i68 



NA TURE 



[February 14, 1901 



"To begin a work of the difficulty of Euclid any 

 earlier than this will hardly be sanctioned by American 

 teachers ; the hard Euclidean method must change, or 

 the subject must remain thus late in the curriculum. If 

 the object were, as seems to be the case in England, to 

 cram the memory for an examination, it could be attained 

 here as easily as there. But the considerable personal 

 experience of the writer, as well as the far more extended 

 researches of others, convinces him that as a valuable 

 training in logic, as a stimulus to mathematical study, 

 and as a foundation for future research, the study of 

 Euclid as undertaken in England is not a success." 



He then quotes Prof. Minchin, who says :— 



" Why then is it that the teacher, when he comes to 

 the teaching of Euclid, is confronted with such great 

 difficulties that his belief in the rationality of human 

 beings almost disappears with the last vestiges of that 

 good temper which he himself once possessed? The 

 reason is simply that Euclid's book is not suitable to the 

 understanding of young boys." 



We wish that Pro*". Minchin had gone further and said 

 that whereas every boy and man takes an interest in ex- 

 perimental science, including geometry and mensuration, 

 only a few ever take an interest in demonstrative geo- 

 metry ; and it is both wrong and foolish to insist on its 

 being learnt by boys whom it stupefies, whatever their age 

 may be. All educationists are agreed that the English 

 system of insisting on all young boys learning demon- 

 strative geometry is quite wrong. Certainly, we know of 

 no educationist who has a word to say in favour of the 

 system prevailing in all English schools. We take it that 

 the system is maintained because it does not " pay " the 

 pupil in any sense whatever. Prof. Hudson is quoted as 

 saying, "To pursue an intellectual study because it 

 ' pays ' indicates a sordid spirit." Working at geometry 

 indicates no sordid spirit in our boys, but we are not so 

 sure as to what it indicates in the masters of English 

 schools. It " pays" them very well indeed. 



Give the brains of an average English boy a chance 

 of development, and he is full of common sense and 

 self-reliance and scientific method ; and yet the average 

 boy leaves our schools uneducated, with no knowledge, 

 and with the belief that he is stupid. Even Pythagoras 

 did not think that more than a very few men were 

 capable of the study of geometry ; hardly one legislator 

 or ruler or warrior from the time of Pythagoras to that 

 of Pappus made a study of geometry, although this was 

 a time when there were i^^^ kinds of intellectual study. 



Mr. Smith's statements as to the history of the subject 

 are fairly acceptable, as he keeps clear of debatable matter.i 

 Throughout, he is unwilling to give Semites much credit, 

 and I presume that it is in consequence of this that, in 

 describing the work of Diophantus, the Alexandrian be- 

 ginner in what we now call algebra, he forgets to mention 

 that in all probability all the early life of Diophantus was 

 spent among Asiatic peoples. Algebra, as we know it, 

 dates from the time of Haroun of the "Arabian Nights." 



1 As this notice was getting too long, we have cut cut much of what we 

 had written. We have here cut out some remarks as to the claim of 

 Napier of Merchiston to the invention of the use of decimals. But it is 

 rather important to re-wnte an observation made long ago b> Prof. 

 Ayrton : — " The units ought to be symmetrical with regard to tens and 

 tenths, and it would be more scientific to write i5oo'o332 as 15000032 

 or 15060032, or in some other way which shows its symmetry. It is 

 astonishing what trouble is given by the difference in rules between firiding 

 the logarithm of a number like 500 and a number like o'os. If they were 

 written 506 and 605 we should have the same rule for bjth. If we must 

 retain the present unscientific meihod, let writers who wish to avoid 

 printers' errors avoid '05 and always write 0*05." 



NO. 1633, VOL. 63] 



No doubt it comes altogether from the Semites of 

 thousands of years before— the Semites who gave us all 

 religions and the usages of older civilisations, without 

 being able to give us their own subtler instincts ; who 

 taught Homer the decoration of a shield and Pericles 

 how to beautify Athens ; who gave Greece all its 

 geometry through Pythagoras the Tyrian ; who allowed 

 Thales and Herodotus and other peripatetic students to 

 absorb their science ; who taught the doctrine of 

 humanity to Socrates, and who did not mind taking to 

 themselves Aryan names either in Troy or Alexandria or 

 London. 



The earnest reader of Mr. Smith's book will probably 

 be led by it to think things out for himself. It is not 

 important that he should subscribe to the author's 

 opinions. Indeed, these opinions are rather in opposition 

 to one another, for Mr. Smith is able to see that there is 

 much to be said in favour of the views of almost all the 

 writers whom he quotes. He gives many hints which 

 will be found very suggestive by a thoughtful teacher of 

 arithmetic and algebra who is not himself a good mathe- 

 matician. They may, however, lead a common man to 

 obscure the minds of his pupils, giving them, for 

 example, all the historical methods of solving quadratics 

 before they know much about quadratics. When 

 one clears an equation of fractions by multiplying all 

 across by some function of the unknown, the resulting 

 equation contains other roots than the original one— yes, 

 but it is not wise to trouble beginners with too much of 

 this. One may philosophise deeply over our very 

 simplest notions, but " Sartor Resartus " ought only to be 

 read by grown-up people. JOHN Perrv. 



HUMAN ORIGINS. 

 In the Beginning {Les Origims). By J. Guibert, S.S. 

 Translated from the French by G. S. Whitmarsh. 

 Pp. xvi -i- 379. (^London : Kegan Paul, Trench, 

 Trubner and Co., Ltd., 1900.) 



THE author of this book is the Superior of the Insti- 

 tute Catholique in Paris, but when he wrote it he 

 was professor of natural science at Issy. The book is 

 the outcome of an endeavour to train young ecclesiastics 

 who, in the future, would have to propagate and defend 

 the faith. It is rightly insisted as most essential that 

 young clerics should be wanting in no knowledge con- 

 cerning humanity ; and it is pointed out that two perils 

 of equal danger have to be avoided— an ill-founded com- 

 pliance with the theories in favour amongst the learned, 

 and a blind attachment to certain ideas which have no 

 firm foundations, but which some men erroneously con- 

 sider as identical with the faith. The author imposes 

 on himself the three following obligations : (i) honestly 

 to explain systems, (2) assert with firmness what is well 

 established, (3) leave the questions open which have not 

 yet received a solution ; and he concludes his preface 

 thus : 



" If, as science advances, it should illuminate some 

 doubtful pojnt, or show the fallacy of some solution 

 which I had looked upon as finally settled, I should not 

 hesitate 10 yield myself to these indications. And if the 

 Church, in whose infallibility I firmly believe, should 

 deliver a judgment contrary to my assertions, I am ready, 

 in advance, to accept her teaching." 



