The Doctrine of Plain and Spherical Trigonometry

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. 1725 edition. Excerpt: ...as to C 50 Rods and there cause a Mark or Staff to be set up. 4. Turn 4. Turn the Index about till thro the Sights you see the said Mark atC, and note what number of Degrees and Minutes the Index cuts, which suppose 11 o2o which set down. 5. Then set up some visible Mark at B, where the Instrument stood, and remove it to C i and rhere setting it up, with the Index upon the North and South Diameter as before, turn the Instrument about till thro the Sights you fee the Mark set up at B, and there fix it, the beginning of the Degrees toward the Mark at B. 6. Turn the Index about till thro the Sights you fee the Tree and note what Degrees the Index cuts, which let be 550 40', which note down j and so have you done ycur Work in the Field. And now to find the Distance from B, or C, to the Tree; you may perceive that the Tree, and the two Stations or Marks at B, and C, do make an oblique, angled Triangle ABC: in.-which is given, 1. The Angle ABC iio02o' observed at the first Station B. 2. The Distance measured BC 50 Rods. 3. The Angle CBA, observed at the second Station Co'. By which you may find the Distances AB, and AC, by the first Cafe of oblique-angled Plain Triangles. For, having the two Angles at B 1 io 20', and at C 5540/, their Sum is t56degrees, which taken out of 1800, there remains 14 deg, for the Angle A. Then, As s. BAC 140 oo' Ar. C. 0.615325 To the measured Side BC 50 Rods 1.698970 Sos. ACB 550 40' 9-916859 To the Length of the Side AB 170.7 2.232154 Again, Ass. BAC 140 oo' Ar. C 0.616325 To the Side BC 50 1.698970 So s. of the Angle ABC no" 20' (Com.? 690 40O 9-972058 To the Length of the Side AC 193-8 2.287353 So the Distance from the first Station to the Tree is 170.9 Rods, and from the second Station to the Tree 193.8...