No. Square. Cube. Square Root. Cube Root. No. Square. Cube. Square Root. Cube Roo 505 255025 128787625 22 4722051 7·963374 568 322624 183250432 23 8327506 8 281635 506 256036 129554216 22 4944438 7·968627 569 323761 184220009 23 8537209 8 286493 507 257049 130323843 22 5166605 7.973873 570 324900 185193000 23.8746728 8-291344 508 258064 131096512 22 5388553 7.979112 571 326041 186169411 23-8956063 8-296190 509 259081 131872229 22·5610283 7·984344 572 327184 187149248 23 9165215 8 301 030| 510 260100 132651000 22·5831796 7·989569 573 328329 188132517 23 9374184 8.305865 511 261121 133432831 22·60530917-994788 574 329476 189119224 23 9582971 8.310694 512 262144 134217728 22 6274170.8.0 575 330625 190109375 23.97915768-315517 513 263169 135005697 22·6495033 8·005205 576 331776 191102976 24-0 8.320335 514 2641 96 135796744 22 6715681 8010403 577 332929 192100033 24 0208243 8 325147 515 265225 136590875 22 6936114 8·015595 578 334084 193100552 24 041 6306 8 329954 516 266256 137388096 22·7156334 8 020779 579 335241 194104539 24 0624188 8.334755 517 267289 138188413 22·7376340 8 025957 580 336400 1951 12000 24 0831892 8.339551 518 268324 138991832 22·7596134 8-031129 581 337561 196122941 24·1039416 8.344341 519 269361 139798359 22 7815715 8 036293 582 338724 197137368 24 1246762 8.349125 520 270400 140608000 22·8035085 8·041451 583 339889 198155287 24 1453929 8353904 521 271441 141420761 22 8254244 8·046603 584 341056 199176704 24·1660919 8-358678| 522 272484 142236648 22 8473193 8051748 585 342223 200201625 24 1867732 8363446 523 273529 143055667 22-8691933 8·056886 586 343396 201230056 24 2074369 8 368209 524 274576 143877824 22 8910463 8 062018 587 344569 202262003 24-2280829 8-372966 525 275625 144703125 22.9128785 8 067143 588 345744 203297472 24-2487113 8-377718 526 276676 145531576 22·9346899 8·072262 | 589 346921 204336469 24-2693222,8-382465 527 277729 146363183 22 9564806 8.077374 590 348100 205379000 24-28991 56 8 387206 528 278784 147197952 22 9782506 8 082480 591 349281 206425071 24 3104916 8391 942 529 279841 148035889 23.0 8-087579 592 350464 207474688 24 3310501 8.396673 530 280900 148877000 23.0217289 8-092672 593 351649 208527857 24 3515913 8-401398 531 281961 149721291 23 0434372 8 097758 594 352836 209584584 24 3721152 8.406118 532 283024 150568768 23 0651252 8-102838 595 354025 210644875 24 3926218,8-410832 533 284089 151419437 23-0867928 8-107912 596 355216 211708736 24 4131112 8.415541 534 285156 152273304 23 1084400 8 112980 597 356409 212776173 24·4335834 8·420245 535 286225 153130375 23 1300670 8.118041 598 357604 213847192 24·4540385 8.424944 536 287296 153990656 23 1516738 8·123096 599 358801 214921799 24-4744765 8·429638 537 288369 1548541 53 23·1732605 8·128144 600 360000 216000000 24 4948974 8-434327 538 289444 155720872 23 1948270 8·133186 601 361201 21 7081 801 24.51 53013 8:439009 539 290521 156590819 23-2163735 8-138223 602 362404 218167208 24 5356883 8 443687 540 291600 157464000 23-2379001 8·143253 603 363609 21 9256227 24·5560583 8:448360 541 292681 158340421 23-2594067 8·148276 604 364816 220348864 24 5764115 8:453027 542 293764 159220088 23.2808935 8·153293 605 366025 221445125 24 5967478 8:457689 543 294849 160103007 23-3023604 8·158304 606 367236 222545016 24·6170673 8:462347 544 295936 160989184 23:3238076 8·163309 607 368449 223648543 24-6373700 8:466999 545 297025 161878625 23.3452351 8·168308 608 369664 224755712 24·6576560 8:471647 546 298116 162771336 23 3666429 8-173302 609 370881 225866529 24 6779254 8 476289 547 299209 163667323 23.3880311 8.178289 610 372100 226981000 24-6981781 8-480926) 548 300304 164566592 23·4093998 8·183269 611 373321 228099131 24-71841 42 8-485557 549 301 401 1654691 49 23 4307490 8-188244 612 374544 229220928 24·7386338 8.4901 84 550 302500 166375000 23 4520788 8·193212 613 375769 230346397 24 7588368 