(From Gregory's Mathematics.)

From this table may be found by inspection the area or circumference of a circle of any diameter, and the side of a square equal to the area of any given circle from 1 to 100 inches, feet, yards, miles, etc. If the given diameter is in inches, the area, circumference, etc., set opposite, will be inches; if in feet, then feet, etc.

 Diam. Area. Circum. Side of equal sq. .25 .04908 .78539 .22155 .5 .19635 1.57079 .44311 .75 .44178 2.35619 .66467 1. 78539 3.14159 .88622 .25 1.22718 3.92699 1.10778 .5 1.76714 4.71238 1.32934 .75 2.40528 5.49778 1.55089 2. 314159 6.28318 1.77245 .25 3.9760/ 7.06858 1.99401 .5 4.90873 7.85398 2.21556 .75 5.93957 8.63937 2.43712 3. 7.06858 9.42477 2.65868 .25 8.29576 10.21017 2.88023 .5 9.62112 10.99557 3.10179 .75 11.04466 11.78097 3.32335 4. 12.56637 12.56637 3.54490 .25 14.18625 13.35176 3.76646 .5 15.90431 14.13716 3.98802 .75 17.72054 14.92256 4.20957 5. 19.63195 15.70796 4.43113 .25 21.64753 16.49336 4.65269 .5 23.75829 17.27875 4.87424 .75 25.96722 18.06415 5.09580 6. 28.27433 18.84955 5.31736 .25 30.67961 19.63495 5.53891 .5 33.18307 20.42035 5.76047 .75 35.78170 31.90975 5.98203 7. 38.48456 21.99114 6.20358 .25 41.28249 27.77654 6.42514 .9 44.17864 23.56194 6.64670 .75 47.17297 24.34734 6.86825 8. 50.26548 25.13274 7.08981 .25 53 45616 25.91813 731137 .5 56.74501 26.70353 7.53292 .75 60.13204 27.48893 7.75448 9. 63.61725 28.27433 7.976)1 .25 67.20063 29.0597a 8.19759 .5 70.88218 29.81513 8.41915 .75 74.66191 30.63052 8.64071 10. 78.53981 31.41592 8.86226 .25 82.51589 32.20132 9.08382 35 86.59014 32.986721 9.30538
 Diam. Area. Circum. Side of equal sq. .75 90.76257 33.77212 9.52693 11. 95.03317 34.55751 9.74849 .25 99.40195 35.34291 9.97005 .5 103.86890 36.12831 10.19161 .75 108.43403 36.91371 10.41316 12. 113.09733 37.69911 10.63472 .25 117.85881 38.48451 10.85627 .5 122.71846 39 26990 11.07783 .75 127.67628 40.05530 11.29939 13. 132.73228 40.84070 11.52095 .25 137.88646 41.62610 11.74250 .5 143.13881 42.41150 11.96406 .75 148.48934 43.19689 12.18562 14. 153.93804 43.98229 12.40717 .25 159.48491 44.76769 12.62873 .5 165.12996 45.55309 12.85029 .75 170.87318 46.33849 1307184 15 176.71458 47.12338 13.29340 .25 182.65416 47.90928 13.51496 .5 188.69190 48.69468 13.73651 .75 194.82783 49.48008 13.95307 16 201.06192 50.26518 14.17963 .25 207.39420 51.05088 14.10118 .5 213.82464 51.83627 14.62271 .75 220.35327 52.62167 14.84430 17. 226.98006 53.40707 15.06535 .25 233.70504 54.19217 15.28741 .5 240.52818 54.97787 15.50897 .75 247.44950 55.76326 15.73052 18. 254.46900 56.54866 15.95208 .25 261.58667 57.33406 16.17361 .5 268.80252 58.11916 16.39519 .751 276.11654 58.90486 16.61675 19. 283.52873 59.69026 16.83831 .25 291.03910 60.47565 17.05986 .5 298.64765 61.26105 17.28142 .75 306.35437 62.04645 17.50298 20. 314.15926 62.83185 17.72453 .25 322.06233 63.61725 17.94609 .5 330.06357 64.40264 18.16765 75 338.16299 65.18304 18.38920 21. 346.36059 65.97341 18.61076
