28 Mr. T. T. Wilkinson's Additions to the late 



I shall conclude this communication by appending a tabular 

 view of all the combinations I have examined. 



Bassicacid . . . C3«H350'' + HO. 

 Bassic jether . . . CseRa^OS + CHSQ. 

 Bassiate of soda . CssH^'^OHNaO. 

 Bassiate of baryta . CssH^sO^ + BaO. 

 Bassiate of silver . CS^HSsO^ + AgO. 



IV, Additions to the late Mr. T. S. Davies's Notes on Geometry 

 and Geometers. The Swale Manicscripts. By T. T. Wil- 

 kinson, Esq., F.R.A.S.* 



WHEN Professor Davies wrote No. VI. of his " Geometry 

 and Geometers" (Phil. Mag. Sept. 1850), he adopted 

 an opinion of mine, in correction of his own, to the effect that 

 Mr. William Chappie was the first English geometer who had 

 formally stated the property, that " the perpendiculars from the 

 angles of a plane triangle on the opposite sides intersect in the 

 same jDoint." Since that time, I have been led to examine the 

 matter inore fully, and in two papers printed in the Mechanics' 

 Magazine, Nos. 1430 and 1458, I have shown that not only was 

 the property published in the " Miscellanies, or Mathematical 

 Lucubrations of Mr. Samuel Foster, sometime Publike Professor 

 of Astronomic in Gresham Colledge in London, 1659," where it 

 is annexed to a commentary on the " Lemmata Archimedis " by 

 the Arabian commentatoi* Abi Alhonin Ali, but that it was un- 

 doubtedly known to the ancients, since it is implied in and fol- 

 lows as an easy inference from "Theorema LVII., Propositio LX." 

 of " Pappi Alexandrini Mathematicfe Collectiones. A. Frederico 

 Commaudino. Venetiis 1589, folio 195 b ;" and that from these 

 sources probably those geometers derived the pi'operty previously 

 to its being formally enunciated by Mr. Chappie in the Mis- 

 cellanea Mathematica. The note to No. VI., page 208, therefore 

 requires correction, and before entering upon other matters it 

 will perhaps not be out of place if I notice one or two other over- 

 sights which elsewhere occur in this singularly exact and inter- 

 esting series of papers. 



In No. VIII., the first issue of the " Mathematical Repository" 

 is put down as " March 1, 1796," and this date appears to have 

 been deduced by reckoning backwards two half-years from the 

 date of the pubhcatiou of the third number. The excellent prac- 

 tice of binding up the covers of each number with each volume 

 of periodical works, seems to have been partially followed in the 

 copy from which Professor Davies quotes, but the title-page jirinted 

 along with the first number of the work must have been omitted, 

 * Communicated by the Author. 



