25 AN TIENT METAPHYSICS. Book I. 



geometry and arithmetic, and has given us an excellent work upon 

 each of thefe fciences. But he did not know the philofophy of ei- 

 ther of them, not even what the fubjcd of them is : At leaft he 

 has not told us that the fuhjedl; of both of them is quantity ; and 

 that quantity is that which is divifible into parts, which parts are 

 either continuous, or difcrete, that is feparated. It the parts are con- 

 tinuous, they make what is called 7nagnitu{h, which is the fubje£t 

 of geometry ; if they are difcrete, they make what is called number, 

 •which is the fubje6t oi arithmetic. Now, a man, who docs not know 

 to what category the fcience he treats belongs, mav be faid, in a 

 philofophical fcnfe, not to know what he treats. Euclid, therefore, 

 not knowing that both the fciences belong to the Category, or ge- 

 neral idea of Quantity, and not being able to diftinguifh the two fpe- 

 ciefes of that quantity, may be faid not to have known, philofophical- 

 ly, what either of the fciences is. And the definition he has given 

 us of what he makes to be the firft principle of geometry, viz. a 

 point, (hows that he was no philofop^er ; for he fays, ' That a Point 

 ' is that which has no parts or magnitude.' Now, that is the defini- 

 tion of an immaterial fubftance, not of a point, which is certainly a 

 material fubftance, being the extremity of a line, as in an after defini- 

 tion he tells us it is. But, bcfides this connexion which it has v/ith 

 aline, it has an exiftence by itfelf : For, as Ariftotle has obferved, it 

 lias a. place, and, confequently, muft be matter or body; whereas, as 

 the fame author tells us, a monade has no place. And this he makes 

 to be the difference betwixt the two Iciences, but which Euclid does 

 not appear to have known; though the difference be fo great, that 

 geometry applies only to matter or body, whereas, arithmetic ap- 

 plies to all things, material or inimaterial, fubftance or quality ; 

 fo that arithmetic, though it be fo common a fcience, is the moft 

 univerfal and moft comprehenfive of all fciences, as it applies to 

 every thing that exifts But though Euclid fe-ms not to have 

 been able to difcriminate thefe two Iciences of arithmetic and geo- 

 metry. 



