A treatise on surveying, comprising the theory and the practice (Volume 2)

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. 1887 edition. Excerpt: ...the same arc as the angle ABE, equal to that supplement by construction. So too with the angle D Q P. Calculation. To obtain PQ = EF--EP--QF, we proceed to find those three lines thus: In the triangle ABE, we know the side A B, the angle ABE, and the angle AEB = APB; whence to find EB. In the same way, the triangle C F D gives. F C. In the triangle EB O are known EB and B C, and the angle EBC=ABC--ABE; whence EC and the angle ECB are found. In the triangle EC F are known EC, FC, and the angle EOF = BCD--ECB--FOD; whence we find EF, and the angles CEFandCFE. In the triangle BEP, we have E B, the angle BEP = BEO + CEP, and the angle B PE = B P A + A P E; to find EP aud P B. In the triangle Q C F, we have C F, and the angles C Q F and C F Q, to find Q C and Q F. Then we know PQ = EF-EP-QF. The other distances, if desired, can be easily found from the above dati, some of the calculations, not needed for P Q, being made with reference to them. In the triangle A B P, we know A B, B P, nnd the angle BAP, to find the angle A B P and A P. In the triangle Q D C we know Q C, C D, and the angle C Q D, to find the angle Q C D and Q D. In the triangle P B C, we know P B, B C, and the angle P B C = A B O--A B P. to find P C. Lastly, in the triangle Q C B, we know Q C, C B, and the angle Q C B = D C B-D C Q. to find Q B. The solution of this problem includes the two preceding; for, let the line B C be reduced to a point so that its two ends come together and the three lines become two, and we havo the problem of Art. 386; and let the line A B be reduced to a point, B, and C D to a point, C, and we have but one line, and the problem becomes that of Art. 385. In these three problems, if the two stations lie in a right line with one of the given points, the...