This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1873 Excerpt: ...P and Q coincide, L OTN = L OPN, and NN becomes the tangent to the locus of N; hence the latter tangent makes the same angle with ON that the tangent at P makes with OP. This property enables us to draw the tangent at any point N on the pedal locus in question. Again, if p' represent the perpendicular on the tangent at ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1873 Excerpt: ...P and Q coincide, L OTN = L OPN, and NN becomes the tangent to the locus of N; hence the latter tangent makes the same angle with ON that the tangent at P makes with OP. This property enables us to draw the tangent at any point N on the pedal locus in question. Again, if p' represent the perpendicular on the tangent at N to the first pedal, from similar triangles we evidently have y Hence if the equation of a curve be given in the form r =f(p), that of its first pedal is of the form--, =/(), m which p and p' are respectively analogous to r and p in the original curve. In like manner the equation of the next pedal can be determined, and so on. 185. Reciprocal Polars.--If on the perpendicular ON a point P' be taken, such that OP'. ON is constant (k? suppose), the point P' is evidently the pole of the line PN with respect to the circle of radius k and centre 0; and if all the tangents to the curve be taken, the locus of their poles is a new curve. We shall denote these curves by the letters A and B, respectively. Again, by elementary geometry, the point of intersection of any two lines is the pole of the line joining the poles of the lines. Now if the lines be taken as two infinitely near tangents to the curve A, the line joining their poles becomes a tangent to B; accordingly the tangent to the curve B has its pole on the curve A. Hence A is the locus of the poles of the tangents to B. In consequence of this reciprocal relation, the curves A and B are called reciprocal polars of each other with respect to the circle whose radius is h. Since to every tangent to a curve corresponds a point on its reciprocal polar, it follows that to a number of points in directum on one curve correspond a number of tangents to its reciprocal polar, which pass through a common p...
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Add this copy of An elementary Treatise On The Differential Calculus, to cart. $36.95, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2016 by Hansebooks.
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New in New jacket. {Size: 14.60 x 22.86 cms} Presenting an Exquisite Leather-Bound Edition, expertly crafted by the prestigious organization “Rare Biblio” with Original Natural Leather that gracefully adorns the spine and corners. The allure continues with Golden Leaf Printing that adds a touch of elegance, while Hand Embossing on the rounded spine lends an artistic flair. This masterpiece has been meticulously reprinted in 2020, utilizing the invaluable guidance of the original edition published many years ago in 1899. The contents of this book are presented in classic black and white. Its durability is ensured through a meticulous sewing binding technique, enhancing its longevity. Imprinted on top-tier quality paper. A team of professionals has expertly processed each page, delicately preserving its content without alteration. Due to the vintage nature of these books, every page has been manually restored for legibility. However, in certain instances, occasional blurriness, missing segments, or faint black spots might persist. We sincerely hope for your understanding of the challenges we faced with these books. Recognizing their significance for readers seeking insight into our historical treasure, we've diligently restored and reissued them. Our intention is to offer this valuable resource once again. We eagerly await your feedback, hoping that you'll find it appealing and will generously share your thoughts and recommendations. Lang: -eng, Pages: -494. If it is a multi-volume set, then it is only a single volume. Product Disclaimer: Kindly be informed that, owing to the inherent nature of leather as a natural material, minor discolorations or textural variations may be perceptible. Explore the FOLIO EDITION (12x19 Inches): Available Upon Request.
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