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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1839 edition. Excerpt: ...three parts follow each other; therefore the complement of Ac is the middle part, the complement of A and the complement of c are the extremes conjunct, that is, they are joined to the middle part Ac Hence, rad x cos AC=cot A X cot c Secondly. Let the hypothenuse Ac, the base Ab, and the perpendicular Bc, be the parts under consideration, in the triangle ABC The complement of Ac is here the middle part, being separated from Ab by the angle A, and from Bc by the angle c; therefore Ab and Bc are the extremes disjunct. Hence, rad x cos Ac=cos Ab X cos Bc Scholium. The preceding cases include all the varieties that can possibly happen in the practice of right-angled spherical triangles. Any of the equations may be turned into a proportion by putting the required term last, that with which it is connected first, and the other two in the middle of any order. These equations are exactly the same as those already given (384), and therefore Napier's rules are universally true. Hence, raaxcos c=---- fittftmr. X Ab, the angle- be the parts wvhrr vmtideratiaiL, in the triangle middle part, The complement of the an. here "X side Ab tonic "-parated from the angle A by Ac; and from the sia CHAP. IV. INVESTIGATION OF GENERAL RULES FOR SOLVING THE DIFFERENT CASES OF OBLIQUE SPHERICAL TRIANGLES, BY DRAWING A PERPENDICULAR. FROM THE VERTICAL ANGLE UPON THE BASE. PROPOSITION XXV. Showing the manner of applying Baron Napier's rules to oblique spherical triangles, from which several useful corollaries are deduced. (392) When the three given parts do not follow each other in a regular order, viz. when an unknown part intervenes, a perpendicular should always be drawn from the end of & given side, and opposite...

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.