318 NOTE ON EUCLID. 



sonable and probable, an observation made on a series of abnormal 

 forms enables me to give a reason for the curious numerical relation 

 in the circles of parts in the two great series of plants, already as a 

 fact determined by observation. If each phyton tends to produce 

 circles of three, and two are combined in the dycotyledonous plant, 

 we consider that there are six parts to be accounted for in each circle 

 of a dycotyledon, and we ask for an explanation of the actual number 

 being only five. I have examined a great many cases of two, and one 

 of even four flowers so adhering together as to become one, and 

 attending particularly to the number of parts in the circles, as com- 

 pared with that of a single flower of the kind, I have found occa- 

 sionally under peculiar pressure two parts lost in the union, one at 

 each point of junction, but much more usually, so as to give a general 

 rule, one part lost in each united circle. Thus, in monstrous Irises 

 formed by a union of two flowers, five parts appear in all the circles, 

 or reduced to four in the inner circle of the perigonium ; in monstrous 

 Oenotheras, there are found seven parts each in the calyx, corolla and 

 carpels, and fourteen in the stamens. If then the natural course is for 

 a union of two circles into one, to be accompanied by the extinction 

 of one part, we at once derive from the union of two phytons, each 

 giving three parts to a circle, the number five, as the normal number 

 for dicotyledonous plants, while the occasional loss of two parts in 

 the united circle, under greater pressure, explains the commonness of 

 the number four in this class of plants. Hence, the number of parts 

 characteristic of the great divisions of the vegetable kingdom, is no 

 longer a mere empyrical observation, but a principle traced to its 

 cause, and accompanied in its announcement by a rational explanation. ' 

 I am withheld by the fear of occupying undue space from extending 

 these remarks, which I can only state are few and short, com- 

 pared with the materials which present themselves. 



NOTE ON EUCLID, PROPOSITION 5, BOOK I. 



BY REV. E. K. KENDALL, E. A. 



PEOFESSOE OF MATHEMATICS AND NATUEAL PHILOSOPHY, TEItflTT COLLE&E, TOEOIfro. 



Read before the Canadian Institute, 20th February,, 1858. 



The .5th proposition, proving the equality of the angles at the base 

 of an isosceles triangle, admits of the following immediate deductioa 

 as a corollary to the 4th proposition. 