8 494806 551 303601 167284151 23·4733892 8·198175 614 376996 231 475544 24 7790234 8-499423 552 304704 1681 96608 23-4946802 8.203131 615 378225 232608375 24 7991935 8.504034) 553 305809 169112377 23 51 59520 8-208082 616 379456 233744896 24·8193473 8 508641 554 306916 170031 464 23 5372046 8-213027 617 380689 234885113 24-8394847 8.513243 555 308025 170953875 23 5584380 8.217965 618 381924 236029032 24.8596058 8.517840 556 3091 36 171879616 23.5796522 8-222898 619 383161 237176659 24-8797106 8·522432) 557 310249 172808693 23 6008474 8-227825 620 384400 238328000 24-8997992 8-527018 558 311364 173741112 23-6220236 8-232746 621 385641 239483061 24-9198716 8-531600| 559 312481 174676879 23 6431 808 8-237661 622 386884 240641 848 24-9399278 8 536177 560 31 3600 17561 6000 23.66431 91 8-242570 623 388129 241 804367 24-9599679 8 540749 561 314721 176558481 23-6854386 8-247474 624 389376 242970624 24·9799920 8-545317 562 315844 177504328 23·7065392 8-252371 625 390625 244140625 25 0 8.549879 563 316969 178453547 23-7276210 8-257263 626 391876 245314376 25·01 99920 8·554437 564 318096 1794061 44 23·7486842 8-262149 627 3931 29 246491883 25 0399681 8.558990 565 31 9225 180362125 23.7697286 8-267029 628 394384 247673152 25 0599282 8.563537 566 320356 181 321 496 23·7907545 8-271903 629 395641 248858189 25 0798724 8.568080 567 321489 182284263 23-8117618 8-276772 630 396900 250047000 25 0998008 8.572618 No. Square. Cube. Square Root. Cube Root. No. Square. Cube. Square Root. Cube Root. 631 398161 251 239591 25 1197134 8.577152 694 481636 334255384 26 34387978-853598 632 399424 252435968 25 1396102 8.581680 695 483025 335702375 26.3628527 8.857849 633 400689 253636137 25 1594913 8 586204 696 484416 337153536 26 381 8119 8.862095 634 401956 254840104 25 1793566 8.590723 697 485809 338608873 26 4007576 8.866337 635 403225 256047875 25 1992063 8·595238 698 487204 340068392 26 41 96896 8 870575 636 404496 257259456 25 21 90404 8 599747 699 488601 341 532099 26-4386081 8.874809 637 405769 258474853 25-2388589 8 604252 700 490000 343000000 26.45751 31 8.879040 638 407044 259694072 25 2586619 8-608752 701 491 401 344472101 26-4764046 8 883266 639 408321 260917119 25-2784493 8 613248 702 492804 345948408 26 4952826 8.887488 640 409600 2621 44000 25.2982213 8.617738 703 494209 347428927 26 51 41 472 8.891 706 641 410881 263374721 25 3179778 8622224 704 495616 34891 3664 26 5329983 8.895920 642 412164 264609288 25-3377189 8 626706 705 497025 350402625 26 551 8361 8.900130 643 413449 265847707 25-3574447 8-631183 706 498436 351895816 26-5706605 8.904336 644 414736 267089984 25·3771551 8.635655 707 499849 353393243 26′5894716 8.908538 645 41 6025 268336125 25 3968502 8640122 708 501264 354894912 26·6082694 8.912736 646 417316 269586136 25 4165301 8 644585 709 502681 356400829 26 6270539 8.91 6931 647 418609 270840023 25 4361947 8-649043 710 504100 357911000 26 6458252 8·121121 648 419904 272097792 25 4558441 8 653497 711 505521 359495431 26-6645833 8 925307 649 421201 273359449 25 4754784 8 657946 712 506944 360944128 26 6833281 8-929490 650 422500 274625000 25 4950076 8 662301 713 508369 362467097 26 7020598 8.933668 651 423801 275894451 25.5147016 8-666831 714 509796 363994344 26·7207784 8.937843 652 425104 277167808 25 5342907 8 671266 715 511225 365525875 26 73948398-942014| 653 426409 278445077 25 5538647 8 675697 716 512656 367061 696 26 7581763 8.9461 80 654 427716 279726264 25 5734237 8 680123 717 51 4089 368601 813 26.7768557 8.950343 655 429025 281011375 25 5929678 8 684545 718 51 5524 3701 46232 26.7955220 8 954502 656 430336 282300416 25-6124969 8.688963 719 516961 371694959 26 81 41754 8.958658 657 431649 283593393 25 6320112 8 693376 720 518400 373248000 26 8328157 8-962809 658 432964 284890312 25 6515107 8-697784 721 51 9841 374805361 26 851 4432 8.966957 659 434281 286191179 