ISBN: 1130291456

Paperback, [EAN: 9781130291452], RareBooksClub.com, RareBooksClub.com, Book, [PU: RareBooksClub.com], RareBooksClub.com, This historic book may have numerous typos and missing text. Purch… Plus…

Paperback, [EAN: 9781130291452], RareBooksClub.com, RareBooksClub.com, Book, [PU: RareBooksClub.com], RareBooksClub.com, 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..., 9, History, 4762, Africa, 4808, Americas, 4873, Ancient, 4884, Asia, 4921, Australia & Oceania, 4935, Europe, 4984, Gay & Lesbian, 4987, Historical Study, 4995, Middle East, 5011, Military, 14450, Military Science, 5032, Russia, 4853, United States, 5035, World, 1000, Subjects, 283155, Books<

ISBN: 1130291456

Paperback, [EAN: 9781130291452], Lightning Source UK Ltd, Lightning Source UK Ltd, Book, [PU: Lightning Source UK Ltd], Lightning Source UK Ltd, 772198, General, 65, History, 1025612, Sub… Plus…

Paperback, [EAN: 9781130291452], Lightning Source UK Ltd, Lightning Source UK Ltd, Book, [PU: Lightning Source UK Ltd], Lightning Source UK Ltd, 772198, General, 65, History, 1025612, Subjects, 266239, Books, 400530011, English, 400529011, Language (feature_browse-bin), 365481011, Refinements, 266239, Books, 492564011, Paperback, 492562011, Format (binding_browse-bin), 365481011, Refinements, 266239, Books, 182018031, Regular Size, 182016031, Font Size (format_browse-bin), 365481011, Refinements, 266239, Books<

ISBN: 9781130291452

Paperback, [PU: Rarebooksclub.com]