Objects, Advantages , And Pleasures Of Science.

perfect evidence in our own reflections ; 01 in other words , they teach the moral nature of man , both 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 SCIENCE . 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 earth—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 connected with many others of a more difficult and complicated kind . Thus , it is another proposition , somewhat less simple , but still very obviousthat 5 multiplied b 10 and

, y , divided by 2 is equal to , or makes the same number with , 100 divided by 4—both results being equal to 25 . So , to find how many farthings there are in £ 1000 , and how many minutes in a year , are questions of arithmetic which we learn to work by

being taught the principles of the science one after another , or , as they are commonly called , the rules of addition , subtraction , multi plication , and division . Arithmetic may be said to be the most simple , though among the most useful of the sciences ; but

it teaches only the properties of particular and known numbers , and it only enables us to add , subtract , multiply , and divide those numbers . But suppose we wish to add , subtract , multiply or divide numbers which we have not yet

ascertained , and in all respects to deal with them as if they were known , for the purpose of arriving at certain conclusions respecting them , and , among other things , of discovering what they are ; or , suppose we would examine properties belonging to

all numbers ; this must be performed b y a peculiar kind of arithmetic , called universal arithmetic , or Algebra * . The common arithmetic , you will presently

perceive , carries the seeds of this most important science , in its bosom . Thus , suppose we inquire what is the number which multiplied by 5 makes 10 ? This is found if we divide 10 by 5—it is 2 ; but suppose that , before finding this number 2 and before knowing what it iswe

, , would add it , whatever it may turn out , to some other number ; this can only be done by putting some mark , such as a letter of the al phabet , to stand for the unknown number , and adding that letter as if it were a kno wn number . Thussuppose

, we want to find two numbers which , added together , make 9 , and multip lied by one another , make 20 . There are many which , added together , make 9 ; as 1 and 8 ; 2 and 7 ; 3 and 6 ; and so on . We have , thereforeoccasion to use the second

con-, dition , that multiplied by one another thay should make 20 , and to work upon this condition before we have discovered the particular numbers . We must , therefore suppose the numbers to be found , and

put letters for them , and by reasoning upon those letters , according to both the two conditions of adding and multiplying , we find what they must each of them be ¦ in figures , in order to fulfil or answer the conditions . Algebra teaches the rules for conducting this reasoning , and obtaining

this result successfully ; and by means of it we are enabled to find out numbers which ara unknown , and of which we only knosv that they stand in certain relations to known numbers , or to one another . The instance now taken is any easy one ; and

you could , by considering the question a little , answer it readily enough ; that is , by trying different numbers , and seeing which suited the conditions , for you plainly see that 5 and 4 are the two numbers sought ; but you see this by no certain or

general rule applicable to all cases , and therefore you could never work more difficult questions in the same way , and even questions of a moderate degree of difficulty would take an endless number of trials or

guesses to answer . Thus a shepherd sold his flock for £ 80 ; and if he had sold four sheep more for the same money , he would have received one pound less for each sheep . To find out from this , how many the flock consisted of , is a very easy question in algebra , but would require a vast many guesses , and a long time to hit D 2