# Elements of analytical geometry and of the differential and integral calculus

Harper & Brothers, 1851 - Calculus - 278 pages

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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?

### Popular passages

Page 36 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Page 259 - The convex surface of a cone is equal to the circumference of the base multiplied by half the slant height.
Page 211 - ... the tangent of the angle which the tangent makes with the axis of abscissas, this coefficient must have as many values as there are intersecting branches.
Page 123 - The value of the ratio of the increment of the function to that of the variable is composed of two parts, 2ax and ah.
Page 205 - O = slope of the indifference curve on A or B = —— It is thus clear from above that if we have to find out the MRS^ at a point on the indifference curve we can do so by drawing tangent at the point on the indifference curve and then measuring the slope by estimating the value of the tangent of the angle which the tangent line makes with the X-axis. Principle of Diminishing Marginal Rate of Substitution An important principle of economic theory is that marginal rate of substitution of X for Y...
Page 281 - Grammar of the Greek Language. For the use of Schools and Colleges. 12mo, Sheep extra, 75 cents.
Page 191 - By differentiating, we have dy" _ m + ~~ 2y" ' hence, the equation of the tangent to a line of the second order is ,, yy'= and the equation of the normal Of Asymptotes of Curves. 125. An asymptote of a curve is a line which continually approaches the curve, and becomes tangent to it at an infinite distance from the origin of co-ordinates. Let AX and AY be the co-ordinate axes, and the equation of any tangent line, as TP.
Page 23 - In this equation n is the tangent of the angle which the line makes with the axis of abscissas, and B is the intercept on this axis from the origin.
Page 10 - In a right angled triangle, the perpendicular is equal to the square of the sum of the hypothenuse and perpendicular, diminished by the square of the base, and divided by twice the sum of the hypothenuse and perpendicular.
Page 197 - Hence, the radius of curvature at any point of a conic section, is equal to the cube of the normal divided by the square of half the y parameter, and the radii at different points are to each other as the cubes of the corresponding normals.