| Description | Corrected and translated copy of a letter in Collins' hand, dated and attributed on blank cover page and dated with recipient at the back of the text.
Likely a draft, the letter is written is English on the verso of pages and translated into Latin on the recto throughout.
The letter discusses all the publications related to Algebra known to Collins at the time in Britain and Europe, including further enquiries that Bertet could carry out, including purchasing books on Collins behalf.
Exchanges news of the latest publications in natural philosophy, including [Pierre de] Fermat, [Gilles de] Roberval, [John] Pell, [Nicholas] Mercator, [Jean-Dominique] Cassini, [Ismael] Bullialdus, [John] Wallis. Peter van Schooten's publications in Leiden in response to Wallis are detailed [method to express irreduscible fraction in short terms; treatise of a solid called "Cono Cuneus"; solution of an algebraic problem]. Expects that [Jean] Picard's treaty on the Measure of the Earth will be very well received; the Royal Society gave order to [Robert] Hooke, the Curator, to perform an experiment to verify it. On the topic, recommends William Oughtred's Circuli Proportionum [Circles of Proportion, 1632] and [Edward] Wright's "De correctione Errorum in arte Navigandi" [Certaine Errors in Navigation, Detected and Corrected, 1610]; [Richard] Norwood "Experimentum sive Nautarum praxis" [likely the Seaman's practice, 1637]; as all valuable English books on the subject of measuring the circumference of the Earth and credits Wright with having invented "the true sea chart" and Norwood's book as very useful to all seamen, he mentions that the author is very aged and still alive in Bermuda.
Details [Jacques de] Billy's harmonic progressions included in his discussion of Diophantus' geometry, hopes that some more of Diophantus' work can be recovered possibly extant if they were translated into Arabic. Asks that enquiries be made if the works could be in the Ethiopian Library in Amara [Amhara], or as part of the 7,000 Arabic manuscripts were taken into the King of Spain's collection. Has heard from [John] Pell that there was a printed catalogue of private libraries in Padua, which mentioned that one of them held Diophantus' work, and that [Johannes] Broscius had seen the book himself.
Discusses the method of Algebra Numerosa [calculus], which is rejected by "the learned here and elsewhere", and cites as proof a long passage of [René-François de Sluse] Slusius in [Mesalabum].
Comments on the design of [Pierre] Carcavi (mathematician and secretary of the National Library in France) to "have a Diophantus in Specious Algebra", which though commendable, has partly been done by Dutch mathematician Frans [van der Huips] has already done the first two books and promised to edit the whole.
Mentions a list of algebraic books, either recently published, or to be expected, including [John] Kersey's volumes of algebra; [John] Pell's algebra and [Edward] Davenant, son of the late Bishop of Salibury of the same name whose algebraic works are promising but will only be published after his death (note: in fact likely the manuscripts in Exeter College (MSS/73/5) and Worcester College (MS/5/5)); James Gregory's geometrical and algebraic methods; the last part of John Wallis' mechanics; [Jeremiah] Horro[cks] astronomical treatise.
Notes "to compose an entire system of algebra is an excellent design, and deserves much to be encouraged, and abundantly the more in regard there is here about 4 years since invented by Mr Isaac Newton a general analytical method for the quadrature of all curvilinear spaces as well of geometrick curves...." This passage, describing Newton's algebraic advances is underlined, with quotation marks in the margin.
Includes arithmetical progression, including a proposed method and discusses past contribution on the topic by Bernhardus Varenius, [Joachim] Jungius and others.
Reassures Bertet that if he spends any money on his behalf, he shall be paid back speedily.
Different hand notes at the top ' No 21: p. 100' in reference to the inclusion of the passages referring to Newton in the printed 'Commercium Epistolicum' 1722 edition, page 100, pargraph XXI. |