CHARACTERS. 



veyance of the knowledge of things. 

 We shall here subjoin the principal of 

 them. 



CHARACTERS used in Algebra and Arith- 

 metic. 



a, b t c, d, &c. the first letters of the al- 

 phabet, are the characters of given quan- 

 tities ; and z, y, x, &c. the last letters, are 

 the characters of quantities sought. See 

 the article ALREBRA. 



m, n, r, s, t, &c. are characters of inde- 

 terminate exponents both of ratios and of 

 powers : thus, x m , y n , z r , &c. denote un- 

 determined powers of different kinds; 

 m x, n if, r z, different multiples or sub- 

 multiples of the quantities x, y, z, accord- 

 ing as m, n, r, are either whole numbers 

 or fractions. 



4- is the sign of the real existence of 

 the quantity it stands before, and is call- 

 ed an affirmative or positive sign. It is 

 also the mark of addition, and is read 

 plus, or more ; thus a 4- 6, or 3 -f- 5, im- 

 plies a is added to b, or 3 added to 5. 



before a single quantity is the sign 

 of negation or negative existence, shew- 

 ing the quantity to which it is prefixed to 

 be less than nothing. But between quan- 

 tities, it is the sign of subtraction, and is 

 read minus, or less ; thus, a b, or 8 4, 

 implies b subtracted from a, or 8 after 4 

 has been subtracted. 



= is the sign of equality, though Des 

 artes and some others use this mark X; 

 thus, a = b signifies that a is equal to b. 

 Wolfius and some others use the mark = 

 for the indentity of ratios. 



X is the sign of multiplication; shewing 

 that the quantities on each side the same 

 are to be multiplied by one another, as 

 a X b is to be read a multiplied into b ; 

 4x8, the product of 4 multiplied into 

 8. Wolfius and others make the sign of 

 multiplication a dot between the two 

 factors ; thus, 5 . 4 signifies the product 

 of 5 and 4. In algebra the sign is com- 

 monly omitted, and the two quantities 

 put together ; thus b d expresses the pro- 

 duct of b and d. When one or both of 

 the factors are compounded of several 

 letters, they are distinguished by a line 

 drawn over them ; thus, the factum of a 

 4- b c Into J, is wrote d X a -f- b c.) 

 Leibnitz, Wolfius, and' others, distin- 

 guish the compound factors by including 

 them in a parenthesis ; thus (a + b c dj 



-T- is the sign of division ; thus, a -7- b 

 denotes the quantity a to be divided by 

 b. In algebra the quotient is often ex- 

 pressed like a fraction ; thus, -7 denotes 



the quotient of a divided by b. Wolfius 

 makes the sign of division two dots ; thus, 

 12 : 4 denotes the quotient of 12 divided 

 by 4 = 3. If either the divisor or divi- 

 dend, or both, be composed of several 

 letters, for example, a -f- b -~ c, instead 

 of writing the quotient like a fraction, 



- ' Wolfius includes the compound 



quantities in a parenthesis ; thus, (a -}* 6) 

 : c. 



is the character of involution : du is 

 the character of evolution. 



7 or CT are signs of majority ; thus a 

 "7 b expresses that a is greater than b. 



or *D are signs of minority ; and 

 when we would denote that a is less than 

 b, we write a b, or a -3 b. 



co is the character of similitude used 

 by Wolfius, Leibnitz, and others : it is 

 used in other authors for the difference 

 between two quantities, while it is un- 

 known which is the greater of the two. 



:: is the mark of geometrical propor- 

 tion disjunct, and is usually placed be- 

 tween two pair of equal ratios, as 3 : 6 

 :: 4 : 8, shews that 3 is to 6 as 4 is to 8. 



the mark of geometrical proportion 

 continued, implies the ratio to be still 

 earned on without interruption, as, 2, 4, 

 8, 16, 32, 64 ~ are in the same uninter- 

 rupted proportion. 



\/ is the character of radicality, and- 

 shews, according to the index of the 

 power that is set over it, or after it, that 

 the square, cube, or other root, is ex- 

 tracted, or to be extracted ; thus, ^/ 16, 

 or v/ 1 16, or ^/ (2) 16, is the square 

 root of 16, ^/ 25, the cube root of 25, 

 &c. This character sometimes affects 

 several quantities, distinguished by a line 

 drawn over them ; thus ^/ b -\- d de- 

 dotes the sum of the square roots of b 

 and d. When any term or terms of an 

 equation are wanting, they are generally 

 supplied by one or more asterisms ; thus, 

 in the equation 



vanishing is marked with an asterism, aS 

 y> #i/> 1 + < ? . 



CHARACTERS used in astronomy. 



Characters of the planets. 

 Ij Saturn Q Sun C Moon 

 ^ Jupiter 9 Venus Earth 

 Mars Mercury. 

 Of the signs. 



f> Aries St Leo / Sagittarius 

 fc! Taurus H Virgo 1ft Cupricornus 

 n Gemini =2= Libra $~ Aquarius 

 05 Cancer n^ Scorpio X Pisces. 



