PREFACE. IX 



matical literature, except \n wliicli is an abbreviation for the pro- 

 duct 1 . 2, ...'?i, frequently but not universally employed : some such 

 symbol is much required, and I do not know of any which is pre- 

 ferable to this, and I have accordingly introduced it in all my 

 publications. 



There are three important authors whom I have frequently 

 cited whose works on Probability have passed through more than 

 one edition, Montmort, De Moivre, and Laplace : it may save trouble 

 to a person who may happen to consult the present volume if I 

 here refer to pages 79, 13G, and 495 where I have stated which 

 editions I have cited. 



Perhaps it may appear that I have allotted too much space to 

 some of the authors whose works I examine, especially the more 

 ancient ; but it is difficult to be accurate or interesting if the nar- 

 rative is confined to a mere catalogue of titles : and as experience 

 shews that mathematical histories are but rarely undertaken, it 

 seems desirable that they should not be executed on a meagre 

 and inadequate scale. 



I will here advert to some of my predecessors in this depart- 

 ment of mathematical history ; and thus it will appear that I have 

 not obtained much assistance from them. 



In the third volume of Montucla's Histoire des Mathematiqiies 

 pages 380—426 are devoted to the Theory of Probability and the 

 kindred subjects. I have always cited this volume simply by the 

 name Montucla, but it is of course well known that the third and 

 fourth volumes were edited from the author's manuscripts after his 

 death by La Landc. I should be sorry to apj^ear ungrateful to 

 Montucla; his work is indispensable to the student of mathema- 

 tical history, for whatever may be its defects it remains without 

 any rival. But I have been much disappointed in what he says 

 respecting the Theory of Probability ; he is not copious, nor accu- 

 rate, nor critical. Hallaui has characterised him with some severity, 

 by saying in reference to a point of mathematical history, " Mon- 

 tucla is as superficial as usual :" see a note in the second Chapter 

 of the first volume of the History of the Literature of Europe. 



There are brief outlines of the history involved or formally 

 incorporated in some of the elementary treatises on the Theory 

 of Probability : I need notice only the best, which occurs in the 

 Treatise on Probability published in the Library of L^seful Know- 

 ledge. This little work is anonymous, but is known to have been 

 written by Lubbock and Drinkwater ; the former is now Sir John 

 Lubbock, aud the latter changed his name to Drinkwater-Bethune : 

 see Professor De Morgan's Arithmetical Books... page 106, a letter 

 by him in the Assurance Magazine, Yol. TX. page 238, and another 

 letter by him in the Times, Dec. 16, 1862. The treatise is inter- 



