(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.