Circumstances induce me to attempt the publication of the courses of analytical trigonometry which I had planed in 1806 and used at the Military Academy of West point, and adapted peculiarly to the habitual mode and order of studying elementary mathematics in this country.

Supposing the Knowledge of the most elementary Books of Euclid, and the simplest Algebra, till quadratic equations inclusive, I bring the Scholar by an easy and clear analysis; in the manner of algebra aplied to geometry, through plane and spherical trigonometry, with examples for the calculations upon all the formulæ, and the use of trigonometric functions in higher analysis, and shew the leading Ideas in the construction of trigonometric tables. I omit differentials, as well as all accessory problems, in order to present the whole doctrine in as close a system as possible, allways following the same principles, and modes of proceeding; that the scholar may the better be able to embrace the whole, and be eased the most possible, while to the man already instructed it will present a symetric table of what he may need in this branch; thinking to take the more extensive applications and consequences both in theory and practice in a second volume if encouragement should be obtained for it

The book will contain about {180 200} pages large 8o which booksellers here say will bring it to $2. in retail, and to be delivered in sheets to subscribers and Booksellers, at $1,50.

But the printing of such a book appears not to be in the line of Book editors here, and difficulties seem to present themselves from that side; the subscription of several public Institutions, Colleges, and Universities, for which it will be adapted as class book, would enable me to give it light, (which it may otherwise perhaps not be able to reach in this country) by the consequent recommendation of it, particularly if it should be allowed to mention it..

This induces me to take the liberty to adress you the present with the request if I could hope some subscription from the University of Virginia; as I dare to hope I might have the pleasure to give you in this as much satisfaction as in the Coast Survey, to which it served of course in part as theory.

The professors of mathematics and of natural philosophy of Columbia College here, have united to introduce it as class book in the college, I have reason to hope its adoption in Union College Schenectady, & little doubt that, when it will have passed the judgement of experience, it may become generally usefull.

In examining lately my papers on the Coast Survey I discovered that I had so often not been understood by the gentleman who corrected my language, as it was thought not to be good english, that it becomes necessary to restore; the nearest possible, my original sense, by a considerable number of Corrections, which I shall give under press this week, and have then the honor to forward to You some copies of it.

Your early answer would be a great favor to me, as it would most likely enable me to proceed directly, if it should be favorable.

Allow me Sir the pleasure of expressing to You the feeling of highest esteem and particular affection with which I have the honor to be