25 6709953 8.702188 722 521284 376367048 26 8700577 8.971100 660 435600 287496000 25 6904652 8.706587 723 522729 377933067 26.8886593 8.975240 661 436921 288804781 25 7099203 8.710982 724 524176379503424 26.9072481 8.979376) 662 438244 290117528 25 7203607 8.715373 725 525625 381078125 26 9258240 8.983508 663 439569 291 434247 25 7487864 8.719759 726 527076382657176 26 9443872 8.987637 664 440896 292754944 25-7681975 8.724141 727 528529 384240583 26.9629375 8.991762 665 442225 294079625 25-7875939 8.728518 728 529984 385828352 26 981 4751 8.995883 666 443556 295408296 25.8069758 8.732891 729 531 441 387420489 270 9.0 667 444889 296740963 25 8263431 8.737260 730 532900 38901 7000 27 01 85122 9 004113 668 446224 298077632 25.8456960 8-741624 731 534361 39061 7891 27-0370117 9-008222 669 447561 299418309 25.8650343 8.745984 732 535824 392223168 27 0554985 9 012328 670 448900 300763000 25.8843582 8.750340 733 537289 393832837 27 0739727 9 016430 671 450241 302111711 25.90366778-754691 734 538756 395446904 27 0924344 9 020529 672 451 584 303464448 25-9229628 8.759038 735 540225 397065375 27·1108834 9 024623 673 452929304821217 25.9422435 8.763380 736 541 696 398688256 27 12931 99 9 028714 674 454276 306182024 25.9615100 8.767719 737 543169 40031 5553 27 1477439 9 032802 675 455625 307546875 25 9807621 8.772053 738 544644 401 947272 27-1661554 9 036885 676 456976 30891 5776 26-0 8.776382 739 546121 403583419 27·1845544 9 040965 677 458329 310288733 26 01 92237 8.780708 740 547600 405224000 27-20294109 045041 678 459684 311665752 26 0384331 8.785029 741 549081 406869021 27-22131 52 9049114 679 461041 31 3046839 26 0576284 8.789346 742 550564 40851 8488 27-2396769 9 053183 680 462400 314432000 26 0768096 8 793659 743 552049 410172407 27-2580263 9 057248 681 463761 315821241 26 0959767 8.797967 744 553536 411830784 27-2763634 9 061309 682 465124 317214568 26·1151297 8.802272 745 555025 413493625 27 2946881 9 065367 683 466489 31 8611987 26 1342687 8 806572 746 5565164151 60936 27-3130006 9 069422] 684 467856 32001 3504 26 1 533937 8.810868 747 558009 41 6832723 27.3313007 9-073472 685 469225 321 419125 26 1725047 8.815159 748 559504 418508992 27 3495887 9 077519 686 470596 322828856 26 191 601 7 8 819417 749 561001 4201 89749 27-3678644 9 081 563 687 471969 324242703 26-2106848 8 823730 750 562500 421 875000 27 3861279 9 085603 688 473344 325660672 26-2297541 8.828009 751 504001 423564751 27 4043792 8 089639 689 474721 327082769 26 2488095 8-832285 752 565504 425259008 27-42261 84 9 093672 690 476100 328509000 26-2678511 8.836556 753 567009 426957777 27 4408455 9.097701 691 477481 329939371 26-2868789 8-840822 754 568516 428661064 27·4590604 9·101726 692 478864 331373888 26·3058929 8-845085 755 570025 430368875 27 4772633 9.105748 693 480249 332812557 26-3248932 8 849344 756 571 536 432081 216 27 4954542 9·109766| No. Square. Cube. Square Root. Cube Root. No. Square. Cube. Square Root. Cube Root. 757 573049 433798093 27.51 36330 9.113781 820 672400551368000 28 6356421 9.359901 758 574564 435519512 27 5317998 9.117793 821 674041 553387661 28 6530976 9.363704 759 576081 437245479 27.5499546 9.121801 822 675684 555412248 28-6705424 9.367505 760 577600 438976000 27·5680975 9.125805 823 677329 557441767 28-6879766 9.371 302 761 579121 440711081 27·5862284 9 129806 824 678976 559476224 28.7054002 9.375096 762 580644 442450728 27·6043475 9·133803 825 680625 561515625 28 7228132 9.378887 763 582169 444194947 27·6224546 9·137797 826 682276 563559976 28-7402157 9.382675 764 583696 445943744 27·6405499 9·141788 827 683929 565609283 28 7576077 9.386460 765 585225 447697125 27·6586334 9·145774 828 685584 567663552 28 7749891 9.390241 766 586756 449455096 27·6767050 9·149757 829 687241 569722789 28-7923601 9.394020 767 588289 451217663 27·6947648 9.153737 830 688900 571787000 28 8097206 