222 % Notices respecting New Books. 



extensive knowledge of science, could have written, — and such we 

 know to be the case with the author*. 



The Elements of Geometry, with Notes. By J . R. Young. 



The great excellence of Euclid is well known to consist in the 

 completeness and perfect accuracy, as well as the general sim- 

 plicity and elegance of his demonstrations, admitting no assumption, 

 no step in the process of his reasoning that has not been previously 

 established, and at the same time, with this requisite, usually adopt- 

 ing the shortest course for arriving at his conclusion. It is not, how- 

 ever, pretended that this admirable work, so long and so deservedly 

 received as the text-book for instruction, is absolutely free from de- 

 fects. Even the very rigour of his proofs is sometimes the source of 

 so much intricacy and abstruseness, especially in the equally difficult 

 and important branch of the mathematics, the doctrine of propor- 

 tions, as to form a serious and discouraging obstacle fc to the progress 

 of the learner. The want of success in every attempt hitherto made 

 to lessen this difficulty, might seem to render the task hopeless. The 

 aim of Mr. Young, however, in the work before us, has been, with- 

 out impairing the completeness and satisfactory nature of his de- 

 monstrations, to contract and facilitate the labour of the student as 

 much as possible by simplicity and conciseness, and also to add to 

 the extent and accuracy of his geometrical knowledge. Nor do we 

 hesitate to recommend his treatise, not certainly as superseding the 

 use of Euclid, but as a useful auxiliary to that great work. His ob- 

 servations on the theory of parallel lines j his demonstration of the 

 converse of every proposition where this is possible, and showing its 

 failure, where it is not ; the labour he has bestowed on the doctrine 

 of proportions, as well as his corrections of many errors of preceding 

 geometers, and supplying their defects, together with his minute 

 attention to accuracy throughout, — may be justly considered as ren- 

 dering his performance valuable, especially to the learner. 



The notes are numerous, and most of them important. Among the 

 various errors and defects of modern geometers detected and cor- 

 rected in them, one instance especially is singular, and deserves to 

 be noticed. Mr. Thomas Simpson, in his Elements of Geometry, has 

 substituted in the place of the seventh proposition of Euclid's sixth 

 book, one which Mr. Young has proved to be absolutely false. This 

 is the more remarkable, as, though the work in which it occurs has 

 been in the hands of geometers more than seventy years, this error 

 has hitherto escaped detection. Even Dr. Robert Sirnsou, the edi- 

 tor of Euclid, though entertaining no very friendly feeling towards 

 his contemporary, suffered it to pass unnoticed. A similar error oc- 

 curs also in Mr. Leslie's Geometry, Prop. xiv. B. vi. last edition. 



As the celebrated propositions of Euclid, (B. i. Prop. 47.) the 

 discovery of which is attributed to Pythagoras, admits of various de- 

 monstrations, Mr. Young has given three j the last of which in the 

 notes is concise and simple, though that inserted in the text instead 

 of Euclid's, is inferior to the latter, not only in elegance but in sim- 

 plicity also. 



* His first Essay was a paper in the 46th vol. of the Phil. Mag. p. 15. 



The 



