VOL. XXX.] PHILOSOPHICAL TRANSACTIONS. 327 



proper to make the outlet narrower. This our author maintains to be oftener 

 false, than true, and endeavours to show from his theorem abovementioned, 

 that making the outlet narrower, will frequently cause the mean velocity of the 

 waters to become less than it was before. But whether a proposition of such 

 consequence, and seemingly so well supported by reason and experience, ought 

 to be condemned on the authority of a theorem founded only on a tentative 

 calculation, must be left to the judgment of the learned. 



77. Apollonii Pergcei Conicorum Libri Octo^ et Sereni Antissensis de Sectione 

 Cylindri et Coni Libri duo. Fol. Reg. e Theatro Oxon. 17 10. N° 354, 

 p. 732. 



The curators of the Oxford press having obliged the public with a very 

 elegant edition of the works of Euclid, Graeco-Latine, were pleased further to 

 proceed in the laudable intention of giving the rest of the ancient Greek ma- 

 thematicians in the same beautiful form. In this design they were chiefly 

 animated by the late learned and beneficent Dean of Christ-church, Dr. Henry 

 Aldrich, who pitching upon Apollonius, as most proper to succeed Euclid, 

 engaged the two Savilian professors to take upon them the care and pains of 

 the edition: Dr. David Gregory promising his assistance as to the first 4 books, 

 which are still extant in Greek; and Dr. Edm. Halley undertaking to translate 

 the 5th, 6th, and 7th books out of Arabic, in which language they were only 

 to be found, and to endeavour to restore the 8th, long since wholly lost. But 

 Dr. Gregory soon after dying, the care of the whole devolved on Dr. Halley, 

 who has spared no pains to render the work complete. 



In his preface, he tells us what helps he had to perfect the text, that he had 

 the use of two Greek MSS. of the first 4 books, one of which was Sir Henry 

 Savile's, and is in the Savilian Study at Oxford, the other is now in the Royal 

 Society's Museum, having been lately presented to them by that skilful mathe- 

 matician Mr. Wm, Jones, F.R.S. That he had only one manuscript of Euto- 

 cius's Commentary, out of the Bodleian Library; and two Greek copies, from 

 the Savilian Study, of Pappus's Collections, out of whose 7 th book he took 

 the Lemmata, which serve as a comment on the more difficult places of his 

 author ; and that he was forced to revise and correct the mistakes and impro- 

 prieties of the Latin translation of Commandine. 



As to the latter books, which were only in Arabic, he informs us, that he 

 made use of the Bodleian transcript of a manuscript which is at Leyden, which 

 itself is a late copy of that ancient Arabic book of the Conies, heretofore 

 Golius's, but since purchased by that great patron of universal learning. 

 Narcissus late primate of Ireland, who was pleased to favour him so far as to 