9.397796 768 589824 452984832 27-7128129 9-157713 831 690561 573856191 28-8270706 9.401 569 769 591361 454756609 27 7308492 9·161686 832 692224 575930368 28-8444102 9.405338 770 592900 456533000 27 7488739 9-165656 833 693889 578009537 28 8617394 9-409105 771 594441 458314011 27 7668868 9.169622 834 695556 580093704 28-8790582 9-412869 772 595984 460099648 27-7848880 9-173585 835 697225 582182875 28.8963666 9-416630 773 597529 461 88991 7 27·8028775 9.177544 836 698896 584277056 28-91366469-420387 774 599076 463684824 27 8208555 9.181 500 837 700569 586376253 28 93095239-4241 41 775 600625 465484375 27-8388218 9.185452 838 702244 588480472 28-9482297 9-427893 776 602176 467288576 27·8567766 9-189401 839 703921 590589719 28 9654967 9-431 642 777 603729 469097433 27 8747197 9.193347 840 705600 592704000 28 9827535 9-435388 778 605284 470910952 27.8926514 9.197289 841 707281 594823321 29.0 9.439130 779 606841 472729139 27-91057159-201228 842 708964 596947688 29 0172363 9-442870 780 608400 474552000 27 9284801 9.205164 843 710649 599077107 29-03446239-446607 781 609961 476379541 27.9463772 9-209096 844 712336 601211584 29 0516781 9-450341 782 611524 478211768 27-9642629 9-213025 845 714025 603351125 29 0688837 9-454071 783 613089 480048687 27·9821372 9-216950 846 715717 605495736 29-0860791 9.457799 784 61 4656 481890304 28.0 9.220872 847 717409 607645423 29 1032644 9.461 524 785 616225 483736025 28-0178515 9-224791 848 719104 609800192 29-1204396 9-465247 786 617796 485587656 28 0356915 9-228706 849 720801 611960049 29-1376046 9 468966 787 619369 487443403 28 0535203 9-232618 850 722500 614125000 29 1547595 9 472682 788 620944 489303872 28-0713377 9-237527 851 724201 616295051 29-1719043 9-476395 789 622521 491169069 28 0891 438 9-240433 852 725904 618470208 29-1890390 9-480106 790 624100 493039000 28·1069386 9-244335 853 727609 620650477 29-2061637 9 483813 791 625681 49491 3671 28.1247222 9-248234 854 729316 622835864 29-2232784 9-487518 792 627264 496793088 28·1424946 9.2521 30 855 731025 625026375 29 2403830 9-491219 793 628849 498677257 28·160-557 9-256022 856 732736 627222016 29-2574777 9-494918 794 630436 500566184 28 1780056 9-259911 857 734449 629422793 29-2745623 9-498614 795 632025 502459875 28·1957444 9-263797 858 736164 631628712 29-2916370 9.502307 796 633616 504358336 28 2134720 9-267679 859 737881 633839779 29-30870189-505998 797 635209 506261573 28 2311884 9.271559 860 739600 636056000 29 3257566 9.509685 798 636804 508169592 28-2488938 9-275435 861 741321 638277381 29-3428015 9.513369 799 638401 510082399 28-2665881 9.279308 862 743044 640503928 29 3598365 9.517051 800 640000 51 2000000 28.2842712 9.283177 863 744769 642735647 29-3768616 9.520730 801 641601 513922401 28 301 9434 9.287044 864 746496 644972544 29 3938769 9.524406 802 643204 51 5849608 28-3196045 9-290907 865748225 647214625 29-4108823 9.528079 803 644809 517781627 28-3372546 9.294767 866 749956 649461896 29-4278779 9-531749 804 646416 51 9718464 28-3548938 9.298623 867 751689 65171 4363 29-4448637 9.535417 805 648025 5216601 25 28 3725219 9.302477 868 753424 653972032 29 461 8397 9.539081 806 649636 523606616 28-3901 391 9.306327 869 755161 656234909 29 4788059 9-542743 807 651249 525557943 28 4077454 9.310175 870 756900 658503000 29-4957624 9.546402 808 652864 527514112 28 4253408 9.314019 871 758641 660776311 29.5127091 9.550058 809 654481 529475129 28-4429253 9 317859 872 760384 663054848 29.5296461 9-553712 810 656100 531441000 28-4604989 9-321697 873 762129 665338617 29-5465734 9.557363 811 657721 533411731 28-4780617 9.325532 874 763876 667627624 29-5634910 9.561010 812 659344 535387328 28-4956137 9-329363 875 765625 669921875 29.5803989 9.564655 813.660969 537367797 28-5131549 9.333191 876 767376 672221376 29-5972972 9-568297 814 662596 539353144 28 5306852 9.337016 877 769129 674526133 