. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. Vol. II. 114 MATHEMATICS. 4. Suppose I want to know the breadth of a river, ormy distance from an inaccessible object O, and that I haveno instrument for taking angles, but only a chain or cordfor measuring distances ; and suppose, that from each ofthe two stations A, B, which are 500 yards asunder, Imeasure in a direct line from the object O 100 yards, and Bb each equal to 100 yards, and that the diagonalAb is by
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. Vol. II. 114 MATHEMATICS. 4. Suppose I want to know the breadth of a river, ormy distance from an inaccessible object O, and that I haveno instrument for taking angles, but only a chain or cordfor measuring distances ; and suppose, that from each ofthe two stations A, B, which are 500 yards asunder, Imeasure in a direct line from the object O 100 yards, and Bb each equal to 100 yards, and that the diagonalAb is by measure 550 yards, and the diagonal aB then is the distance of the object from each ofthe stations A and B ?. Let fall the perpendiculars AP, BQ. Then, in the tri-angle ABa Ba : BA-fAa :: BA—Aa : BP—P#, That is, 560 : 600 :: 400 : 428*=BP—P<7t Its half 214|Half sum 280 BP49JfaP 65{ HEIGHTS AND DISTANCES. 115 And Bp_ 560+428 j 2 „ 560—42S|2ThenAa 100 : a? 65f :AB 500 : BP 494f : _988-£_ 100 :BA 500 : £Q 56TTAQ 493TT :: rad. : s. Z£BQ 34 37?:: rad. : s. ZABQ 80 32 The sum 115 9Taken from 180 0 Leaves ZABO 64 51Add BAO 57 35 The sum 122 26Taken from 180 00 Leaves ZO 57 34* * Or the angles ABO and BAO may be otherwise foundthus : 116 MATHEMATIC ;s. Whence ZO 57° 34 9-926350? ZA 57 35 9-9264310 AB 500 2-6989700 BO 500-1 2-6990503 ZO 57° 34 9-9263507 ZB 64 51 9-9567437 AB 500 269 8 9 700 AO 53625 27293630 PROBLEM XI. To
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