Mathematicians have given much attention to the construction of such trigonometrical formulas as require only the operations of multiplication, division, involution, and evolution. For examples of this, see Articles 866 and seq. in Plane Triangles, and Articles 880 and seq. in Spherical Triangles. EXERCISES. 916.—1. Calculate the value of these expressions: √/8932.045726, 12 760910, 137 × 14° ÷ 1.256. 2. Find the area of a circle, the radius being 3 feet (500). 3. What is the diameter of a circle whose circumference is 314 feet 3 inches? 4. What is the area of a triangle whose sides are 417, 1493, and 1307 feet? (390.) 5. The diameter of the earth at the equator being 41850000 feet, what is the length in miles of one degree of longitude on the equator, there being 5280 feet in one mile? 6. The earth being a sphere with a radius of 20890000 ft., how many square miles are there in its surface? Ational exercises may be made upon the formulas of Art. 807. TABLES OF LOGARITHMS OF NUMBERS, FROM 1 TO 11000, LOGARITHMS OF 168 PRIME NUMBERS, To 15 PLACES OF DECIMALS, NATURAL SINES AND TANGENTS, FOR EVERY TEN MINUTES, AND LOGARITHMIC SINES AND TANGENTS, FOR EVERY MINUTE OF THE QUADRANT. N. 0 1 2 3 4 5 6 7 8 9 | D. 101 102 103 012837 101 7033 100 000000 0434 0868 1301 1734 2166 2598 3029 3461 3891 432 4321 4751 5181 5609 6038 6466 6894 7321 7748 8174 428 8600 9026 9451 9876 .0300 .0724 .1147 .1570.1993] .2415 424 3259 3680 4100 4521 4940 5360 5779 6197 6616 420 7451 7868 8284 8700 9116 9532 9947 .0361 .0775 416 1603 2016 5715 6125 2428 2841 3252 3664 4075 4486 4896 6533 6942 7350 7757 8164 8571 8978 408 9789 .0195 .0600 .1004 .1408 .1812 .2216 .2619 .3021 401 3826 4227 4628 5029 5430 5830 6230 6629 7028 401 7825 8223 8620 9017 9414 9811 .0207 .0602 .0998 397 412 120 121 122 123 124 4820 079181 9543 9904 .0266 .0626 .0987 .1347 .1707 .2067 .2426 360 6438 6748 7058 7367 7676 7985 8294 8603 8911 309 9527 9835 .0142 .0149 .0756 .1063 .1370.1676 .1982 307 2594 2900 3205 3510 3815 4120 4424 4728 5032 305 5640 5943 6246 6549 6852 7154 7457 7759 8061 303 8664 8965 9266 9567 9868 .0168 .0469 .0769 .1068 301 180 255273 181 182 260071 0310 0548 183 2451 2688 2925 184 4818 5054 5290 5514 5755 5996 6237 6477 6718 6958 7198 7439 241 7679 7918 8158 8398 8637 8877 9116 9355 9594 9833 239 0787 1025 1263 1501 1739 1976 2214 238 3162 3399 3636 3873 4109 4346 4582 237 5525 5761 5996 6232 6167 6702 6937 235 190 278754 191 281033 192 193 194 8982 9211 9439 9667 1261 1488 1715 1942 3301 3527 3753 3979 4205 5557 5782 6007 6232 6456 7802 8026 8249 8473 8696 8920 9143 9366 9589 9812 223 195 290035 0257 0480 0702 0925 1147 1369 1591 1813 2034 222 2256 2478 2699 2920 3141 3363 3584 3804 4025 4246 221 4466 4687 4907 5127 5347 5567 5787 6007 6226 6446 220 7101 7323 7542 7761 7979 8198 8416 8635 219 9289 9507 9725 9943 .0161 .0378 .0595 .0813 218 8 9 1 2 3 4 5 9843 6 7 89 D. 1247 1464 1681 1898 2114 2331 2547 2764 2980 217 3112 3628 3844 4059 4275 4191 4706 4921 5136 216 5566 5781 5996 6211 6425 6639 6854 7068 7282 215 7710 7924 8137 8351 8564 8778 8991 9204 9417 213 .0056 .0268 .0481 .0693 .0906 .1118 .1330 .1542 212 205 311754 206 207 2031 209 320146 0562 0769 0977 1966 2177 2389 2600 2812 3023 3234 3445 3656 211 3867 4078 4289 4499 4710 4920 5130 5340 5551 5760 210 5970 6180 6390 6599 6809 7018 7227 7436 7646 7854 209 8063 8272 8481 8689 8898 9106 9314 9522 9730 9938 208 0354 1184 1391 2620 2817 3014 3212 3409 3606 3802 3999 4196 197 1917 2105 2294 2482 2671 2859 3048 3236 3424 188 3612 3800 3988 4176 4363 4551 4739 4926 5113 5301 188 232 5488 5675 5862 6049 6236 6423 6610 6796 6983 7169 187 233 7356 7542 7729 7915 8101 8287 8473 8659 8845 9030 186 231 9216 9401 9587 9772 9958 .0143 .0328 .0513 .0698 .0883 185 240 380211 0392 0573 0754 0934 1115 241 2017 2197 2377 2557 2737 2917 3097 3277 3456 3636 180 242 3815 3995 4174 4353 4533 4712 4891 5070 5249 5428 179 243 5606 5785 5964 6142 6321 6499 6677 6856 7034 7212 178 244 7390 7568 7746 7923 8101 8279 8456 8634 8811 8989 178 |