84 INTRODUCTION 



other hand, the endeavour to find a Logical Calculus 

 (implying a universal philosophical language or system 

 of signs) is an attempt to apply in theological and philo- 

 sophical investigations an analytic method analogous to 

 that which had proved so successful in Geometry and 

 Physics ! . It seemed to Leibniz that if all the complex 



given magnitude in datis or in the antecedents [ce qui est pose] it will neces- 

 sarily also be diminished below every given magnitude in quaesitis or in the 

 consequents [ce qui en resulte]. Or, to put it more simply : when the 

 cases (or wJiat is given] continually approach and are finally lost in one 

 another, the consequences or results (or what is required) must do the same. 

 This again depends upon a more general principle, to wit : datis 

 ordinatis etiam quaesita sunt ordinata. [If there is order in the grounds 

 there will also be order in the consequents.] But, for the under- 

 standing of this, instances are necessary. It is known that the case 

 or supposition of an ellipse may be made to approximate, as much 

 as we like, to the case of a parabola, so that the difference between 

 the ellipse and the parabola may become less than any given differ- 

 ence, provided that one of the foci of the ellipse be made sufficiently 

 distant from the other, for then the radii vectores proceeding from 

 this distant focus will differ from parallel radii vectores as little as 

 we like. Consequently all the geometrical theorems which may be 

 proved of the ellipse in general can be applied to the parabola by 

 considering it as an ellipse one of whose foci is at an infinite 

 distance, or (to avoid this expression) as a figure which differs 

 from some ellipse by less than any given difference. The same 

 principle holds in Physics. For instance, rest may be regarded as 

 an infinitely small velocity or as an infinite slowness. Accordingly, 

 whatever is true of slowness or velocity in general ought also to be 

 true of rest, thus understood ; so that the law of rest should be 

 regarded as a particular ease of the law of motion. Otherwise, if 

 this does not hold, it will be a sure sign that these laws are ill- 

 constructed. In the same way equality may be regarded as an 

 infinitely small inequality, and inequality may be made to approxi- 

 mate to equality as much as we like.' See also New Essays, Intro- 

 duction, p. 376, and Nouveaux Essais, bk. iv. ch. 16, 12 (E. 392 a ; 

 G. v. 455) : ' But the beauty of nature . . . requires the appearance 

 of discontinuity [sauts~] and, so to speak, musical cadences among 

 phenomena.' In the letter to Bayle above quoted, Leibniz also 

 remarks (E. 106 a ; G. iii. 54) : ' It is true that in compound 

 things a small change may sometimes produce a great effect. For 

 instance, a spark falling upon a large mass of gunpowder might 

 overthrow a whole town ; but that is not contrary to our principle, 

 and might indeed be explained on general principles. But in the 

 case of elements or simple things nothing like this could happen ; 

 otherwise nature would not be the i-esult of infinite wisdom.' 



1 As to the analogy between Symbolic Thought and Algebra, &c., 

 cf. Locke, Essay, bk. ii. ch. 29, 9 (Eraser's ed. vol. i. p. 490). 

 See also Fraser, vol. ii. pp. 12 and 124, where further references 

 will be found. 



