An Introduction to the Theory and Practice of Plain and Spherical Trigonometry: And the Stereographic Projection of the Sphere: Including the Theory of Navigation
An Introduction to the Theory and Practice of Plain and Spherical Trigonometry: And the Stereographic Projection of the Sphere: Including the Theory of Navigation
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. 1826 Excerpt: ...of chords. II. To measure any part of a right circle as pa, pp, pv, &c. From the pole, draw cqf, cpe, cpg, cvw; then ef applied to a scale of chords is the measure of pa, eg of pp, and gw ofpv. Or, pa, Tp, pv, applied to the line of semi-tangents, will give their respective measures. And, it is evident that v/ is the ...
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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. 1826 Excerpt: ...of chords. II. To measure any part of a right circle as pa, pp, pv, &c. From the pole, draw cqf, cpe, cpg, cvw; then ef applied to a scale of chords is the measure of pa, eg of pp, and gw ofpv. Or, pa, Tp, pv, applied to the line of semi-tangents, will give their respective measures. And, it is evident that v/ is the difference between the measures of Pv, and pp, and that ap is the sum of the measures of pa and pp. III. To measure any part of an oblique circle as cr, ro, oa, &c. Find p the pole thus: draw caf, make fg an arc of 90 degrees, and join gc, then p is the pole. From p through r, o, a, m, draw pR, po, pA, . Then Ro, applied to a scale of chords, is the measure of an arc on the sphere represented by ro; Oa is the measure of an arc on the sphere represented by oa; and Am is the measure of an arc on the sphere represented by dirt, &c. (L. 159.) Proposition xviii. Problem. (Plate V. Fig. 2.J (D) To cut any number of degrees from the arc of a great circle; or, from a given point, in a projected great circle, to cut off an arc equal to a given arc. This proposition is the reverse of Prop. XVII. I. If the projected great circle be the primitive whose pole is P, and e the given point. Take the number of degrees in the given arc from a scale of chords and apply the extent from to b, then eb is the arc required. II. If the projected great circle be a right circle (as ) whose pole is c, and a the given point. From the pole c, through a, draw cqf, makefg equal to the given arc, by a scale of chords, and join eg, then will pa contain the required number of degrees. Or, any number of degrees may be cut from by the scale of semi-tangents, in the same manner as the arcs were measured in the XV...
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