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Arca Seg.

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•066140

Ticigit. Aica Seg.

085 .032186 ·086

*032745 .087.033307 .c33 .033372 •c89 •034441 ogo •035011 *o91 *035585 092036162 *093 036741 *094 *037323 *095037909

•038496 *097039087 .098039680 099 040276 :100 040875 :101 *041476

102 042080 -103042687 •104

*043296 •105

•043908 •106 :044522 107 *045139 . 108 ::045759 !109 046381 •110

He ght.

Height. Area Seg. *124 056003 163 083320

• •125.056663 •164.084059 .126:057326 •165.084801 127 057991 .166.085544 •I 28 .058658 1.167 | •036289 129 ! *059327-4-768087036 •130 059999 .169.087785 .131 •060672 -170 .088535 .132 061348 171

*089287 *133

C62026 172 090041 •134.062707 173 *090797 -135 063389

174

091554 136 064074 175 *092313 137, 004760

176.093074 •138 •065449 177 093836 139

178094601 140.066833

*179095366 141

067528 •180.096134 142.068225

•181 096903 •143 .068924 •

•182.097674 •144.069625 •183 098447 •145 070328 •

184

*099221 .146.071033 •185099997: 147 071741

•186.100774 •148 072450 •187 101553 •149073161

.

*047005 III 047632 I12 .048262 •113.048894 114 *049528 115 050165 116.050804

• 117 051446 •118 052090

119 *052736 •I 20 053385 • 121 :054036 122 •054689 123 •055345

•188 •102334 •150073874 .189.103116 •151 074589 •

•190 | 103900 152075306 191 •104685 •153 076026 192.105472 •154 .070747 193

•106261 •155 077469 •194 107051 •156 078194 195 •107842

157 078921 196 •108636 •158 079649 •197 •109430 •159 | .080380 .198110226 чбо 081112 •199 I11024 •161 081846 • 200 •111823 .o 82582

112624

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•152

• 201

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Height. l. Area

Seg Height. | Area Seg. Height, Arta SC • 202 •113426 .241 145 799 •280 •180019 :203 •114230 242146655 •281 •180918 •204 •115035

243
*147512

•282 181817 *205115842 .244.148371

.283182718 • 206116650

.245 149230 •284 183619 •207 | •117460 246 :150091

•285 1.184521. *208 118271 247150953 :

:286185425

• 209 119083 248 .151816 287 186329 210 119897

*249152680
:

• 288187234 •211 120712 .250 •153546 | .289.188140 212 •121529 .251 154412 •290

.189047 .213 •122347 252155280 *291 189955

• 214123167 •253 156149 292190864 215123988 2541 :157019 293191775 216 •124810 .255.157890

294.192684 21.7125634 -256158762

•158762 1.295193596 218.1 26459

257159635

• •159635 1.296194509 .219127285 .258160510 • 297 *195422 .220.128113 -259161386 1.298 196337 .221128942 •260 .162 263 299

•197252 .222 129773 •261 •163140

300 .198168 .223130605 -262-164019

301 .199085 .224 •131438 •263 164899

302 •200003 .225 •132272

.264 165780 *303 •200922 .226 133108 .265 166663

304

.201841 227 •133945 •266, •167546 .305

.202761 .228134784 -267 168430 •

306.203683 •229135624 ..268

268 169315

307.204605 *230136465 .269 170202 308.205527 •231 | 137307 • 270 171089

*309 .206451 .232.138150 271 •171978. || .310 .207376 .233 •138995 272 •172867

311

203301 .234 139841 273173758

312209227

• *235 •140688

274 174649 313 •210154 •236 •141537 ,275 •175542

314 •211082 237142387 .276 176435 315 2 I 2011 .238 •143238 277 177330 *316 •212940 239 •144091 *278

178225

317 •213871 .240 144944 .279 / 179122 318.214802

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Height. Area Seg. | Height. Area Seg. Height. L Area Seg. *319 215733.358 252631 *397 290432

• 320 -216666

•359 .253590 .398.291411 *321 217599

-360
.254550

*399

.292390 *322.218533 .361 | .255510 •400 293309 323 219468 -362-256471 401 *294349 *324 •220404 -363257433 •402 .295330 *325 221340 364.258395 -403 .296311 *326 222277 -365.259357 *404 297292

• 327 .223215 -366-260320 •405.298273 *328224154 367 +261 284 *406299255 329 .225093

368.262248 407 300238 *330 •226033 •369 •263213 .408.301220 *331 •226974 .370.264178

409 302203 332 .227915 :371 265144 -410-303187 •333 •228858 .372 •266111

411 *304171 *334 .229801 -373.267078

•4i2 •305155 *335.230745 •374-268045

'413 306140 *336.231689 •375 -269013 414 | *307125 337.232634 376 269982 415 *308110 *338233580 .377.1 270951 .416.309095 *339 234526 .378271920

417310081 •340 235473 -379-272890 ·418 | *311068

3 *341-236421 380

273861 419 312054 342 237369 381274832 •4 20 313041 *343 •238318 382 -275803

314029 344 239268 +383 276775 -4 22 315016 345 .240218 384.277748 •

•4 23

+316004 346 241169 385-278721

-424 -316992 347 .242121 .386.279694

425 348

.243074 | +387 | 280668 •426:318970 *349.244026 388

281642

*427 350 •244980 • 389282617

-428 351 .245934 * 390.283592

'429 •352.246889

391

•284568 430 *353 .247845 *392

431
354 248801 393 •286521 -432
*355
.249757

394.287498

•433 •356 | .250715 395 •288476

434 •357 251673 *396 1.289453

•435

•4 21

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*317981

•285544

319959 *320948 *321938 322928 *323918 *324909 325900 326892 327882

6 484 376702 441 +333836 0463 355732:485

Height. Area Seg. Height. Area Seg. Height. Area Seg. *436 328874 | .458 1 350748 | 480

*480 372704 437 | 329866 •459 351745 481373703

' 438330858 460 352742

482 *374702 439 331850

461 353739 '440332843 -462 +354736 '

-485 377701

* 442 | +334829-464 +356730

464 356730486 378701 '443 | 335822 465 357727

487 379700 444-336816 '466 358725

*488

*380700 445 337810 .467 | +359723 *489 381699

* *446338804 468360721 *490 382699

• -447339798 *469 361719 °|

491 ‘383699 *448 | '340793 470*362717 492 384699

*

* *449 *341787 471 363715.493 385699 450 * 342782 472 •364713 494

*494 | 386699

* •451 343777 473 365712 495 *387699 *452 '344772 *474 366710 *496 *388699 453'345768.475 367709

*

497 389699 *454 +346764 || -476 | +368708 498 390699 455 347759

-477369707 499 *391699 '456 348755 *478 370706 *500 *392699 .457 *349752 479 *371705

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USE OF THE TABLE.

In the table, each number in the column of area seg. is the area of the circular segment, whose height, or the versed sine of its half arc, is the number immediately on the left of it, in the column of heights ; the diameter of the circle being 1, and its whole area •785398.

The

The use of this table is to find the area of a" segment of any other circle, whatever be the diameter. See the Rule, page 69.

a

In dividing the given height: by the diameter, if the quotient do not terminate in three places of decimals without a fractional remainder, then for the area answering to that fractional part proportion ought to be made thus ;--having found the tabular area answering to the first three decimals of the quotient, take the difference between it and the next following tabular area, which difference multiply by the fractional remaining part of the quotient, and the product will be the corresponding proportional part to be added to the first tabular area.

EXAMPLE.

If the height of the proposed segment be 31, and the diameter 50 ; required the area.

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