Publisher's Synopsis
Excerpt from The Progressive Higher Arithmetic: For Schools, Academies, and Mercantile Colleges, Combining the Analytic and Synthetic Methods; And Forming a Complete Treatise on Arithmetical Science, and Its Commercial and Business Applications
There are two general methods of presenting the ele ments of arithmetical science, the Synthetic and the Ana lytic. Comparison enters into every Operation, from the simplest combination Of numbers to the most complicated problems in the Higher Mathematics. Analysis first generalizes a subject and then develops the particulars Of which it consists; Synthesis first presents particulars, from which, by easy and progressive steps, the pupil is led to a general and comprehensive View Of the subject. Analysis separates truths and properties into their ele ments or first 'principles; Synthesis constructs general principles from particular cases. Analysis appeals more to the reason, and cultivates the desire to search for first principles, and to understand the reason for every process rather than to know the rule. Hence, the leading method in an elementary course Of instruction should be the Synthetic, while in an advanced course it should be the Analytic.
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