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TABLE V <br />CURVE FORMULAE FOR SIMPLE CURVES <br />COMPILED BY J. CALVIN LOcI:E, C.E. <br />(1) c = \/2Ra (2) c = ,\/a2+b2 <br />(3) c = '1/2R (R—,\/CR b) (R — b) = 2R(R <br />(4) c = 2,\/m (2R—in) <br />(5) c = 2R sin V2 I (6) c = 2T cos % I <br />(7) e = R exsec % I <br />(8) e= R tan % I tan % I (9) e= T tan Y4 I <br />(10) b = 1/a (22R—a) <br />C2 l ( C2 C° <br />(11) b = I (c I --2R—) \e 2R — � c2 4R2 <br />(12) b=Rsin I (13) b=a cot %I <br />a2+b2 c2 d2 C2+4m2 <br />(14) R 2a 2a (15) R = 2m Sin <br />(16) d = -\/R (2R —,\/(2R + c) (2R •— c) = \/R(2R — \/4R2 — c2) <br />(17) d = 1/2Rm r (18) dd = 2R sin % I (19) in d2 <br />= 2R <br />(20) m=R�_I(R+ l (R <br />— 2F� <br />)=T_IR2— 4 <br />(21) m = R versey2 I (22) m = R sin % I tan % I (23) m = y2c tan % I <br />(24) a = 2R (25) a = R —1/(R + b) (R — b) = R — ,\/R2 — b2 <br />(26) a = 2 R (sin2 % I)2 (27) a = R vers I (28) a = R sin I tan <br />(29) a = b tan % I (30) a = T sin I (31) T = R tan % I <br />(32) I= R X 57.295780 (33) R= I X 57.295780 <br />(34) L = IRX0.01745329 (35) L = 8d—c <br />3 <br />LR — R2 Sin I LR — Rb <br />(36) Area Seg. = 0 = 0 <br />TABLE VI <br />SINES, COSINES, TANGENTS, COTANGENTS <br />ei <br />sin <br />tan <br />sin <br />tan <br />sin <br />tan <br />sin <br />tan <br />sin <br />tan <br />sin <br />tan <br />0' <br />0' <br />10, <br />10' <br />20' <br />20' <br />130' <br />30 <br />40' <br />40' <br />60' <br />60' <br />00000 <br />0000 <br />0029 <br />0029 <br />0058 <br />0058 <br />0087 <br />0087 <br />0116 <br />0116 <br />0145 <br />014589 <br />1 <br />175 <br />0175 <br />0204 <br />0204 <br />0233 <br />0233 <br />0262 <br />262 <br />291 <br />291 <br />320 <br />32088 <br />2 <br />349 <br />349 <br />378 <br />378 <br />407 <br />407 <br />436 <br />437 <br />465 <br />466 <br />494 <br />49587 <br />3 <br />523 <br />524 <br />552 <br />553 <br />581 <br />582 <br />610 <br />612 <br />640 <br />641 <br />669 <br />70686 <br />4 <br />698 <br />699 <br />727 <br />729 <br />756 <br />758 <br />785 <br />787 <br />814 <br />816 <br />843 <br />86485 <br />5 <br />872 <br />875 <br />901 <br />904 <br />929 <br />934 <br />958 <br />963 <br />987 <br />9921016 <br />102284 <br />6 <br />1045 <br />1051 <br />1074 <br />108C <br />1103 <br />1110 <br />1132 <br />1130 <br />1161 <br />1169 <br />190 <br />19883 <br />7 <br />219 <br />228 <br />248 <br />257 <br />279 <br />287 <br />305 <br />317 <br />334 <br />346 <br />363 <br />37682 <br />8 <br />392 <br />405 <br />421 <br />435 <br />449 <br />465 <br />478 <br />495 <br />507 <br />524 <br />536 <br />55481 <br />9 <br />564 <br />584 <br />593 <br />614 <br />622 <br />644 <br />650 <br />673 <br />679 <br />703 <br />708 <br />73380 <br />10 <br />736 <br />763 <br />765 <br />793 <br />794 <br />823 <br />822 <br />853 <br />851 <br />883 <br />880 <br />91479 <br />11 <br />908 <br />944 <br />937 <br />974 <br />965 <br />2004 <br />994 <br />2035 <br />2022 <br />2065 <br />2051 <br />209578 <br />122079 <br />2126 <br />2108 <br />2156 <br />2136 <br />1862164 <br />217 <br />193 <br />247 <br />221 <br />27877 <br />13 <br />250 <br />309 <br />278 <br />339 <br />306 <br />370 <br />334 <br />401 <br />363 <br />432 <br />391 <br />46276 <br />14 <br />419 <br />493 <br />447 <br />524 <br />476 <br />555 <br />504 <br />586 <br />632 <br />617 <br />560 <br />64875 <br />15 <br />588 <br />679 <br />616 <br />711 <br />644 <br />742 <br />672 <br />773 <br />700 <br />805 <br />728 <br />83674 <br />16 <br />756 <br />867 <br />784 <br />899 <br />812 <br />931 <br />840 <br />962 <br />868 <br />994 <br />896 <br />302673 <br />17 <br />924 <br />3057 <br />952 <br />3089 <br />939 <br />3121 <br />3007 <br />3153 <br />3035 <br />3185 <br />3062 <br />21772 <br />183090 <br />2493118 <br />2813145 <br />314 <br />173 <br />346 <br />201 <br />378 <br />228 <br />41171 <br />19 <br />256 <br />443 <br />283 <br />476 <br />311 <br />508 <br />338 <br />541 <br />365 <br />574 <br />393 <br />60770 <br />20 <br />420 <br />640 <br />448 <br />673 <br />475 <br />706 <br />502 <br />739 <br />529 <br />772 <br />557 <br />80569 <br />21 <br />584 <br />839 <br />fill <br />872 <br />638 <br />906 <br />665 <br />939 <br />692 <br />973 <br />719 <br />400668 <br />22 <br />746 <br />4040 <br />773 <br />4074 <br />800 <br />4108 <br />827 <br />4142 <br />854 <br />4176 <br />881 <br />21067 <br />23 <br />907 <br />245 <br />934 <br />279 <br />961 <br />314 <br />987 <br />3484014 <br />3834041 <br />41766 <br />244067 <br />4524094 <br />4874120 <br />5224147 <br />557 <br />173 <br />592 <br />200 <br />62865 <br />25 <br />226 <br />663 <br />253 <br />699 <br />279 <br />734 <br />305 <br />770 <br />331 <br />806 <br />358 <br />84164 <br />26 <br />384 <br />877 <br />410 <br />913 <br />436 <br />9504462 <br />986 <br />488 <br />5022 <br />514 <br />505963 <br />27 <br />540 <br />5095 <br />566 <br />5132 <br />592 <br />5169 <br />617 <br />5206 <br />643 <br />243 <br />669 <br />28062 <br />28 <br />695 <br />317 <br />720 <br />354 <br />746 <br />392 <br />772 <br />430 <br />797 <br />467 <br />823 <br />50561 <br />29 <br />848 <br />543 <br />874 <br />581 <br />899 <br />619 <br />924 <br />658 <br />950 <br />696 <br />975 <br />73560 <br />395000 <br />7745025 <br />5812 <br />5050 <br />8515075 <br />8905100 <br />9305125 <br />96959 <br />31 <br />150 <br />6009 <br />175 <br />6048 <br />200 <br />6088 <br />225 <br />6128 <br />250 <br />6168 <br />275 <br />620858 <br />32 <br />299 <br />249 <br />324 <br />289 <br />348 <br />3305373 <br />371 <br />398 <br />412 <br />422 <br />45357 <br />33 <br />446 <br />494 <br />471 <br />536 <br />495 <br />577 <br />519 <br />619 <br />544 <br />661 <br />568 <br />70356 <br />34 <br />592 <br />74.5 <br />616 <br />787 <br />640 <br />830 <br />664 <br />873 <br />688 <br />916 <br />712 <br />95955 <br />35 <br />736 <br />7002 <br />760 <br />7046 <br />783 <br />7089 <br />807 <br />7133 <br />831 <br />7177 <br />854 <br />722154 <br />36 <br />878 <br />265 <br />901 <br />310 <br />925 <br />355 <br />948 <br />400 <br />972 <br />445 <br />995 <br />49053 <br />376018 <br />5366041 <br />5816065 <br />6276088 <br />6736111 <br />7206134 <br />76652 <br />38 <br />157 <br />813 <br />180 <br />860 <br />202 <br />907 <br />225 <br />954 <br />248 <br />8002 <br />271 <br />805051 <br />39 <br />293 <br />8098 <br />316 <br />8146 <br />338 <br />8195 <br />361 <br />8243 <br />383 <br />292 <br />406 <br />34250 <br />40 <br />428 <br />391 <br />450 <br />441 <br />472 <br />491 <br />494 <br />541 <br />517 <br />591 <br />539 <br />64249 <br />41 <br />561 <br />693 <br />583 <br />744 <br />604 <br />796 <br />626 <br />847 <br />648 <br />899 <br />670 <br />95248 <br />42 <br />691 <br />9004 <br />713 <br />9057 <br />734 <br />9110 <br />756 <br />9163 <br />777 <br />9217 <br />799 <br />927147 <br />43 <br />820 <br />325 <br />841 <br />380 <br />862 <br />435 <br />884 <br />490 <br />905 <br />545 <br />926 <br />60146 <br />44 <br />947 <br />657 <br />967 <br />713 <br />988 <br />7707009 <br />8277030 <br />8847050 <br />94245 <br />457071 <br />1.0000 <br />7092 <br />1.0058 <br />7112 <br />1.0117 <br />133 <br />1.0176 <br />153 <br />1.0235 <br />173 <br />1.0295 <br />44 <br />t o <br />60' <br />60' <br />50' <br />50' <br />40' <br />40' <br />30' <br />30' <br />20' <br />20 <br />10' <br />101 <br />4 <br />'w <br />cos <br />cot <br />cos <br />cot <br />cos I <br />cot <br />cos <br />cot <br />cos <br />cot <br />cos <br />cot <br />b <br />