Prodromus of a Practical Treatise on the Mathematical Arts, 1838: Containing Directions for Surveying and Engineering

Excerpt from Prodromus of a Practical Treatise on the Mathematical Arts, 1838: Containing Directions for Surveying and Engineering

This book is chiefly made up of selections from a mass of heterogeneous materials, which I have been depositing in my common journal for more than thirty years - some of which, however, I published in 1830, under the title "Art without Science." 1 may add, that I had published a very small treatise under the same title, in the year 1800.

Students have made use of manuscript copies from my notes, for a kind of guide in their course of exercises, for the last four years. Examiners, appointed by the Patron of this Institute, have followed them, mostly, for the same period.

Though it is offered as the Prodromtus of a full treatise on Mathematical Arts; I have progressed too far on the way to the borne of three score and ten, to give any assurances. I have materials enough to complete the object; but "there is a point by nature fixed, whence life must downward tend."

Logarithms arc not used in this book for purposes of calculation. It is a mistake to suppose that logarithms expedite calculations in trigonometry, in common applications of it. The tedious processes of multiplication and division, when we use natural sines, are over-balanced by the trouble of looking out logarithms and accommodating them to the various cases. This opinion is to be proved or disproved by trial alone. But in a long tedious process of several days labor, logarithms arc generally useful.

Algebraic expressions are not used; because they are unnecessary, and very few are sufficiently versed in algebra to apply them to advantage. In truth, our lives are too short to devote much time to speculative mathematics. In past ages, when the science of nature was in its infancy, more time could be devoted to "mere tricks to stretch the human brain," than in this day of astonishing developements of nature's wonders.

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