Vertical Angle to the Middle of the Base; to find the sides of the Triangle. PROBLEM XI. IN a Triangle, having given the two Sides about the Vertical Angle, with the Line bisecting that Angle, and terminating in the Base; to find the Base. PROBLEM XII. To determine a Right-angled Triangle; having given the Lengths of two Lines drawn from the acute angles, to the Middle of the opposite Sides. PROBLEM XIII. To determine a Right-angled Triangle; having given the Perimeter, and the Radius of its Inscribed Circle. PROBLEM XIV. To determine a Triangle; having given the Base, the Perpendicular, and the Ratio of the two Sides. PROBLEM XV. To determine a Right-angled Triangle; having given the Hypothenuse, and the Side of the Inscribed Square. PROBLEM XVI. To determine the Radii of three Equal Circles, described in a given Circle, to touch each other and also the Circumference of the given Circle. PROBLEM XVII. IN a Right-angled Triangle, having given the Perimeter, or Sum of all the Sides, and the Perpendicular let fall from the Right Angle on the Hypothenuse; to determine the Triangle, that is, its Sides. PROBLEM XVIII. To determine a Right-angled Triangle; having given the Hypothenuse, and the Difference of two Lines drawn from the two acute angles to the Centre of the Inscribed Circle. PROBLEM PROBLEM XIX. To determine a Triangle; having given the Base, the Perpendicular, and the Difference of the two other Sides. PROBLEM XX. To determine a Triangle; having given the Base, the Perpendicular, and the Rectangle or Product of the two Sides. PROBLEM XXI. To determine a Triangle; having given the Lengths of three Lines drawn from the three Angles, to the Middle of the opposite Sides. PROBLEM XXII. IN a Triangle, having given all the three Sides; to find the Radius of the Inscribed Circle. PROBLEM XXIII. To determine a Right-angled Triangle; having given the Side of the Inscribed Square, and the Radius of the Inscribed Circle. PROBLEM XXIV. To determine a Triangle, and the Radius of the Inscribed Circle; having given the Lengths of three Lines drawn from the three Angles, to the Centre of that Circle. PROBLEM XXV. To determine a Right-angled Triangle; having given the Hypothenuse, and the Radius of the Inscribed Circle. PROBLEM XXVI. To determine a Triangle; having given the Base, the Line bisecting the Vertical Angle, and the Diameter of the Circumscribing Circle. LOGARITHMS LOGARITHMS OF THE NUMBERS FROM NJ Log. N. 1 to 1000. N. Log. 77 1.886491 78 1.892095 79 1-897627 80 1.903090 811-908485 82 1.913814 83 1.919078 84 1.924279 85 1.929419 86 1.934498 87 1.939519 88 1.944483 89 1.949390 90 1.954243 91 1.959041 921-963788 93 1.968483 94 1.973128 95 1-977724 96 1.982271 97 1.986772 Log. N. Log. 10-000000|| 261414973 51 1.707570 76 1.880814 20-301030 27 1·431364 || 52 1716003 3 0.477121 28 1447158|| 53 1-724276 40-602060 29 1.462398 541-732394 5 0.698970 30 1.477121 || 55 | 1.740363 60-778151 31 1.491362 || 56 | 1.748138 7 0.845098 32 1505150|| 571-755875 8 0.903090 33 1.518514 58 1763428 90-954243 34 1.531479 || 59 1.770852 10 1.000000 35 1.544068 60 1.778151 111041393| 361.556303 61 1.7853301 121-079181 37 1568202 62 1.792392 131-113943 38 1.579784 63 1.799341 141-146128 39 1.591065 || 64 |1.806180 151.176091|| 40|1·602060 || 65 | 1·812913 16 1-204120 || 41 1612784 66 1.819544 171 230449 || 42 | 1·623249 67 1.826075 181-255273 || 43 1·633468 || 68 | 1·832509 