MATHEMATICAL ELEMENTS 



OF 



NATURAL PHILOSOPHY. 



PART I. 



PURE MATHEMATICS. 



SECTION I. OF QUANTITY AND NUMBER. 



1. Definition. The letters of the al- 

 phabet are employed at pleasure for de- 

 noting any quantities, as algebraical sym- 

 bols or abbreviations. But, in general, the 

 first letters in order are used to denote known 

 quantities, and the last to denote unknown 

 quantities ; and constant quantities are often 

 distingwished from variable quantities in the 

 same manner. 



2. Definition. Quantities are equal 

 when they are of the same magnitude. 



Scholium. The abbreviation al^i implies that a is 

 equal to hi a'>h that a is greater than h; and a < i that 

 « is less than /•. 



3. Definition. Addition is the join- 

 ing of magnitudes into one sum. 



Scholium. The symbol of addition is an erect cross: 

 « + i implies the sum of a and I; and is called a more b. 



4. Definition. Subtraction is the tak- 

 ing as much from one quantity as is equal 

 to another. 



Scholium. Subtraction is denoted by a single line, as 

 a—b, or a less b, which is the part of a remaining when a 

 part equal to b has been taken from it. 



VOL. II. 



5. Definition. A negative quantity is 

 of an opposite nature to a positive one, with 

 respect to addition or subtraction ; the con- 

 dition of its determination being such, that 

 it must be subtracted where a positive quan- 

 tity would be added, and the reverse. 



Scholium. A negative quantify is denoted by the sign 

 of subtraction ; thus if a + ''^o— <",'!'——<" and cr: — b, 

 A debt is a negative kind of property, a loss a negative gain, 

 and a gain a negative loss. 



6. Definition. A unit is a magnitude con- 

 sidered as a whole complete within itself. 



Scholium. When any quantities are enclosed in a pa- 

 renthesis, or have a line drawn over them, they are con- 

 sidered as one quantity with respect to other symbols; 

 thusa— (fc+c) or a—b-{-c implies the excess of a above the 

 sum of b and c. 



7. Definition. A whole number is a 

 number composed of units by continued ad- 

 dition. 



Thus one and one compose two, 2+1—3, 34-i::z4, 

 or 2-f-2=4. Such numbers are also calltd multiples of 

 unity. 



8. Definition. A simple fraction is a 

 number which by continual addition coni- 



B 



