342 ON THE ULTIMATE 



in such a way that as many as possible may be contained 

 in a given area. 



Thus it is wonderfully made known to us how in the 

 very origination of things a certain Divine mathematics 1S 

 or metaphysical mechanics is employed and the greatest 

 quantity is brought into existence [lit. the determination 

 of the greatest quantity takes place]. So among all 

 angles the determined [fixed] angle in geometry is the 

 right angle 19 , and so also liquids put into heterogeneous 

 media take the form of greatest capacity, that of a sphere. 

 But best of all is the illustration we get in ordinary 

 mechanics, where, when several heavy bodies act against 

 one another, the resultant motion is that which produces 

 the greatest fall on the whole 20 . For as all possible 

 things by an equal right tend to exist in proportion to 

 their reality, so all weights by an equal right tend to 

 fall in proportion to their gravity ; and as in the case of 

 the latter there is produced a motion which involves the 

 greatest possible fall of the heavy bodies, so in the case of 

 the former there is produced a world in which the greatest 

 number of possible things comes into existence. 

 / And thus we have physical necessity coming from 

 metaphysical necessity ; for although the world is not 

 metaphysically necessary, so that its opposite involves 

 a contradiction or logical absurdity, it is nevertheless 

 physically necessary or so determined that its opposite 

 involves imperfection or moral absurdity. And as possi- 

 bility is the principle of essence, so perfection or degree 



coming into existence. Only compossible essences can give rise 

 to co-existing phenomena, and time and space are the order of 

 co-existence of these phenomena. See Introduction, Part iii. p. 102. 

 is < \\nhen God calculates and employs thought, the world is 

 made.' De connexione inter res et verba (1677) (E. 77 a ; G. vii. 191). 

 The phrase was written by Leibniz on the margin of the MS. and 

 may accordingly be of later date. 



19 The right angle is always 90 ; but an acute or an obtuse angle 

 is variable in size. The right angle is thus l fixed ' or ' determined, ' 

 and the right angle is the greatest angle at which one line can 

 meet another. 



20 The suggestion is of some such arrangement as we have in 

 a system of pulleys. 