29 6141858 9.571937 815 664225 541313375 28.5482048 9.340838 878 770884 676836152 29-6310648 9-575574 816 665856 543338496 28-5657137 9.344657 879 772641 6791 51 439 29-6479325.9.579208 817 667489 545338513 28.5832119 9.348473 880 774400 681472000 29.6647939 9.582839 818.569124 547343432 28 6006993 9.352285 881 776161 683797841 29-6816442 9-586468 819 670761 549353259 28.6181760 9.356095 882 777924 686128968 29.6984848 9.590093 883 779689 688465387 29-71 531 59 9.593716 942 887364 835896888 30 6920185 9.802803 884 781456 690807104 29-7321375 9.597337 943 889249 838561807 30 7083051 9.806271 885 783225 6931 54125 29-7489496 9-600954 944 891136 841232384 30 7245830 9.809736 886 784996 695506456 29.7657521 9.604569 945 893025 843908625 30.7408523 9.813198 887 786769 697864103 29.7825452 9.608181 946, 894916 846590536 30 7571130 9.816659 888 788544 700227072 29-7993289 9-611791 947 896809 849278123 30 7733651 9.820117 889 790321 702595369 29.8161030 9.61 5397 948 898704 851971392 30.7896086 9.823572 890 792100 704969000 29.8328678 9.61 9001 949 900601 854670349 30-8058436 9.827025 891 793881 707347971 29-8496231 9.622603 950 902500 857375000 30.8220700 9.830475 |892 795664 709732288 29.8663690 9.626201 951 904401 860085351 30 8382879 9.833923 893 797449 712121957 29.8831056 9.629797 952 906304 862801 408 30-8544972 9.837369 894 799236 714516984 29·8998328 9.633390 953 908209 865523177 30.8706981 9.840812 895 801025 716917375 29.9165506 9.636981 954 910116 868250664 30.8868904 9.844253 896 802816 719323136 29-9332591 9 640569 955 912025 870983875 30.9030743 9.847692 897,804609 721734273 29.9499583 9.644154 956 913936 873722816 30 9192497 9.851128 898 806404 724150792 29.9666481 9.647736 957 915849 876467493 30 9354166 9.854561 899 808201 726572699 29 9833287 9 651 316 958 917764 879217912 30.9515751 9.857992 900 810000 729000000 30.0 9.654893 959 919684 881974079 30.9677251 9.861421 901 811801 731432701 30 0166620 9.658468 960 921600 884736000 30.9838668 9.864848 902 813604 733870808 30 0333148 9.662040 961 923521 887503681 31 0 9.868272 903 815409 73631 4327 30 0499584 9.665609 962 925444 890277128 31 0161248 9.871694 904 817216 738763264 30 0665928 9-669176 963 927369 893056347 31 0322413 9.875113 905 81 9025 741217625 30 0832179 9.672740 964 929296 895841344 31 0483494 9.878530 906 820836 743677416 30 0998339 9.676301 965 931225 898632125 31 0644491 9-881945 907 822649 746142643 30.1164407 9.679860 966 933156 901428696 31 0805405 9.885357 908 824464 748613312 30·1330383 9.683416 967 935089 904231063 31 0966236 9.888767 909 826281 751089429 30·1496269 9.686970 968 937024 907039232 31·1126984 9-892174 910 828100 753571000 30·1662063 9 690521 969 938961 909853209 31 1287648 9.895580 911 829921 756058031 30-1827765 9'694069 970 940900 912673000 31·1448230 9.898983 912 831744 758550528 30 1993377 9-697615 971 942841 915498611 31 1608729 9.902383 913 833569 761048497 30-2158899 9 701158 972 944784 918330048 31·1769145 9.905781 914 835396 763551944 30-2324329 9.704698 973 946729 921167317 31 1929479 9.909177 915 837225 766060875 30-2489669 9.708236| 974 948676 924010424 31 -2089731 9.912571 916 839056,768575296 30-2654919 9.711772 975 950625 926859375 31 -2249900 9.915962 917 840889 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9.939636 9.943009 9.940379 9.949747 9.953113 9-956477 SECT. II. GEOMETRY. 