Notices respecting New Books. 71 



Indeed Mr. Potts tells us that there is only one single work pub- 

 lished in England where it is fully discussed, or even mentioned at 

 all ; and we believe the first use even of the term in any English book 

 was made in this Magazine in 1826 by the author to whom Mr. 

 Potts refers, in a paper on Pascal's Mystic Hexagram. 



We come in the last place to a series of " Geometrical Exercises," 

 above a thousand in number. These are collected exclusively from 

 the Cambridge University papers — either those given in the Senate 

 House or in the different Colleges during the present century. 

 Opinions will be divided as to the wisdom shown by Mr. Potts in 

 confining himself to those sources from which to draw his "prol^lems" 

 — as it is the somewhat fanciful practice of the University to deno- 

 minate all propositions whatever. We shall offer no opinion on 

 this question ; but assume that Mr. Potts had reasons satisfactory 

 to his own mind for this act of deference to his University prede- 

 cessors. At all events we have here a vast mass of " Exercises " of 

 all degrees of difficulty, from the most simple to the most trans- 

 cendent ; and certainly a great number of them are as remarkable for 

 their elegance as for their difficulty. 



The practice of "problem-solving" is much and very properly in- 

 sisted on in the Cambridge course of reading. Possibly the study of 

 problems which have been set in former years may be the best means 

 of preparing the men to solve those which may be set hereafter. It 

 may be under such a supposition that Mr. Potts so limited his grounds 

 of selection. After all, as the Euclid is for the most part confined to 

 the " Freshman's year," these exercises would have far transcended 

 the powers of the men without occasional, indeed frequent, sugges- 

 tions from a tutor. Many of them would embarrass even an expert 

 geometer, if placed before him suddenly in the course of his tutorial 

 duties — and some of them, under the same circumstances, the ablest 

 geometers of the present century. To obviate this objection, Mr. 

 Potts has published in his Appendix, a series of " Hints " more or 

 less full as the occasion seemed to demand. To use the language 

 of a respected cotemporary, in which we fully concur, we should 

 describe them thus : — " In some cases references only are made to 

 the proposition on which a solution depends ; in others we have a 

 step or two of the process indicated ; in one case the analysis is briefly 

 given to find the construction or demonstration ; in another case the 

 reverse of this. Occasionally, though seldom, the entire process is 

 given as a model ; but most commonly, just so much is suggested as 

 will enable a student of average ability to complete the whole solu- 

 tion — in short just so much (and no more) assistance is afforded as 

 would, and must be, afforded by a tutor to his pupil. Mr. Potts ap- 

 pears to us to have hit the ' golden mean ' of geometrical tutorship." 



In order to render iiis work more extensively useful, Mr. Potts has 

 printed a smaller edition for the use of schools, containing the first six 

 books of Euclid with the principal notes on each, and a selection from 

 the Exercises sufhcicnt for all the purposes of school-education. 

 Being printed on the same arrangement as the larger edition, and 

 published at a price lower, we believe, than any other edition of 

 Euclid, it cannot fail to meet the wants of a large class of schools in 