 Diam. Area. Circum. Side of equal sq. 21.25 354.65635 66.75884 18.83232 5 363.05030 67.54424 19.05337 .75 371.54241 68.32964 19.27543 22. 380.13271 69.11503 19.49699 .25 388.82117 69.90043; 19.71854 .5 337.60782 70.68583 19.94010 .75 406.49263 71.47123 20.16166 23. 415.47562 72.25663 20.38321 .25 424.55679 73.04202 20.60477 .5 433.73613 73.82742 20.82633 .75 443.01365 74.61282 21.04788 24. 452.38934 75.39822 21.26944 .25 461.86320 76.18362 21.49100 .5 471.43524 76.96902 21.71255 .75 481.10546 77.75441 21.93411 25. 490.87385 78.53981 22.15567 .25 500.74041 79.32521 22.37722 .5 510.70515 80.11061 22.59878 .75 520.76306 80.89601 22.82034 26. 530.92915 81.68140! 23.04190 .25 541.18342 82.466800 23.26345 .5 551.51586 83.25220 23.48501 .75 562.00147 84.03760 23.70657 27. 572.55526 84.82300: 23.92812 .25 583.20722 85.60839 24.14968 .5 593.95736 86.39379 24.37124 .75 604.80567 87.17919 24.59279 28. 615.75216 87.96459 24.81435! .25 626.79682 88.74999 25.03591 .5 637.93965 89.53539 25.25746 .75 649.18066 90.32078 25.47902 29. 660.51985 91.10613 25.70058 .25 671.95721 91.39158 25.92213 .5 683.49275 92.67698 26.14359 .75 695.12646 93.46238 26.36525 30. 706.85834 94.24777 26.58680 .25 718.68840 95.03317 26.80836 .5 730.61664 95.81857 27.02992 .75 74264305 96.60397 27.25147 31. 751.76763 97.38937 27.47303 .25 766.99039 98.17477 27.69459 .5 779.31132 98.96016 27.91614 .75 791.73043 99.74556 28.13770 32. 804.24771 100.53096 23.35926 .25 816.86317 101.31636 28.58081 .5 829.57681 102.10176 28.80371 .75 842.38861 102.88715 29.02393 33. 855.29859 103.67255 29.24548 .25 868.30675 104.45795 29.46704 .5 881.41308 105.24335 29.68860 .75 894.61759 10602875 29.91015 34. 907.92027 106.81415 30.13171 25 921.32113 107.59954 30.35327 .5 934.82016 108.33494 30.57482 .75 948.41736 109.17034 30.79638 35. 962.11275 109.95574 31.01794 .25 975.90630 110.74114 31.23949 .5 989.79803 111.52653 31.46105 .75 1003.78794 112.31193 31.68261 36. 1017.87601 113.09733 31.90416 .25 1032.06227 113.88273 32.12572 .5 1046.34670 114.66813 32.34728 .75 1060.72930 115.45353 32.56383 37. 1075.21003 116.23892 32.79039 .25 1089.78903 117.02432 33.01195 .5 110.446616 117.80972 33.23350 .75 1119.2414 118.59572 33.45506
 Diam. Area. Circum. Side of equal sq. 38 1134.11494 119.38052 3367662 .25 1149.08660 120.16591 33.89817 .5 1164.15642 120.95131 34.11973 .75 1179.32442 121.73671 34.34129 39. 1194.59060 122.52211 34.56285 .25 1209.95495 123.30751 34.78440 .5 1225.41748 12409290 35.00596 .75 1210.97818 124.87830 35.22752 40. 1255.63704 125.66370 35.44907 .25 1272.39411 126.44910 35.67063 .5 1288.24933 127.23450 35.89219 .75 1304.20273 128.01990 36.11374 41. 1320.25431 123.80529 36.33530 .25 1336.40406 129.59069 36.55686 .5 1352.65198 130.37609 36.77841 .75 1368.99808 131.16119 36.99997 42. 1335.44236 131.91689 37.22153 .25 1401.98480 132.73228 37.44308 .5 1418.62543 133.51768 37.66464 .75 1435.36423 134.30308 37.88620 43. 1452.20120 135.08348 38.10775 .25 1469.13635 135.87388 38.32931 .5 1486.16967 136.65928 38.55087 .75 1503.30117 137.44467 38.77242 44. 1520.53084 138.23007 38.99338 .25 1537.85869 139.01547 39.21554 .5 1556.23471 139.80087 39.43709 .75 1572.80890 140.58627 39.65865 45. 1520.43128 141.37166 39.88021 .25 1608.15182 142.15706 40.10176 .5 1625.97054 142.94246 40.32332 .75 1643.88744 143.72786 40.54488 46. 1661.90251 144.51326 40.76643 .25 1680.01575 145.29866 40.98799 .5 1698.22717 146.08405 41.20955 .75 1716.53677 146.86945 41.43110 47. 1734.94454 147.65485 41.65266 .25 1753.45048 148.44025 41.87422 .5 1772.05460 149.22565 42.09577 .75 1790.75639 150.01104 42.31733 48. 1809.55736 150.79644 42.53889 .25 1828.45601 151.58184 42.76044 .5 1847.45282 152.36724 42.98200 .75 1866.54782 153.15264 43.20356 49. 1885.74099 153.93804 43.42511 .25 1905.83233 154.72313 43.64667 .5 1924.42184 155.50883 43.86823 .75 1943.90954 156.29423 44.08978 50. 