbolicarum, quæ fiunt ab Hyperbolis in dato Cono recto sectis, & quarum Axes sint Axi ejusdem Goni paralleli; which he finds to be an Hyperbole,

Chap. 9. He treats of the Center of Gravity of the Lunula of Hippocrates Chius, and sheweth, that if Hippocrates had given that, as he did the Quadrature of the Lunula, he had squared the Circle.

Chap. 10. Treats of Arithmetical Problems, wherein he asserts, that Diophantus was wont to solve Arithmetical Questions with great subtilty, but useth numbers only, whereas the same may often be more easily and universally solv'd by Algebra; and takes for examples, the third Question of the Fourth Book, which he reformes, and reduceth divers of the like kind, that Bachet hath added, to one Proposition and Resolution; the 44th of the Fourth Book of the same Diophantus, which being solved with much trouble, he sheweth to have a briefe Analysis; the 13th of the third Book, and the 36th of the fourth Book, by reason of the likeness of it's Operation with the former

Thus we have given an account of the Authors Book. What Repute he hath among the Learned, needs not to be insisted on. The famous Pascal Or Dettonville in a Letter to this Author, saith (to give it in English;) I believe, that to make it known that 'tis You, who hath round (for Example) this Parabola, which is Rh