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I see this book as it's been scanned in and digitized, and I compare it against my own copy.
Mine is dated 1859 and apart from differences on the colophon page (Harper & Brothers moved their offices between 1851 and 1859) the books appear identical. That is, up until page 266, at which the main text finishes. After that, both books end with a series of (in the 1851 edition) "Miscellaneous Examples" and in the 1859 one: "Examples for Practice". This section in the later edition is an expanded version of that in the earlier edition.
The final pages of the later edition consist of reviews (as advertisements) of Loomis's previous works, described as "Loomis' Course of Mathematics, published by Harper & Brothers, New York".
But I don't understand what this means:
"Designed for Beginners. 12mo, p. 260, Sheep extra, 62 1/2 cents."
I presume "Sheep extra" refers to the binding, which will presumably be leather made from sheepskin. Anyone?
Other editions - View all
Loomis, Elias, 1811-1889. cn Elements of analytical geometry and of the differential and integral calculus / by Elias Loomis. ...
digital.library.pitt.edu/ cgi-bin/ nietz/ nietzbibl-idx.pl?type=control&
With Alexander Wylie, Li translated Elements of Analytical Geometry and of the Differential and Integral Calculus which had been written by Elias Loomis and ...
www-groups.dcs.st-and.ac.uk/ ~history/ Printonly/ Li_Shanlan.html
Historia Mathematica : The first Chinese translation of the last ...
(The Elements of Analytical Geometry and of the Differential and Integral Calculus), which is in the Prentis Library of Columbia University. ...
linkinghub.elsevier.com/ retrieve/ pii/ S0315086003001095
Collection of Early American Mathematics Books
Main Title TM: Elements of analytical geometry and of the differential and integral calculus / by Elias Loomis. Edition ED: 19th ed. ...
www.math.gatech.edu/ ~hill/ publications/ books/ booklist.html