CHAPTER X 



SOME USES OF MATHEMATICS 



WE are all familiar with the convenience of abbreviat- 

 ing words by single letters. Certain cases are found 

 in dictionaries and are taught in schools so that their 

 use is practically universal within the limits of the 

 particular language. The letter is used as a symbol 

 for the word just as the word is itself a symbol for the 

 idea. The convenience is, of course, one of brevity in 

 writing. In mathematics symbols are used which 

 are universally recognized without regard to the lan- 

 guage of the student. This is a convenience, but the 

 chief advantage which mathematics offers to science 

 is its methods of handling symbolized ideas so as to 

 reach conclusions which in some instances would be 

 practically unattainable by any other form of reason- 

 ing. In fact, mathematics, usually defined as "the 

 science concerned with the logical deduction of con- 

 sequences from general premises," may be concisely 

 defined as "symbolized logic." Let us then examine 

 a few illustrations which will show this convenience 

 of abbreviation and also in a very elementary way 

 the logical deduction of consequences from assumed 

 premises. 



In determining the area of a rectangle we multiply 

 the length by the breadth. Thus if the sides are 3 

 and 4 inches we say the area is 12 square inches since 



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