66 MEMOIR OF AUGUSTUS DE MORGAN. 



1834. tion of incommensurable ratios, that is, of ratios which 

 have no arithmetical representation. The whole number of 

 students is divided into two classes : those who do not 

 feel satisBed without rigorous definition and deduction ; 

 and those who would rather miss both than take a long 

 road, while a shorter one can be cut at no greater expense 

 than that of declaring that there shall be propositions 

 which arithmetical demonstrations declare there are not. 

 This work is intended for the former class.' 



Most of his books were illustrated after his own fashion. 

 The connexion of Number and Magnitude is shown by a 

 gigantic father having the contents of his pocket rifled by 

 a crowd of dwarfish children, one meaning of which I 

 understand to be, to represent the properties of magnitude 

 analysed by the aid of number. 



The author made a great descent in his next book, as 

 he tells a correspondent. The Useful Knowledge Society, 

 which, notwithstanding the Rev. Dr. Folliott's low esti- 

 mate of the ' learned friend ' in Peacock's ' Crotchet 

 Castle,' was a most useful instrument in raising the 

 objects and methods of thought of both those who had, 

 and those who had not thought before, out of a foggy 

 region of half-knowledge into a comparatively clear and 

 systematised state, had published ( Maps of the Stars,' for 

 students of Astronomy, together with smaller ones for 

 popular use, and six maps of the Earth. Mr. De Morgan 

 wrote for the Society an explanation of all these maps. 1 



Mr. Lubbock furnished some of the materials for the 

 * Explanation,' &c., in the account of the selection of 

 objects, the authorities, and the notation employed. 



On the back of the title-page is written by the author, 

 ' Ce coquin de livre a ete commence pendant 1'ete de 1833, 

 et n'a ete fini que dans le mois de Mai 1836.' 



1 Entitled An Explanation of the Gnoinonic Projection of the Sphere, 

 ' and of such points of Astronomy as are most necessary in the use of 

 Astronomical maps; being a description of the construction and use of the 

 smaller and larger maps of theU.K.S. ; also of the six maps of the Earth.' 



