136 Prof. DeMorgan on the Use of the Sign + iy L. Da Vinci. 



friend Mr. Panizzi that they were in possession of a large 

 number of notes by L. da Vinci, consisting of manuscript 

 scraps on various subjects. These are bound up in a book, 

 which was shown to me. It consists of loose memoranda prin- 

 cipally on mechanics, and is written in Italian, from right to 

 left, after the Oriental fashion, as if it had been written with 

 the left-hand : any Christian who wishes to make it out, must 

 use a looking-glass, and examine the reflexion of the page, 

 instead of the page itself. At a glance I was struck with the 

 frequent occurrence of the sign + in arithmetical processes, 

 with an occasional use of — : but on looking more closely, I 

 found that + always stood for the numeral 4, which at the 

 beginning of the book is a cross with two adjacent points 

 joined, and gradually degenerates into nothing but the cross, 

 sometimes with one of the corners a little crooked. For ex- 

 ample (p. 221 of the manuscript), we see (putting Da Vinci's 

 written numerals into common type, except in the case of 

 the 4) 



3—1 _2^ 1_ 2 3^ 



T-T^S'"'' 2"-3~4* 

 This sign of division x (a very significant one, evidently 

 imagined from the process) is used throughout : but the acci- 

 dental mark = by which equality is here denoted in effect, 

 does not occur again, or it might have been supposed that 

 Da Vinci was the first who used the sign = . Other instances 

 in the same page are — 



8 _ 2 3 



"9" ~ T "^ T' 

 35 _ 5 6 

 '36 "~ ^ ■ 7 ' 



A ^ A - ^ 

 T"^~6' ~ 25 * 



On turning to other pages, I found myself able to interpret 

 every operation, -|- invariably (as far as I examined) mean- 

 ing 4, and x being the symbol of division. 



The occurrence of such a use of the sign + makes it de- 

 sirable that M. Libri should quote those manuscripts of Leo- 

 nardo da Vinci in which it takes a totally different significa- 

 tion. As I said before, I should think he would turn out to 

 be right in his assertion, it being a point in which an historian 

 who has shown himself both acute and accurate, and versed 

 moreover in the manuscripts of this very writer, could hardly 

 be deceived ; nevertheless it would be a strange thing if Da 

 Vinci, having got into the habit of using + for 4, should af- 



or 