191278754 || 44 | 1·643453 || 691·838849 201301030 || 45 | 1·653213 70 1.845098 21 1-322219|| 46 1:662758 71 1-851258 22 1.342423 || 47 1.672098 72 1.857833 25 1.361728 || 48 | 1·681241 73 1.863323 241-380211 || 49 | 1·690196 74 1.869232 99 1995635 251-397940 || 50 | 1·69897075 1.875061 100 2.000000 98 1991226 N. B. In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to 0's, large dots are now introduced instead of the O's through the rest of the line, to catch the eye, and to indicate that from thence the corresponding natural number in the first column stands in the next lower line, and its annexed first two figures of the Logarithm in the second coiumn. 100 000000 0434 0868 1301 1734 2166 2598 3029 3461 3891 10104321 4751 5181 5609 6038 6466 6894 7321 7748 8174 102 8600 9026 9451 9876.300.724 1147 1570 1993 2415 103 012837 3259 3680 4100 4521 4940 5360 5779 6197 6616 104 7033 7451 7868 8284 8700 9116 9532 9947.361.775 105 021189 1603 2016 2428 2841 3252 3664 4075 4486 4896 106 5306 5715 6125 6533 6942 7350 7757 8164 8571 8978 107 9384 9789.195.600 1004 | 14081812 2216 2619 3021 108 033424 3826 4227 4628 5029 5430 5830 6230 66297028 109 7426 7825 8223 8620 9017 9414 9811.207.602.998 110 041393 1787 2182 2576 2969 3362 3755 4148 4540 4932 111 5323 5714 6105 6495 6885 7275 7664 8053 8442 8830 112 9218 9606 9993 .380.766 11531538 1924 23092694 113 053078 3463 3846 4230 4613 4996 5378 5760 6142 6524 114 6905 7286 7666 8046 8426 8805 9185 9563 9942.320 115 060698 1075 1452 1829 2206 2582 2958 | 3333 37094083 116 4458 4832 5206 5580 5953 | 6326 66997071 7443 7815 117 8186 8557 8928 9298 9668.38.407.776 1145 1514 118 071882 2250 2617 2985 3352 3718 4085 4451 4816 5182 119 5547 5912 6276 66407004 7368 7731 8094 8457 8819 120 9181 9543 9904 .266.6266987 1347 1707 2067 2426 121 082785 3144 3503 3861 4219 4576 4934 5291 5647 6004 122 6360 6716 7071 74267781 8136 8490 8845 9198 9552 123 9905 .258.611.963 13151667 2018 2370 2721 3071 124 093422 3772 4122 4471 4820 5169 5518 5866 6215 6562 125 6910 7257 7604 7951 8298 8644 8990 9335 9681.026 126 100371 0715 1059 1403 1747 2091 2434 2777 3119 3462 127 3804 4146 4487 4828 5169 5510 5851 6191 6531 6871 128 7210 7549 7888 8227 85658903 9241 9579 9916253 129 110590 0926 1263 1599 1934 2270 26052940 3275 3609 130 3943 4277 4611 4944 5278 5611 5943 6276 6608 6940 131 7271 7603 7934 8265 8595 8926 9256 9586 9915 245 132 120574 0903 1231 1560 1888 2216 2544 2871 3198 3525 133 3852 4178 4504 4830 5156 5481 5806 6131 6456|6781 134 7105 7429 7753 80768399|8722 9045 93689690..12 135 130334 0655 0977 1298 1619 | 1939 2260 2580 2900 3219 3539 385841774496 4814 5133 54515769 6086 6403 6721 7037 7354 7671 7987 83038618 8934 9249 9564 9879.194.508.8221136│14501763 2076 2389 2702 139 143015 3327 3639 3951|4263 4574 4885 5196 5507 5818 140 6128 6438 6748 7058 7367 7676 7985 8294 8603 8911 141 9219 95279835.142.44975610631370 1676 1982 142 152288 2594 2900 3205 3510 3815 4120|4424 47285032 143 5336 5640 5943 6246 6549 68527154|7457 7759 8061 144 8362 86648965 9266 9567 9868.168.469.7691068 145 161368 1667 1967 2266| 2564 2863 3161 3460 3758 4055 146 4353 4650 4947 5244 5541 5838 6134 6430|6726|7022 147 7317 7613 79088203 8497 8792 9086 93809674 9968 148 170262 0555 0848 1141 1434 1726 2019 2311 2603 2895 149 3186 3478 376940604351|4641|4932|5222|551215809 136 137 138 368 LOGARITHMS. N. 0 1 2 3 4 5 161 7 8 9 175 176 179 186 192 193 |