Page:Philosophical Transactions - Volume 003.djvu/66

 much in a little, each distinct step of Ratiocination or Operation hath a distinct Line: the Author putting small Letters for unknown Quantities, and great Letters for known ones; and the Method is such, that most of the Book, if not all, may be understood by those not vers'd in the English Tongue, that are vers'd in Specious Algebra; most of the Questions being propounded in Symbols, and the progress of the work so described by the Marginal quotations, that for those exercised in Algebra, that would transcribe a Problem in this Method, it were sufficient, only to take the Margent, omitting the works it self, till farther leisure is afforded to perform it.

Next, as to the Matter, the Book consists of many excellent Problems; some whereof are such, as Bachet (that famous Commentator on Diophantus) either confesseth he did not attain, or at least left obscure: and others of them are such, as the celebrated DesCartes and Van Schooten have left doubtful, as not being by them, thoroughly understood. And some of them are such, as being unlimited, have for their Answers certain ranks or Series of all possible whole or rational Numbers, whereby the Student may be accomplisht for the resolution of other Questions of the like Nature.

Thirdly, as to the Table of Incomposits, no Book but this, extends it to above Ten thousands; some of the uses whereof are declared in the Title, others in the Book; and even in Common Arithmetick, it is of excellent Use for the Abbreviation of Fractions, and for giving of all the aliquot parts of a Number proposed, useful for the Depression and Resolution of Æquations, as is taught by Albert Gerard, and Van Schooten. Besides, it is observable in this Treatise, that the Author declineth the Exegesis numerosa of Vieta, which following Writers use for the finding of the Roots of Æquations.

As to the Remaining part of the Book, as it was published by John Henry Rohn in High Dutch, reasons may be given, why it was omitted in this English Edition.

The First Part of it handles the Taction of Circles; about which Argument some Epistles of Descartes are published in the Third Volume of his Posthumous Letters. Rh