244 REASONING. 



so-called Definitions. The remainder of the science is made 

 up of the processes employed for bringing unforeseen cases 

 within these inductions ; or (in syllogistic language) for prov- 

 ing the minors necessary to complete the syllogisms; the 

 majors being the definitions and axioms. In those definitions 

 and axioms are laid down the whole of the marks, by an artful 

 combination of which it has been found possible to discover 

 and prove all that is proved in geometry. The marks being 

 so few, and the inductions which furnish them being so obvious 

 and familiar ; the connecting of several of them together, 

 which constitutes Deductions, or Trains of Keasoning, forms 

 the whole difficulty of the science, and with a trifling excep- 

 tion, its whole bulk; and hence Geometry is a Deductive 

 Science. 



5. It will be seen hereafter* that there are weighty 

 scientific reasons for giving to every science as much of the 

 character of a Deductive Science as possible ; for endeavouring 

 to construct the science from the fewest and the simplest 

 possible inductions, and to make these, by any combinations 

 however complicated, suffice for proving even such truths, 

 relating to complex cases, as could be proved, if we chose, by 

 inductions from specific experience. Every branch of natural 

 philosophy was originally experimental ; each generalization 

 rested on a special induction, and was derived from its own 

 distinct set of observations and experiments. From being 

 sciences of pure experiment, as the phrase is, or, to speak 

 more correctly, sciences in which the reasonings mostly con- 

 sist of no more than one step, and are expressed by single 

 syllogisms, all these sciences have become to some extent, and 

 some of them in nearly the whole of their extent, sciences of 

 pure reasoning ; whereby multitudes of truths, already known 

 by induction from as many different sets of experiments, have 

 come to be exhibited as deductions or corollaries from induc- 

 tive propositions of a simpler and more universal character. 

 Thus mechanics, hydrostatics, optics, acoustics, thermo- 



* Infra, book iii. ch. iv. 3, and elsewhere. 