1963.49540 157.07963 44.31134 .25 198317944 157.96503 44.53290 .5 2002.96166 153.65042 44.75445 .75 2022.84205 159.43582 44.97601 51. 2042.82062 160.22122 45.19757 .25 2062.89736 161.00662 45.41912 .5 2083.07227 161.79202 45.64068 .75 2103.31536 162.57741 45.86224 52. 2123.71663 163.36281 46.083880 .25 2144.18607 164.14821 46.30535 .5 2164.75368 164.93361 46.52691 .75 2185.41947 165.71901 46.74847 53. 2206.18344 166.50441 46.97002 .25 2227.04557 167.28980 47.19158 .5 2248.00589 168.07520 47.41314 .75 2269.06433 168.86060 47.63469 54. 2290.22104 169.64600 47.85625 .25 2311.47588 170.43140 48.07781 .5 2332.82889 171.21679 48.29936
 Diam. Arca Circum. Side of equal sq. 54.75 2354.28008 172.00219 48.52092 55. 2375.82844 172.78759 48.74248 .25 2397.47698 173.57299 48.96403 .5 2419.22269 174.35839 49.18559 .75 2141.06657 175.14379 49.40715 56. 2463.00864 175.92918 49.62870 .25 2185.04887 176.71458 49.85026 .5 2507.18728 177.49998 50.07182 .75 2520.42337 178.28538 50.29337 57. 2551.75863 179.07078 50.51493 .25 2574.19156 179.85617 50.73649 .5 2596.72267 180.64157 50.95304 .75 2619.35196 181.42697 51.17960 58. 2642.07942 182.21237 51.40116 .25 2664.90505 182.99777 51.62271 .5 2687.82836 183.78317 51.84427 .75 2710.85084 184.56856 52.06583 59. 2733.97100 185.35396 52.28738 .25 2757.18933 186.13936 52.50894 .5 2780.50584 186.92476 52.73050 .75 2803.92053 187.71016 52.95205 60. 2327.43338 188.49555 53.17364 .25 2851.04442 189.28095 53.39517 .5 2874.75362 190.06635 53.61672 .75 2898.56100 190.85175 53.83328 61. 2922.46656 191.63715 54.05984 .25 2946.47029 192.42255 54.28139 .5 2970.57220 193.20794 54.50295 .75 2994.77223 193.99334 54.72451 62 3019.07054 191.77374 54.94606 .25 3043.46697 195.56414 55.16762 .5 3067.96157 196.34954 55.38918 .75 3092.55135 197.13493 55 61073 63. 3117.21531 197.92033 55.83229 .25 3142.03444 198.70573 56.05335 .5 3166.92174 199.49113 56.27540 .75 3191.90722 200.27653 56.49696 64. 3216.99087 201.06192 56.71852 .25 3242.17270 201.84732 56.94007 .5 3267.45270 202.63272 57.16163 .75 3292.83088 203.41812 57.38319 65. 3318.30721 204.20352 57 60475; .25 33138.8176 234.98892 57.82630 .5 3369.55447 205.77431 53.04786 .75 3395.32534 206.5597 53.26942 66. 3421.19439 207.34511 53.49097 .25 3417.16162 203.13051 53.71253 .5 3173.22702 203.91591 58 93109 .75 3199.39060 209.70130 59.15564 67. 3525.65235 210.48670 59.37720 .25 3552.01228 211.27210 59.59876 .5 3573.47038 212.05750 59.82031 .75 3605.02665 212.84290 60.04187 68. 3631.68110 213.62830 60.26343 .25 3658.43373 214 41360 60.48498 .5 3685.28153 215.19909 60.70654 .75 3712.23350 215.98449 60.92810 69. 3739.28065 216.76989 61.14965 .25 3766.42597 217.55529 61.37121 .5 3798.66947 218.34068 61.59277 .75 3821.01115 219.12608 61.81432 70. 3348.45100 219.91148 62.03538 .25 3875.98902 220.69688 62.25744 .5 3803.62522 221.48228 62.47899 .75 3931.35959 222.26768 62.70055 71 3959.19211 223.053071 62.92211 .25 3987.12286 223.83847 63.14366
 Diam. Area. Circum. Side of equal sq. 71.5 4015.15176 224.62337 63.36522 .75 4043.27833 225.40927 63.58678 72. 4071.50407 226.19467 63.80833 .25 4099.82750 226.98006 64.02989 .5 4128.24909 227.76546 64.25145 .75 4156.76886 228.55086 64.47300 73. 4185.38681 229.33626 64.69456 .25 421410293 230.12166 64.91612 .5 4212.91722 230.90706 65.13767 .75 4271.82969 231.69245 65.35923 74. 4300.84034 232.47785 65.58079 .25 4329.94916 233.26325 65.80234 .5 4359.15615 234.04865 66.62390 .75 4388.46132 234.83405 66.21516 75. 