INTRODUCTORY DISCOURSE OF THE 



Rotates the facultie. .bore low puwuiU, purifier nd reBne. the pMsion., and helps our reason to assuage 

 their violence. . . , . 



It is very true, that the fundamental lessons of philosophy may to many, at first ;ht, i 

 forbidding aspect, because to comprehend them requires an effort of the mind somewhat though 

 not much, greater than is wanted for understanding more ordinary matters; and the most important 

 branches of philosophy, those which are of the most general application, are for that very r 

 less easily followed, and the less entertaining when apprehended, presenting as they do, few parti 

 or individual object, to the mind. In discoursing of them, moreover, no figures will be at present^ 

 to assist the imagination ; the appeal is made to reason, without help from the senses. But be not, there- 

 fore, prejudiced against the doctrine, that the pleasure of learning the truths which ph.losophy unfolds is 

 truly above all price. Lend but a patient attention to the principles explained, and giving us , 

 stating nothing which has not some practical use belonging to it, or some important doctrme cot 

 with it you will soon perceive the value of the lessons you are learning, and begin to interest yourselves 

 in comprehending and recollecting them ; you will find that you have actually learnt something of science, 

 while merely engaged in seeing what its end and purpose is ; you will be enabled to calculate for yourselves, 

 how far it is worth the trouble of acquiring, by eiamining samples of it; you will, as it were, taste a 

 little, to try whether or not you relish it, and ought to seek after more; you will enable yourse 

 go on and enlarge your stock of it; and after having first mastered a very little, you will proceed so far, 

 as to look back with wonder at the distance you have reached beyond your earliest acquirement*. 



The Sciences may be divided into three great classes: those which relate to Number and Quanh/y- 

 those which relate to Matter-m& those which relate to Mind. The first are called the Mathematwt, 

 and teach the property of numbers and of figures; the second are called Natural Philosophy , and teach the 

 properties of the various bodies which we are acquainted with by means of our senses; the third are called 

 AJrfferfM! or Moral Philosophy, and teach the nature of the mind, of the existence of winch we have the 

 most perfect evidence in our own reflections; or, in other words, they teach the moral nature of man, b 

 as an individual, and as a member of society. Connected with all the sciences, and subservient to them, 

 though not one of their number, is History, or the record of facts relating to all kinds of knowledge. 



I. MATHEMATICAL 



THE two great branches of the Mathematics, or the two mathematical sciences, are Arithmetic, the science 

 of number, from the Greek word signifying number, and Geometry, the science of figure, from the Greek 

 words signifying measure of the ^A.-land-measuring having first turned men's attention to it. 



When we say that 2 and 2 make 4, we state an arithmetical proposition, very simple indeed, but 

 nected with many others of a more difficult and complicated kind. Thus, it is another proposition, somewhat 

 ess simple but still very obvious, that 5 multiplied by 10, and divided by 2, is equal to, or make. 



mber wi h 100 divided by 4-both results being equal to 25. So, to find how many farthings there are 



n 1 000* and how many minutes in a year, are questions of arithmetic which we learn to work by being 



tauMit the principles of the science one after another, or, as they are commonly called, the rules of add.t.on, 



subtraction, multiplication, and division. Arithmetic may be said to be the most simple, though among 



,e most useful of the sciences; but it teaches only the properties of particular and known numbers and it 



oi.tr enables us to add, subtract, multiply, and divide those numbers. But suppose we wish to add subtract 



iuitiplr or divide numbers which we have not yet ascertained, and in all respects to deul with them as it 



they were known, for the purpose of arriving at certain conclusions respecting them, and among other thing., 



of discovering what they are; or, suppose we would examine properties belonging to all numbers ; tins 



be performed by a peculiar kind of arithmetic, called Universal arithmetic, or Algebra.' 



arithmetic, you will presently perceive, carries the seeds of this most important science m its bosom That, 



P pL wi/inquire what is the number which multiplied by 5 makes 10? Th is found it we d.vide 



-it is 2 but suppose that, before finding this number 2, and before knowing what it is, we would 



a,' 1 it whatever it mny turn out, to some other number; this can only be done by putting some mark, such 



a letter of the alphabet, to stand for the unknown number, and adding that letter as it it were a known 



imbrr Thus, suppose we want to find two nu,nl,,r* which, added together, make 9, and multiplied by 



1 another, make iT There are many which, ad.1,,1 together, make 9; a, 1 and 8; 2 and 7; 8 and 6; 



\Vo have thrr,foro, orrn,n to use th, MOOnd ,-ondition, that multiplied by one another they 



,,ld make ->0 and to work upon this condition before we have discovered the particular numbers. We 



must therefore/suppose the number, to be found, and put letter, for them, and by reasoning upon those 



ucordinir to both the two condition, of adding and multiplying, we find what they must each of them 



Rnm n order to fulfil or answer the conditions. Algebra teaches the rules for conciuctmg th 



rewoning, and obtaining this result successfully; and by means of it we are enabled to flnd o 



Algebra, from th Arabic word, -ikying the ** tffraclio.., th Arab, having brought the knowledge of it into 



