. 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]. e 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. Tojind the distance of two inaccessible objects from each other, EXAMPLES. Wanting to know the distance between a house and a mill,which were separated from me by a river, I took anotherstation B at the distance of 300 yar
. 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]. e 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. Tojind the distance of two inaccessible objects from each other, EXAMPLES. Wanting to know the distance between a house and a mill,which were separated from me by a river, I took anotherstation B at the distance of 300 yards from the first stationA : now, from the first station A, the angle subtended by B Draw the perpendiculars Ag, Bh. Then, by Eucl. II. 12, AndAB : Bg :: rad. : -425 = cosine of 64° 51 the ZABQ. t i-i m. B<T—AB —Aa2 like manner A/t= =263 ; \ 2-A And AB : Ah :: rad. : -536 the cosine of 57° 35thcZBAO ; both the same as above. HEIGHTS AND DISTANCES. 11* and the mill was 58° 20, and by the mill and the house 57°;from B, the angle subtended by A and the house was 53*30, and by the house and the mill 45° 15. What is the dis-tance of the house and mill ?. 37° 0058 2053 30 148 50 180 00 58° 2053 3045 15 157 05180 00 53° 30f45 15 98 45ZAB1H ZAHB 31 10 ZAHB 31 10ZABH 53 30AB 300 22 55 A MB 971393499*905178724771213 AH4659776 2*6683651 518 MATHEMATICS. ZAMB 22c 55ZABM 98 45, or 81 15AB 300 AM 761*4655AH 4659776 Tang. Sum 12274431Diff. 295*4879AHM+AMH 2 T AHM-AMH nK AAJ ang. 35 44 9*59038699*99491582*4771213 28816502 3*08900132*4705397 71° 30 10 4754801 9-8570185 AMH 35 46 ZAMH 35° 46ZHAM 37 00AH HM 479*7933 yards 9*76677399*77946302*6683651 2*6810542 Note. Much after the manner of the last examplesmany curious and useful problems may be resolved ; for ifwe can determine our distance from one remote object, wecan do the same for any number of objects; or if the dis-tance between two remote objects can be determined, thosebetween any number of objects may be determ
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