BIO 



BIO 



The sum of the co-efficients 

 Ill + &c.is2'. 



For if or=a=l, then 07+01/1 

 1 



+ n a x n I + n . 



n l 



And x a i=.r n a xn *+n. 



By addition, ^r+7/^ + xd\ n = 2 . xn 

 ^.l_a*ii >+&c, 



Or 



2^ 2 



'+&C. 



By subtracting one seriesfromthe other, 



n 1 



&c. 



n 2 3 . 



3 



The trinomial a+6+cmaybe raised 

 to any power by considering two terms 

 as one factor, and proceeding as before. 



Thus, a+6+?=a+w . 6+c . fl~i 



A 



&c. and 



the powers of b-\-c may be determined 

 by the binomial theorem. 



BIOGRAPHY, a very entertaining 1 and 

 instructive species of history, containing 

 the life of some remarkable person or 

 persons. 



Lord Bacon regrets, that the lives of 

 eminent men are not more frequently 

 written : for, adds he, though kings, 

 princes, and great personages, be few ; 

 yet there are many other excellent men, 

 who deserve better than vague reports 

 and barren elogies. 



Biography, or the art of describing 

 and writing lives, is a branch or species 

 of history, in many respects as useful and 

 Important as that of history itself; inas- 

 much as it represents great men more 

 distinctly, unencumbered with associates ; 

 and descending into the detail of their 

 actions and characters, their virtues and 

 failings, we obtain a more particular, and, 

 of course, a more interesting acquaint- 

 ance with individuals, than general his- 

 tory allows A writer of lives may, and 

 ought, to descend to minute circum- 

 stances and familiar incidents. He is ex- 

 pected to give the private, as well as the 

 public, life of those whose actions he re- 



cords ; and it is from private life, frottl 

 familiar, domestic, and apparently trivial 

 occurrences, that we often derive the 

 most accurate knowledge of the real cha- 

 racter 



The subjects of Biography are not on- 

 ly the lives of public or private persons, 

 who have been eminent and beneficial to 

 the world, but those also of persons no- 

 torious for their vice and profligacy, 

 which may serve, when justly character- 

 ised, as warnings to others, by exhibit- 

 ing the fatal consequences, which, sooner 

 or later, generally follow licentious prac- 

 tices. As for those who have exposed 

 their lives, or devoted their time and 

 talents, for the service of their fellow- 

 creatures, it is but a debt of gratitude to 

 perpetuate their memories, by making 

 posterity acquainted with their merits 

 and usefulness. In the lives of public 

 persons, their public characters are prin- 

 cipally, but not solely, to be regarded ; 

 the world is interested in the minutest 

 actions of great men, and their examples, 

 both as public and private characters, 

 may be made subservient to the well be- 

 ing and prosperity of society. 



It has been a matter of dispute among 

 the learned, whether any one ought to 

 write his own history. There are in- 

 stances, both ancient and modern, that 

 may be adduced as precedents for the 

 practice : and the reason assigned for it 

 is, that no man can be so much the mas- 

 ter of the subject as the person himself: 

 but, on the other hand, it is a very diffi- 

 cult task for any one to write an impartial 

 history of his own actions. Plutarch men- 

 tions two cases, in which it is allowable 

 for a man to commend himself, and to be 

 the publisher of his own merits ; which 

 are, when the doing of it may be of con- 

 siderable advantage either to himself or 

 to others. Notwithstanding this high au- 

 thority, the former case is unquestion- 

 ably liable to great objections, because a 

 man is to be the judge in his own cause, 

 and therefore very liable to exceed the 

 limits of truth, when his own interests 

 are concerned, and when he wishes to 

 render himself conspicuous for virtue or 

 talents. The ancients, however, had a 

 peculiar method of diverting the reader's 

 attention from themselves, when they 

 had occasion to record their own actions, 

 and of thus rendering what they said less 

 invidious, which was, by speaking of 

 themselves in the third person. Among 

 the moderns a practice has been intro- 

 duced, which cannot be too strongly re- 

 probated, though sanctioned by men of 

 great talent, integrity, and real worth ; 