874. Geometry is that science which treats of the relations and properties of the boundaries of either body or space. The invention of the science has been referred to a very remote period: by some, to the Babylonians and Chaldeans; by others, to the Egyptians, who are said to have used it for determining the boundaries of their several lands, after the inundations of the Nile. Cassiodorus says that the Egyptians either derived the art from the Babylonians, or invented it after it was known to them. It is supposed that Thales, who died 548 B. C., and Pythagoras of Samos, who flourished about 520 B. c., introduced it from Egypt into Greece. We do not, however, consider it useful here to enter into the history of the science; neither is it necessary to enter into the reasons which have induced us to adopt the system of Rossignol, from whom we extract this section, otherwise than to state that we hope to conduct the student by a simpler and more intelligible method to those results with which he must be acquainted. The limits of body or space are surfaces, and the boundaries of surfaces are lines, and the terminations of lines are points. Bounded spaces are usually called solids, whether occupied by body or not; the subject, therefore, is naturally divided into three parts, lines, surfaces, and solids; and these have two varieties, dependent on their being straight or curved. 875. Geometrical inquiry is conducted in the form of propositions, problems, and demonstrations, being always the result of comparing equal parts or measures. Now, the parts compared may be either lines or angles, or both; hence, the nature of each method should be separately considered, and then the united power of both employed to facilitate the demonstration of propositions. But the reader must first understand the following DEFINITIONS. 1. A solid is that which has length, breadth, and thickness. A slab of marble, for instance, is a solid, since it is long, broad, and thick. 2. A surface is that which has length and breadth, without thickness. though not in strictness, inasmuch as it has thickness, may convey the A leaf of paper, idea of a surface. As in the case of 3. A line is that which has length, but neither breadth nor thickness. a surface, it is difficult to convey the strict notion of a line, yet an infinitely thin line, as a hair, may convey the idea of a line: a thread drawn tight, a straight line. 4. A point is that which has neither length, breadth, nor thickness. A very fine grain of sand may give an idea of it. 5. If a line be carried about a point A, so that its other extremity passes from B to C, from C to D, &c. (fig. 223.), the point B, in its revolution, will describe a curve BCDFGLB. This curve line is called the circumference of a circle. The circle is the space enclosed by this circumference. The point A, which, in the formation of the circle is at rest, is called the centre. The right lines AC, AD, AF, &c. drawn from the centre to the circumference, are called radii. A diameter is a right line which passes through the centre, and is terminated both ways by the circumference. The line DAL, for example, is a diameter. An arc is a part of a circumference, as FG. D B Fig. 223. 6. The circumference of a circle is divided into 360 equal parts, called degrees; each degree is divided into 60 parts, called minutes, and each minute into 60 parts, called seconds. Every circle, without relation to its magnitude, is supposed to be equally divided into degrees, minutes, and seconds. same point, and diverging from each other, form an An angle is commonly 7. Two right lines drawn from the A B B R Fig. 224. M Fig. 225. 8. The magnitude of an angle does not depend on the lines by which it is formed, but upon their distance from each other. How far soever the lines AB, AC are continued, the angle remains the same. One angle is greater than another when the lines of equal length by which it is formed are more distant. Thus the angle BAL (fig. 223.) is greater than the angle CAB, because the lines AB, AL are more distant from each other or include a greater are than the lines AC, AB. If the legs of a pair of compasses be a little separated, an angle is formed; if they be opened wider, the angle becomes greater; if they be brought nearer, the angle becomes less. |