'J 12 i^HILOSOPHICAL TRANSACTIONS. [aNNOI 699, 



merly passed between Mr. Oldenburgh, the Lord Brounker, Mr. Newton, Mon. 

 Leibnitz ; and more lately between Dr. Wallis, Mons. Leibnitz, Mons. Mens 

 kenius, and some others; wherein maybe seen by what steps some of the late 

 methods for the improving and promoting of mathematics have proceeded, and 

 by whom truly made, and to whom justly owing; as that of Dr. Wallis's Arith- 

 metica Infinitorum: which, by way of induction and interpolation, has given 

 an inlet to many new discoveries. And that of Mr. Newton's Methodus Fluxi- 

 onum ; and Mons. Leibnitz's Calculus DifFerentialis, with some others. There 

 is also an account of the business of deciphering, wherein Dr. Wallis has been 

 so remarkable ; also an account of his methods for teaching persons deaf and 

 dumb to speak, and to understand a language, and thereby to express their 

 minds by writing. 



And lastly, here is a letter of Mr. Flamsteed, giving an account of a very 

 remarkable discovery of the parallaxis of the earth's annual orb, observable in 

 some of the fixed stars. Which is a noble phenomenon, diligently sought 

 after for some ages, but hitherto without success, and now at length discovered 

 in England, and confirmed by the concurrent observations of 8 years, compared 

 together, by which the Copernican hypothesis seems to be clearly established. 



After these treatises he subjoins divers other miscellaneous tracts ; which, 

 though not so purely mathematical, may at least be acceptable to inquisitive 

 persons, and show how useful mathematics are in most other studies, where the 

 author has so dexterously and successfully applied them. Amongst these is first 

 his Tractatus de Loquela Grammatico-Physicus, wherein he gives a very parti- 

 cular account of the physical or mechanical formation of all sounds used in 

 speech, expressed by the letters of several languages. Then a grammar of the 

 English tongue, adapted to the peculiar genius of this language. 



Then follows his Institutio Logica, first published in the year l687, giving a 

 clear account of tlie true foundation of logic, and reducing it from the ordinary 

 disputes in the schools to its true use in the common affairs of life. To which 

 arc annexed three theses, or particular discourses, for rectifying some mistakes 

 commonly committed by logicians in their treatises of logic. 



After this follow some Latin sermons, and theological discourses made on 

 several particular occasions. 



Pari of a Letter from Mr. Lemvenlioeck, concerning his Answers to Objections 

 made to his Opinio7is on the Animalcula in Semine Masculino. N° 255, p. 270. 



Having seen in the Phil. Trans. N° 247, the objections which Dr. Lister 

 makes against many positions concerning the procreation ot an animal out ot 

 the masculine seed ; Mr. Leuwenhoeck here takes occasion to stale that the 



