employed ly Ptolemy and those now in Use. 455 
tract from the trigonometrical tables now in use.—Before in- 
serting the table, we may borrow the following example for the 
purpose of showing how near Ptolemy approached to our cus- 
tomary ratio of 1:3:1416: the chord of 2° in sexagesimals to 
radius £ or 60° is 6 ¢ wz or 2° 5’ 40", which in decimals is nearly 
-034907 to radius 1, and this multiplied by = = 90 gives 
3-1416 nearly : now as the chord of 2° is almost the measure of 
its are, the above number may be taken as the length of the 
semicircumference. 
Edinburgh, 12th November 1818. 
2° 5' 40" 9° 5! 303" 
4 11 16 4 11 163 
6 16 49 6 106 49 
“0349074 | °0349048 
‘0697903 | °0697990 
-10467 13 -1046720 
"1395139 | ‘1395130 
"1743148 | °1743114 
2090555 | *2090570 
2437361 *2437386 
2783472 | °*2783462 
*3128657 | °3128090 
| *3472963 "3472004 
22 53 49 | 22 53 4yz | °3816157 *3810180 
*41§S261 | °4158234 
4498981 | “4498024 
; 29 1.50). 29 1,50 4838426 | ‘4838438 
3L 3.30| 31 3 30 5176389 | °5176380 
33 435 | 33 4 35 *5512731 | °5512748 
35 5 5\ 35 5 44 | °5847454 | 5847434 
37 455 | 37 455 -6180324 | °6180340 
39 4 5| 39 4 53 | °6511343 “6511364 
41 233] 41 2 33 ‘6840417 | °6840402 
Az OL), 4B (Oy 35 *7167301 | °7167358 
7492130 | *7492132 
“7814630 | *7814622 
8134722 | °8134732 
"8452301 | «8452360 
*8767407 | °8707422 
‘9079815 | °9079810 
9389444 | “9380432 
-9696204 | ,9696192 
1:0000000 | 1 OOOGO00 
10300787 | 1°0300762 
1:0598426 | 1:0598386 
1'0892778 | 1:0892780- 
1'1183889 | 111183853 
171471528 |} 171471528 
11755694 | 1°1755706 
72 ASA IDALS, & 1'2036296 | 1°2030300 
73 52 46| 73 52 46 1°2313¢61 | 1°2313230 
75 31 7| 75 81 6% | 1:2586435 | 1:2586408 
