AN ANALYSIS OF THE SCIENCE OF NUMBERS, MENTAL TRAINING AND DEVELOPMENT - SUGGESTIONS. Ters wol. kis designed both for primary and advanced claasea The first part. is adapted to beginners, while the latter part is peculiarly fitted to give to the more advanced student that cho rough mental drilling, in the Analysis of Nt rnbcrs, mlJch fur niehtrs the t u eba sis of all mathematical knowledge. Jt iQ suggested that clasees in I-Iigher Arithmetic, and cveu in Algebra. not fam ar with worlzs of this kind, mill be greatly benefited by a thorolcgh exercise in this most important bram11 of mathematical science. ThC Tertchq should require the class to dispense with their books at tbd e, of recitation. . He should read each example, apd then call upon some member of the class to solve it. fie ipil, sl16u1d rise. hnd repeat the ex n2plein the same language . wed by the. tek h i should then proceed to analyze it. The analysis mill be found to consist of three parts two pro positions and a conclusion thus What mill 4 barrels of cider cost at 3 dollars a barrel IST PROPOS T I F O o N ur barrels will cost 4 times as much , zs 1 barreL ZD PROPOSITI O If N 1 barrel costs 3 dollars, 4 barrels mill cost 4 times 3 dollars, which are 12 dollars CONCLUS O T N h erefore, 4 barrels of cider at 3 dollare a bar rel, mill cost 12 dollars. The u p islh ould never be allowed to omit either of the steps and be should be required alwavs to adhere strictly to a cowed and uniform p iraseology in the analysis. The forms of analysis are thought t - o be of great service bcttl to the teacher and pupil. It is also suggested, that the pupil be thoroughly drilled iu Lr eons 111, and IV, Sect. VII., as they afford very valuable meutal exel ises an - d a great variety of Arithmetical process - INTRODUCTION - EVER b Y o ok of instruction should have a specifiu object to which the entire work, both in matter and urethod, should strictly conform. It is the object of this book to train and develop the mind by means of the science of numbers. Numbers are the iilstruments here employed to strengthen the memory, to cultivate the faculty of abstraction and to give force and vigor to the reasoning powers. b All our ideas of numbers-are either of unity or of multiplicity-unity being the elementary idea from which all others are derived. A true analysis must conform to the nature of the subject analyzed. It must separate all the ideas and prihcip es into their primary elements, nd then explain and make manifest the laws by which these elements are connected with each other. Hence, the analysis of numbers must begin Gith the - unit 1,-for this is the foundation, and the science is hut the developlnent of the various processes by which 611 other - numbers are derived fro111 1, as a base, and a comparison of the base 1, W-ith-then umbers so derived. Every number has what we call a 6ase that is, number being a collection of things of the same kind, one of these things is . the base of the number mid this thi zu. is called a unit. If we have. the u111-, ber 3 hundred, we may consider it in several points of view l st. It ia one hundred taken 3 times, and if me regard one hundred as the base, then, the base is taken 3 times to make up the number and 100 is the unit. 2nd...