4417.86466 235.61944 66.46701 .25 4447.36618 236.40484 66.68857 .5 4476.96538 237.19024 66.91043 .75 4506.66374 237.97564 67.13168 76. 4536.45979 238.76104 67.35324 .25 4566 35400 239.54613 67.57480 .5 4596.34640 240.33183 67.79635 .75 4626.43696 241.11723 68.01791 77. 4656.62571 241.90263 68.23947 .25 4636.91262 242.68803 68.46102 .5 4717 29771 243.47343 68.68258 .75 4747.78098 244.25382 68.90414 78. 477836242 245.04422 69.12570 .25 4809.04204 245.82962 69.31725 .5 4839.81983 246.61502 69.56881 .75 4870.79579 247.40042 69.79037 79. 4901.66993 248.18581 70.01192 .25 4932.74225 218.97121 70.23318 .5 4963.91274 249.75661 70.45504 .75 4995.18140 250.34201 70.67659 80. 5026.54824 251.32741 70.89815 .25 5058.01325 252.11281 71.11971 .5 5039.57614 252.89820 71.34126 .75 5121.23781 253.63360 71.56282 81. 5152.99735 251.46900 71.78433 .25 5184.85506 255.25440 72.00593 .5 5216.81095 256.03980 72.22749 .75 5218.86501 256.82579 72.44905 82. 5281.01725 257.61059 72.67060 .25 5313.26766 258.39599 72.89216 .5 5345.61621 259.18139 73.11372 .75 5378.06301 259.96679 73.33527 83. 5410.60794 260.75219 73.55633 .25 5443.25105 261.53753 73.77839 .5 5475.99234 262.32298 73.99994 .75 5508.83180 263.10838 74.22150 84. 5541.76911 263.89378 74.44306 .25 5574.80525 264.67918 74.66461 .5 5607.93923 265.46457 74.88617 .75 5641.17139 266.21997 75.10773 85. 5674.50173 267.03537 75.32928 .25 5707.93023 267.82077 75.55084 .5 5741.45692 268.60617 75.77240 .75 5775.08178 269.39157 75.99395 86. 5806.80481 270.17696 76.21551 .25 5842.62602 270.962 76.43707 .5 5876.54540 271.74776 76.65362 .75 5910.56296 272.53316 76.88018 87. 5944.67869 273.31856 77.10174 .25 5978.89260 274.10395 77.32320 .5 6013.20468 274.88935 77.54485 .75 6047.61404 275.67475 77.76641 88. 6082.12337 276.46015 77.98796
 Diam. Area. Circum. Side of equal sq. 88.25 6110.72993 277.24555 78.20952 .5 6151.43476 278.03094 78.43103 .75 6186.23772 278.81634 78.65263 89. 6221.3885 279.60174 78.87419 .25 6256.13815 230.33714 79.09575 .5 6291.23563 281.17254 79.31730 .75 6326.43129 281.95794 79.53386 90. 6361.72512 282.74333 79.76042 .25 6397.11712 233.52873 79.98198 .5 6432.60730 284.31413 80.20353 .75 6468.19556 285.09953 80.42509. 91. 6503.83219 285.83493 80.64669 .25 6539.66639 286.67032 80.85820 .5 6575.54977 287.45572 81.08976 .75 6611.53082 238.24112 81.31132 92. 6647.61005 239.02652 81.53287 .25 6683.78745 289.81192 81.75443 .5 6720.06303 290.59732 81.97599 .75 6756.43678 291.33271 82.19754 93. 6792.90871 292.16811 82.41910 .25 6829.47831 292.95351 82.04066 .5 6866.14709 293.73391 82.86221 .75 6902.91354 294.52431 83.03377 94. 6939.77817 295.30970 83.30533
 Diam. Area. Circum. Side of equal sq. 94 25 6976.74097 296.09510 83.52688 .5 7013.80194 296.88050 83.74844 .75 7050.96109 297.66590 83.97000 95. 7083.21842 298.45130 84.19155 .25 7125.57992 299.23670 84.41311 .5 7163.02759 390.02209 84.63467 .75 7200.57944 300.80749 84.85622 96. 7238.22947 301.59239 85.07778 .25 7275.97767 302.37829 85.29934 .5 7313.82404 303.16369 85.52089 .75 7351.76859 303.94908 85.74245 97. 7389.81131 304.73448 85.96401 .25 7427.95221 305.51988 86.18556 .5 7466.19129 306.30528 86.40712 .75 7504.52853 307.09068 86.62868 98. 7542.96396 307.87608 86.85023 .25 7581.19755 308.66147 87.07179 .5 7620.12933 309.44637 87.29335 .75 7653.85927 310.23227 87.51490 99. 7697.68739 311.01767 87.73646 .25 7736.61369 311.80307 87.95802 .5 7775.63816 312.58346 88.17957 .75 7814.76031 313.37336 88.40113 100. 7353.98163 314.15926 88.62269

