I 



Length and Space. 75 



the science, and remove the prhicipal obstacles that He iti 

 tlie way of the young student's advancement. Besides these 

 assumptions, a new one has been usually found necessary 

 to the illustration of parallel lines. Legendrc is said to 

 have removed the necessity of this assumption in two ways. 

 — Leslie professes to have removed the difficulty, in 

 prop. 23d, book I. of his Elements of Geometry, but 

 has not entirely succeeded. If logical definitions could 

 be found for a straight line and angle, which would 

 lea<l to direct proofs of the different properties of these 

 two objects, as well as of parallel lines ; it appears to 

 me, that the theory of geometry would be complete. — 

 Our notions of length, breadth, thickness; of a body, a 

 surface, aline; are derived from the senses, and cannot, 

 in all probability, be derived from any other source. 



Number is derived from all the senses, and is a property 

 of all objects whatever, even of such as are incorporeal. 

 Arithmetic is therefore the simplest of all sciences. The 

 only terms which it requires to be understood without 

 definition are, one, sum, dincrence. When the import of 

 these terms is settled by convention, and by reference to 

 the senses, all the others required, may be defined ; and 

 thus, the science is erected by the contempliilions of the 

 mind itself. 



In this imperfect Essay, I have endeavoured to invcitigate, 



1.— How idea* of leiigUi and kliurtai-M ui°c iiitrodiicvd, mid wliut we 

 undcritaiid of tlicic qualities, aud the rUc of llic wurd» deiiutiug 

 tlii-ni. 



2.— My wliuthc-ii'citiliry arc conveyed to ii«. 



3.— Ili>w our liiiiKunic)' on tliU itiilijfcl l(i fuillicr iin|ir(ivi-nii'iil. 



