29 57 13456 928 3059 14400,50 56 111 50176 1792 57 113 51984 1824 8 58 115 53824 1856 59 117 55696 1888 60 119 57600 11920 64 MENSURATION, &c. PROBLEM IX. To measure heights and diflances by the geometrical square. When the plane is horizontal, the instrument is to be fupported and placed horizontally at any point A, and it is to be turned till the remote point F, whose distance is to be meafured, is feen through the fixed fights; then turn the index, till, through the fights upon it, you fee any accessible object B; then place the inftrument at the point B, directing the fixed fights to the first station A, and the moveable ones to the point F; and if the index cut the reclined fide of the square, as in the point E, then, from fimilar triangles, ES: SB:: as BA: AG; but if the index cut the right fide of the square K, it will be BR: RK:: BA: AF. In either of these cafes, the distance required may be found by the rule of three *. Perpendicular heights, when acceffible, may be obtained by the quadrant only. For example, If you wanted the height of a house, tree, &c. approach towards or retire from the object, till it fubtends an angle of 45°; then shall the height of the object be equal to its horizontal distance. Euclid, I. 6. A fimilar observation may be made of the other instruments used for heights and distances; but this, and many more, will daily occur in practice. * The fide DE is called the right fide, E the reclined fide. TABLES. N°. Log. N°. Log. (No. Log N°. Log. (N°. Log. 10.00000 21 1.32222 41 1.61278 61 1.78533 811.90848 20.30103 22 1.34242 42 1.62325 62 1.79239 82 1.91381 30.47712 23 1.36173 43 1.63347 63 1.79934 83 1.91908 40.60206 24 1.38021 44 1.64345 64 1.80618 84 1.92428 50.69897 25 1.39794 45 1.65321 65 1.81291 85 1.92942 60.77815 26 1.41497 46 1.00276 66 1.81954 86 1.93450 70.84510 27 1.43136 47 1.67220 67 1.82607 87 1.9.3952 80.90309 28 1.44786 48 1.68124 68 1.83251 88 1.94448 90.95424 29 1.46240 49 1.69020 69 1.83885 89 1.94939 101.00000 30 1.47712 50 1.69897 70 1.84510 90 1.95424 111.04139 31 1.49136 51 1.70757 71 1.85126 91 1.95904 12 1.07918 32 1.50515 52 1.71600 72 1.85733 92 1.96379 13 1.11394 33 1.51851 53 1.72428 73 1.86332 93 1.96848 14 1.14613 34 1.53148 54 1.73239 74 1.86923 94 1.97.313 1.5 1.17609 35 1.54407 551.74036 75 1.87506 95 1.97772 16 1.20412 36 1.55630 56 1.74819 17 1.23045 37 1.56820 571.75587 18 1.25527 38 1.57978 58 1.76343 19 1.27875 39 1.59106 59 1.77085 20/1.30105 40 1.60200 60 1.77815 CONTAINING, I. A TABLE OF THE LOGARITHMS OF NUMBERS FROM I TO 10000. II. A TABLE OF LOGARITHMIC SINES, TANGENTS, SECANTS, AND VERSED SINES, TO EVERY DEGREE AND MINUTE OF THE QUADRANT. III. A TABLE OF LOGARITHMIC SINES, TANGENTS, AND SECANTS, TO EVERY POINT, HALF POINT, AND QUARTER POINT OF THE COMPASS. A TABLE of the LOGARITHMS of NUMBERS from 1 to 10000, 76 1.88081 90 1.93227 77 1.88649 9 1.98677 78 1.89209 98 1.99123 79 1.89763 90 1.99563 80 1.90302/502.00000 64 MENSURATION, ৮০. PROBLEM IX. To measure heights and dislances by the geometrical square. When the plane is horizontal, the instrument is to be fupported and placed horizontally at any point A, and it is to be turned till the remote point F, whose distance is to be meafured, is feen through the fixed fights; then turn the index, till, through the fights upon it, you fee any accessible object B; then place the instrument at the point B, directing the fixed fights to the first station A, and the moveable ones to the point F; and if the index cut the reclined fide of the square, as in the point E, then, from fimilar triangles, ES: SB:: as BA: AG; but if the index cut the right fide of the square K, it will be BR: RK:: BA: AF. In either of these cases, the distance required may be found by the rule of three *. Perpendicular heights, when accessible, may be obtained by the quadrant only. For example, If you wanted the height of a house, tree, &c. approach towards or retire from the object, till it fubtends an angle of 45°; then shall the height of the object be equal to its horizontal distance. Euclid, I. 6. A fimilar observation may be made of the other instruments ufed for heights and distances; but this, and many more, will daily occur in practice. * The fide DE is called the right fide, E the reclined fide. TABLES. LOGARITHMIC TABLES; CONTAINING, I. A TABLE OF THE LOGARITHMS OF NUMBERS FROM I TO 10000. II. A TABLE OF LOGARITHMIC SINES, TANGENTS, SECANTS, AND VERSED SINES, To EVERY DEGREE AND MINUTE OF THE QUADRANT. III. A TABLE OF LOGARITHMIC SINES, TANGENTS, AND SECANTS, TO EVERY POINT, HALF POINT, AND QUARTER POINT OF THE COMPASS. A TABLE of the LOGARITHMS of NUMBERS from 1 to 10000, ¡No. Log. No. Log. No. Log N°. Log. (N°. Log. 10.00000 21 1.32222 41 1.61278 61 1.78533 811.90848 20.30103 22 1.34242 42 1.62325 62 1.79239 82 1.91381 30.47712 23 1.36173 43 1.63347 63 1.79934 83 1.91908 40.60206 24 1.38021 44 1.64345 64 1.80618 84 1.92428 50.69897 25 1.39794 45 1.65321 65 1.81291 85 1.92942 60.77815 26 1.41497 46 1.06276 66 1.81954 86 1.93450 70.84510 27 1.43136 47 1.67220 67 1.82607 87 1.93952 80.90309 28 1.44786 48 1.68124 68 1.83251 88 1.94448 90.95424 29 1.46240 49 1.69020 69 1.83885 89 1.94939 10 1.00000 30 1.47712 50 1.69897 70 1.84510 90 1.95424 11 1.04139 31 1.49136 51 1.70757 71 1.85126 91 1.95904 12 1.07918 32 1.50515 52 1.71600 72 1.85733 92 1.96379 13 1.11394 33 1.51851 53 1.72428 73 1.86332 93 1.96848 141.14613 34 1.53148 541.73239 74 1.86923 94 1.97313 15 1.17609 35 1.54407 55 1.74036 75 1.87506 95 1.97772 16 1.20412 361.55630 56 1.74819 76 1.88081 90 1.93227 171.23045 37 1.56820 571.75587 77 1.88649 9, 1.98677 18 1.25527 38 1.57978 58 1.76343 78 1.89209 981.99123 19 1.27875 39 1.59106 59 1.77085 79 1.89763 90 1.99565 20/1.3010340/1.60200 60 1.77815 80 1.90102/10 12.00000 |