On Euclid's Twelfth Axiom. 207 



8. Salts. 



9. Lignin. 



The leaves of the Matico are easily reduced to a fine pow- 

 der, which has the colour of powdered senna ; when mixed 

 with any thick vehicle, as syrup, &c., it presents an excellent 

 mode of administering them, though, as will be evident, only 

 adapted for extemporaneous prescription, as the essential oil, 

 upon which it is probable much of their medicinal effect de- 

 pends, would be rapidly dissipated by keeping. The cold 

 infusion (Exp. 1), as it extracts all the active principles con- 

 tained in the plant, seems the best form for obtaining its me- 

 dicinal properties. The time required for its preparation 

 need not exceed four hours, as in that time water extracts all 

 that can be taken up by a single maceration, and but little is 

 gained by maceration in fresh water, even though continued 

 for a considerable time, as the liquid rapidly acquires its 

 maximum density. 



XXXIV. On Euclid's Twelfth Axiom. By X. Y. 

 To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 

 f N addition to the innumerable attempts which have so often 

 *• been made to demonstrate the twelfth axiom of Euclid, 

 one of a novel description has been given by Mr. Meikle in 

 Jameson's Journal for April last. For this purpose, he proves, 

 1st, that triangles, the areas of which are equal, have the sums 

 of their angles equal ; 2ndly, that if in one triangle the sum of 

 the angles differed from two right angles, so it would in every 

 triangle, and the difference would always be proportional to 

 the area. Thus far the process is liable to no objection ; and 

 if it be granted that there is no triangle which can have the 

 sum of its angles inappreciably small, his third step or infer- 

 ence from the second would be a complete reductio ad ahsur- 

 dum, viz. that a triangle of a certain magnitude would have its 

 angles either negative, or some two of them amounting to at 

 least two right angles. 



It will now be for mathematicians to decide on the doubtful 

 point just stated ; but at any rate the first and second propo- 

 sitions will form, as it were, two new instruments wherewith 

 to perfect the theory of parallel lines. Mr. M. has shown 

 that they are fatal to the celebrated demonstration of Ber- 

 trand; in which, besides, it is laid down as self-evident that any 

 angle, however minute, may be multiplied to exceed any given 

 angle. This is nearly the same with what is employed by 

 Mr. Meikle, as noticed above. 



X.Y. 



