6 
Notes bearing on Mathematical History/’ by Sir James 
Cockle, F.H.S., Corresponding Member of the Society. 
1. To the list of Professor Boole’s writings which follows 
the preface to the Supplementary Volume of his “Differen- 
tial Equations” [2nd (posthumous) ed., 1865, pp. viii — xi] 
may be added a paper entitled “ Mr. Boole’s theory of the 
mathematical basis of logic,” published in the Mechanics 
Magazine (1818, voL xlix, pp. 254-255). 
2. Mr. Blissard in his “theory of generic equations” (Q 
of Math. vol. iv, p. 279 ; vol. v, pp. 58 and 185, see also pp. 
184 and 325) has applied “representative notation” very 
extensively. Professor J. B. Young had noticed {Mech. 
Mag., 1847, vol. xlvii, p. 627) that the law of Bernoulli’s 
numbers is expressed by 
(l+B)'^-B„-0 
if we write the exponents of B below instead of above that 
symbol. J udging from what purports to be an examination 
paper, I see that Prof Young, examining for the Andrews 
Scholarship, 1851, at University College, London, again 
noticed (in question 7) the law. 
3. In Notes and Queries (1854, vol. x, p. 48; see also p. 
191 ; and 2nd Ser. vol. viii, p. 465, vol. ix, p. 340, vol. x, p. 
162; and 4th Ser. vol. ii, p. 316) I long ago pointed out that 
Barociiis, in the margin of p. 264 of his Proclus (1560) cites 
the Geometricce enarrationes of Geminus, and I suggested 
that there might yet be some hope of recovering that work. 
In a comment (jh. 2nd Ser. vol. ix, p. 449) on something I 
had said, De Morgan remarked that he took “ enarrationum” 
as a printer’s mistake for “ effectionum,” if Heilbronner were 
right; adding that if there be, as both Petavius and Heil- 
bronner seem to state, a printed catalogue of the manu- 
scripts of Barocius, it would be desirable to revive the 
knowledge of it. De Morgan states that Petavius is the 
authority for manuscripts of Barocius being brought to 
England, and that it may be that a manuscript book of 
