LOG 



LOG 



product wrll be the logarithm of the 

 power sought. 



Example. Let the cube of 32 be re- 

 quired bv logarithms. The logarithm 

 of 32 = 1.5051500, which, multiplied by 

 3, is 4.51 5-1-500, the logarithm of 32768, 

 the cube of 32. But in raising powers, 

 viz, squaring, cubing, &c. of any decimal 

 fraction by logarithms, it must be observ- 

 ed, that the first significant figure of the 

 power be put so many places below the 

 place of units, as the index of its loga- 

 rithm wants of 10, 100, &c. multiplied by 

 the index of the power. 



LOGARITHMS, in extract the roots of 

 powers by. Divide the logarithm of the 



number by the index of the power, the 

 quotient is the logarithm of the root 

 sought. 



To fold mean proportionals between any 

 two numbers. Subtract the logarithm of 

 the least term from the logarithm of the 

 greatest, and divide the remainder by a 

 number more by one than the number 

 of means desired"; then add the quotient 

 to the logarithm of the least term (or 

 subtract it from the logarithm of the great- 

 est) continually, and it will give the 

 logarithms of all the mean proportionals 

 required. 



Example. Let three mean proportionals 

 be sought, between 106 and 100. 



Logarithm of 106 = 2.0253059 

 Logarithm of 100 = 2 0000000 



Divide by 4)0.0253059(0.0063264.75 

 2.0000000 



Logarithm of the least term 100 added 



Logarithm of the first mean . . . 101.4673846 2.0063264.75 



Logarithm of the second mean . 102 9563014 2 OU'6529.5 



Logarithm of the third mean . . 1U4467U483 2.0189794.25 



Logarithm of the greatest term . 106 2.0253059 



LOGIC, the art of reasoning 1 . As the 

 necessities of our existence oblige us to 

 think, and to arrange eur thoughts in 

 such a manner as m^iy enable us to com- 

 municate with each other, we are habitu- 

 ally impelled towards a conclusion, that it 

 is unnecessary to teach reasoning as an art. 

 It is hardly needful to combat this notion by 

 arguments which will easily occur to most 

 men of reflection ; and indeed the contrary 

 persuasion was so prevalent in the middle 

 ages, that men seem to have been more 

 occupied with the art, than with the pro- 

 per use of it. 



In order to reason well, it is necessary 

 that the nature of our perceptions and 

 ideas, and the notions or conclusions we 

 draw from them, should be well under- 

 stood. Logic, therefore, is a science of 

 extensive occupation ; which has its be- 

 ginning in the constitution of things, and 

 the processes of the human intellect, and 

 its practical termination in the structure, 

 use, and application of language. Its 

 objects are no less than the universal 

 acquisition of knowledge, and that mu- 

 tual communication which constitutes 

 a large part of the employment, and 

 is the most distinguishing character of 

 man. 



The impressions made by external ob- 

 jects upon the senses, are called sensa- 

 tions or ideas of sensation. See IDEOLO- 



GY. The recollection or remembrance 

 of those sensations are simply called ideas. 

 The general notions which are produced 

 in the mind by reflecting upon ideas have 

 been called ideas of reflection ; but as 

 they all grow out of the comparison of 

 the first-mentioned ideas, and do univer- 

 sally in the last result imply propositions, 

 it appears much preferable to call them 

 notions. 



Logical writers divide ideas into simple 

 and complex ; but as we have no simple 

 sensations, and can therefore have no sim- 

 ple ideas but by the artificial process of 

 abstraction, the division seems useless. 

 The word complex here signifies com- 

 pounded, and the compounded nature of 

 our ideas will practically depend, in a 

 great measure, upon our choice or deter- 

 mination in the subject of our reasoning. 

 Thus, a lemon is soft, fragrant, yellow, 

 and acid. If I throw a lemon at another, 

 the attention will be chiefly directed to 

 the organ of touch, and its "fragrance, its 

 tint, and its acidity, will be abstracted or 

 left out. But the perfumer, the designer, 

 and the chemist, would separately attend 

 to those parts of the idea which were sug- 

 gested by the organs of smell, of vision, 

 and of taste. And in this manner it is 

 that we may separate the simple ideas of 

 yellowness, acidity, and fragrance; though, 

 in nature, their causes never appear insw- 



