xlviii MODERN GEOMETRY IN ENGINEERING PRACTICE. 



first, until now, only complete text-book upon the subject, the " Geometric 

 der Lage," by Reye (Hannover, 1868), as the direct result of the graphical 

 statics of Culmann. 



Since then, the modern geometry has been introduced into all technical 

 institutions throughout Germany, and thus placed at the disposal of the 

 arts and sciences. 



As, according to its founder, Poncelet, it reaches the highest range of 

 speculation, so also in the most practical relations it acts to simplify and 

 condense : " Peu d peu let connaissances algebriques deciendront mains in- 

 dispensable*, et la science, reduite d ce qu'elle doit etre, d ce qu'elle devrait etre 

 dejd, sera ainsi mite d la portee de cette classe d'hommes, qui n'a que des mo- 

 ments fort rares d y consacrer" 



[For illustrations of the method of the modern geometry, the reader may 

 consult the Appendix to this chapter.] 



IX. 



THE MODERN GEOMETRY IN ENGINEERING PRACTICE. 



One who should infer that a science created thus from its very inception 

 with reference to the needs of practice* must have found access, above all, 

 in technical circles, would be much mistaken. As Culmann sent out his 

 graphical" statics, deep silence prevailed, and if the modern geometry ap- 

 peared here and there in the lecture plan of one and another polytechnic, it 

 was, without doubt, due to the zeal of some enthusiastic privat decent who 

 had undertaken the thankless task of holding forth to empty benches. 



Whence came this indifference to a discipline proceeding from the Ecole 

 poly technique? It is hard, indeed, to find a sufficient reason. We often 

 hear it said that by reason of the colossal extension which engineering 

 sciences have experienced, students are already overburdened. Most true ! 

 and it is just here that the modern geometry comes to our assistance. It 

 is precisely to this that the learned critic of Monge, Dupin, alludes : " II 

 itemize que dans Vetat actuel des sciences mathematiqucs U seul moyen d'em- 

 pScher que leur domaine ne devienne trap vasts pour notre intelligence, c'est 

 de generaluer de plus en plus les theories que ces sciences eiribrassent, afin 

 qu'un petit norribre des verites generales et fecondes soit dans la tete des 

 hommes ^expression abregee de la plus grande variete des f aits particuliers.' 1 '' 



The modern geometry in its present form starts with a small number of 

 elementary constructions whose properties are first set forth, and then, pro- 

 ceeding from these by combination and comparison, it covers the entire 

 department of space. The engineer, during and after his preparation, has 

 to do with space problems, with geometrical principles and constructions ; 



* Poncelet himself set upon the title-page of his work : " Ouvrage utile d 

 eeux qvi s'occupent des applications de la Geometric descriptive et d'operations 

 geometriques ur le terrain." 



