M ATH EM ATIOS. ALGEBRA. 



[USB OF THE TABLES. 



be ha done to, he may then, for practice, work some 

 more complicated examples, such M the following : 



Find the value of 31* x (-Qff796) 



Ujl 



(a) 



log. 



log. (-03796)* 



(r) log. 15 



Henco log. 31* 



log. (-05796)' 



Ar. 0. log. 15 10. 



Ar. C. log.V2 10 



90577 



14913617 

 2 



3)2-9827234 



9942411 

 8-7631284 10 

 3 



62893832 10 

 1-1760913. 

 2) -3010300 



1505150 



6-2893852 10 

 8-8239087 10. 

 9-849485010 



6.9570200 

 9070179 



21 

 19 



00009057744 Ans. 



N.B. To find the logarithms of a mixed number, 

 reduce it to an improper fraction. 



To find the logarithm of a vulgar fraction, use the 

 formula 



If N - ? then log. N = log. o + Ar. Com. log. 6 10, 



b 



precisely as in division, excepting that there is no occasion 

 to find N itself. 



Thus, in the following example 



log. 37052 = 4-5688117 

 Ar. Com. log. 674161 = 6 -1712370 10 



9.7400487 10 



[Before entering into another department of mathe- 



matics, we shall make a few observations on those which 

 have already been explained. Although few of our 

 readers will have perused the preceding sections of this 

 volume without possessing some knowledge of mathe- 

 matics ; still the chapters on Arithmetic and Algebra, 

 by Professor Young, are admirably calculated to intro- 

 duce, in an easy and consecutive method, not only the 

 first elements of the sciences, but also to prepare the 

 way for the more difficult studies involved in Trigo- 

 nometry, and Algebra applied generally to Geometry 

 and the Conic Sections. With the exception of the 

 chapter on Series and Logarithms, we think that all our 

 readers will have readily mastered what has been ad- 

 vanced. There is no doubt that the last subject pre- 

 sents many points of interest, and yet requires con- 

 siderable attention so as to permit of its thorough 

 acquaintance. Much of the success of the student, in 

 this respect, will depend on his having well studied what 

 has been taught in reference to the Binomial Theorem, 

 and Arithmetical and Geometrical Progression. Before 

 commencing the study of the later books in Euclid, we 

 advise that he should re-read the chapters devoted to the 

 consideration of the subjects we List named, together 

 with that on Series, <tc. The necessity of this he will 

 find out when he arrives at the investigation of the 

 values of sines, tangents, <ko., in our future pages. 

 The calculation of trigonometrical tables depends en- 

 tirely on the application of the principles already ex- 

 plained, in combination with those involved in the 

 elements of Geometry, both plane and spherical. With- 

 out such a preparation as we urge on our readers, the 

 study of Trigonometry will be very perplexing. On the 

 other hand, one who has thoroughly acquainted himself 

 with all that has preceded it, will find his future pro- 

 gress comparatively easy. We have arranged each 

 branch of tliis section on the plan of gradually unfold- 

 ing the subject. The reader, therefore, cannot, with 

 advantage to himself, omit any part. Our plan is pro- 

 gressive, as his course must also be ; and following that 

 method, we can promise that his difficulties will gra- 

 dually melt away before perseverance and close atten- 

 tion. We may extend these remarks also to the study 

 of Euclid. If a person will only dip here and tin re 

 into that admirable compendium of reasoning, he will 

 never understand it. The whole of each "book" de- 

 pends on reasoning based on the premises eniim 

 at its beginning. Each proposition is not only derived 

 from its predecessors, but prepares the way for that 

 which follows. Hence, the study of geometry must be 

 taken as a whole ; and any one link in the chain being 

 broken, is fatal to the success of those who attempt its 

 study. If any of our readers intend pursuing mathe- 

 matical science in its higher branches, nothing is more 

 essential than a thorough knowledge of the principles 

 taught in the preceding and subsequent chapters in this 

 section. ED.] 



