rOL. ir.] PHILOSOPHICAL TRANSACTIONS. 253 



generated, and the height equal to the circumference which the centre of gra- 

 Tity of the perimeter of the figure describes. — 3. A method for straightening of 

 curved lines in the first six propositions ; and in particular he finds a right line 

 equal to a parabolical cur\^e, Prop. 51. — i. Divers optic propositions toward* 

 the end of the book, concerning the imperfection of the eye and the confusion 

 of the sight ; the apparent magnitude of the sun low and high ; the tails of 

 comets ; what proportion the earth's illumination by the sun, at the full of 

 the moon, bears to the illumination of the earth by the moon ; and the like 

 comparison between the sun and Sirius ; that vision by aid of a telescope or 

 microscope is not deceitful : and an observation of the similitude between the 

 earth and the moon. 



This same author, in his letter to Mr. John Collins, suggests, that Cassini 

 has observed the motion of Jupiter about his axis in 10 hours ; of Mars in 23 

 hours ; that Venus has the like rotations, but the precise period not yet 

 known. That Cassini h.'js published tables of the motion of the satellites of 

 Jupiter, with an ephemeris of the same for this present year. The like tables 

 have been formerly published by the learned John Baptist Hodierna at Rome 

 about 1656. — In another letter of this author to the same Mr. Collins, he 

 states that Mich. Angelo Ricci only, since Viviani, has written de Maximis et 

 Minimis in two sheets, but to extraordinary good purpose. 



II. An Introduction to Algebra, translated out of High Dutch into English 

 by Tho. Branker, M. A. much altered and augmented by Dr. John Pell. Also 

 a table of such odd numbers as are less than one hundred thousand, showing 

 those that are incomposite, and resolving the rest into their factors or coeffi- 

 cients. Printed at London in 4to. 



The author of this book, in the German language, was J. H. Rohn. The 

 method of it is new, containing much in a little, and each distinct step of 

 ratiocination or operation has a separate line, the operations being registered in 

 the margin. The author puts small letters for unknown quantities, and capitals 

 for known ones. — The book consists of many excellent problems ; some of 

 which are such as Bachet either confesses 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 such as being unlimited, have for their answers certain ranks or 

 series of all possible whole or rational numbers, whereby the student may be 

 accomplished for the resolution of other questions of the like nature. 



The remainder of Rohn's book, but omitted in this translation, treats of cir- 

 cular tangencies ; also of the construction of equations by means of the circle 

 and parabola ; and of sines, tangents and secants, in 105 propositions. 



