PROOF OF THE PROPERTIES OE PARALLEL LINES. 519 



"With these and all other ancient relics, the object of the intelligent 

 collector is not the mere gratification of an aimless curiosity, or the 

 accumulation of rarities of difficult acquisition, but the preservation 

 of objects calculated to furnish valuable scientific or historical truths. 

 As, however, such remains lose much of their value when the local- 

 ity and circumstances of their discovery are unknown, it is extremely 

 desirable not only to attach to each skull, package of bones, or 

 accompanying relics, the name and description of the locality where 

 they have been found, but also as soon as possible to mark this neat- 

 ly and indelibly upon the object itself. Where more than one skull 

 has been procured, and any of them are in a fragmentary state, it is 

 scarcely necessary to add that the utmost care should be taken to 

 keep the several portions of each skull distinct from the others ; as 

 even where it may be possible afterwards to separate them, this must 

 always be attended with much additional labor, and generally with 

 some uncertainty. In most cases the greater number of the teeth, 

 if not already loose, will be apt to fall out so soon as the skull becomes 

 dry ; it is therefore extremely desirable to prevent those belonging to 

 different skulls from becoming mixed. If this is attended to, there 

 can be no difficulty in correctly replacing them. When perfect they 

 add considerably to the value of such remains, as indications of the 

 physiognomical characteristics of the race to which they pertain, while 

 their condition supplies evidence of the nature of the food, and 

 the consequent habits and degree of civilization of the race. Finally, 

 however, it may be added that even very imperfect osseous fragments, 

 and relics of an apparently trivial character, are frequently well wor- 

 thy of preservation ; and many valuable and interesting deductions 

 may be based, by the intelligent scientific observer, on what would 

 appear to others insignificant trifles, or even, perhaps, a mere 

 handful of rubbish. 



AN EXAMINATION OF LEGENDEE'S PEOOF OF THE 

 PEOPEETIES OF PAEALLEL LINES. 



BY THE REV. GEORGE PAXTON YOUNG, M. A.., 



PROFESSOR OF LOGIC AND METAPIIT9ICS, KNOX'S COLLEGE, TORONTO. 



In order to establish the properties of parallel straight lines, Euclid 

 assumed it as an Axiom, that " if a straight line meet two other 

 " straight lines, so as to make the interior angles on the same side of 

 " it less than two right angles, these straight lines, being continually 



