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. 1892 Excerpt: ... sector IOP, the analogy between the circular and excircular functions is complete. The sector IOP = sector IOp = u quadrants of the unit circle TT =-)iorS square units. If the angle IOP = f radians, e2s--1 tan d = tanh 0 =-rr---e1" + 1 so that therefore the area of the sector IOP in terms of f is I log tan-+ square ...
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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. 1892 Excerpt: ... sector IOP, the analogy between the circular and excircular functions is complete. The sector IOP = sector IOp = u quadrants of the unit circle TT =-)iorS square units. If the angle IOP = f radians, e2s--1 tan d = tanh 0 =-rr---e1" + 1 so that therefore the area of the sector IOP in terms of f is I log tan-+ square units. 6. If IOPv P1OP2 P2OP3... are the hyperbolic sectors corresponding to the successive quadrants of the circle, and Mv M2... the feet of the ordinates to Pv P2..., OMi = cosh 1L = 2. 5, OM2 = cosh 2L = 11.5, OM3 = cosh 3L= 55. 5, OMi = cosh 4L= 245. 5, approximately. These values show the rapidity with which the arcs IPV PXP2, PiP% corresponding to successive quadrantal arcs of the circle, increase. The successive sectors, corresponding to successive complete revolutions of a radius of the circle, form a series of more and more elongated sectors with smaller and smaller angles, of which no finite number will fill up the space between the curve and its asymptotes, so that this area is infinite. Riemann, in his researches on the complex variable, found it convenient to conceive a revolving radius after completing each revolution to continue its path, not on the same plane, but on a plane superposed upon the previous one, thus moving on a continuous surface without passing through the same position a second time. In the present case, if we suppose an infinite number of circles superposed on the unit circle above and below it and all of them cut along the radius O1', and then each terminal radius of the one (the revolution being supposed in the positive direction) united with the coincident initial radius of the next above it, we shall have a Riemann's surface (a screw surface with a zero pitch), whose folds, infinite in number, cor...
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Add this copy of The Algebra of Coplanar Vectors and Trigonometry to cart. $21.42, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
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