PHILOSOPHICAL TRANSACTIONS. 527 



it falling precisely on her greatest equation, wherefore by the theory and num- 

 bers of Horrox, the true place of the moon at 2h. 53m. at London, is found 

 Aquarius 29° 22' 10'': but at ph. 13m. at Ballasore, her place was in Aquarius 

 29° 41' 17" ; that is 19' 7" more than at London, which in time gives 36m.: 

 so that 3h. 29m. at London, was 9h. 13m. at Ballasore, and the difference of 

 longitude 5h. 44m. or 86'' OO' precisely; which the Dutch maps make full out 

 99°. And the French maps of Sanson, pretending to correct them, have made 

 them 5 degrees worse, and the error 18 degrees completely. 



An Idea of Mathematics, written to S. H [Samuel Hartlib.~\ By Dr. John 

 Pell.* Translated from the Latin. Philos. Collect. N° 5, p. 127. 



Concerning what I formerly wrote and explained to you, on the improvement 

 of the mathematical sciences, the amount is chiefly as follows : — ^When men are 

 without inclination, genius, assistance, and leisure requisite for these studies, 

 it is no wonder if they make but little progress in them. But it seems to me, 

 that by help of the following means, a tolerably good remedy may be provided 

 for this evil. Namely, if, 



L 1. There be composed a Mathematical Monitor, as it might be called, 

 which may contain proper answers to these three questions : 1st, What advan- 

 tages may be expected from the study of the mathematics ? 2d, What helps are 



* John Pell, D. D. and F. R. S. an eminent mathematician of the 17th century, was bom at 

 Southwake in Sussex, 161O, and educated at Cambridge, In l628 he drew up the " Description 

 and Use of the Quadrant, written for a friend, in two books," tlie original M S. of which is extant 

 among his papers in the Royal Society, &c. ; the same year he held a correspondence with Mr, Briggs 

 on the subject of logarithms. In 1643 he went to Amsterdam, where he was appointed professor of 

 mathematics; and in l646 the prince of Orange sent for him, to be professor of philosophy and ma- 

 thematics at Breda, In \6o2 he returned to England, and in l654 was sent by the protector Crom- 

 well, as agent to the protestant cantons of Switzerland. In his negociations abroad it seems he was 

 not unmindful of tlie interests of Charles II, by whom he was afterwards promoted to the living of 

 Fobbing, in Essex. Assisted by Sancroft, afterwards archbishop of Canterbury, he brought the re- 

 formed calendar into tlie upper house of convocation. He was declared a fellow of the Royal Society 

 in l66'3. Dr. Pell was author of a great many writings in mathematics, on algebra, geometry, 

 astronomy, &C.3 he made great alterations and additions to Rhonius's algebra, translated by Mr. 

 Branker; and it seems he introduced into tliat science the method of registering the steps in the 

 margin, in the reduction of equations; he demonstrated the 2d and 10th books of Euclid, also some 

 parts of Archimedes, and the greatest part of Diophantus's 6 books on arithmetic ; he had thoughts 

 also of publishing an edition of Apollonius. But few, however, of Dr. Pell's writings have been 

 published; many of them were left in the library of Lord Brereton, at Brereton in Cheshire, and 

 many others were placed in the house of the Royal Society by Dr. Birch in 1755, who has given a 

 pretty full account of his life, in the History of the Royal Society, vol. 4, p. 444. Dr. Pell died in 

 great distress in l685, in the 76th year of his age. 