The following rules are for extending the use of the above table.

To find the area, circumference, or side of equal square, of a circle having a diameter of more than 100 inches, feet, etc. Rule. - Divide the given diameter by a number that will give a quotient equal to some one of the diameters in the table; then the circumference or side of equal square, opposite that diameter, multiplied by that divisor, or the area opposite that diameter, multiplied by the square of the aforesaid divisor, will give the answer.

Example. - What is the circumference of a circle whose diameter is 228 feet? 228, divided by 3, gives 76, a diameter of the table, the circumference of which is 238.761, therefore:

238.761

3

716.283 feet. Ans.

Another example. - What is the area of a circle having a diameter of 150 inches? 150, divided by 10, gives 15, one of the diameters in the table, the area of which is 176.71458, therefore:

176.71458

100 = 10 x 10

17,671.45800 inches. Ans.

To find the area, circumference, or side of equal square, of a circle having an intermediate diameter to those in the table. Rule. - Multiply the given diameter by a number that will give a product equal to some one of the diameters in the table; then the circumference or side of equal square opposite that diameter, divided by that multiplier, or the area opposite that diameter divided by the square of the aforesaid multiplier, will give the answer.

Example. - What is the circumference of a circle whose diameter is 6 1/8, or 6.125 inches? 6.125, multiplied by 2, gives 12.25, one of the diameters of the table, whose circumference is 38.484, therefore:

(2)38.484 19.242 inches. Ans.

Another example. - What is the area of a circle, the diameter of which is 32 feet? 3.2, multiplied by 5, gives 16, and the area of 16 is 201.0619,therefore

5 x 5 = 25)201.0619(8.04244 + feet. Ans. 200

106 100

61

50

119 100

19

Note. - The diameter of a circle, multiplied by 3.14159, will give its circumference; the square of the diameter, multiplied by .78539, will give its area; and the diameter, multiplied by .88622, will give the side of a square equal to the area of the circle.