DIAGONAL 
' Taser If. In the annexed table, the polygon has been in general 
7 — taken above the meafure of the circumference, but the devia- . 
© a aaer Circum, Lite Quadrant. cel is very {mail, and cannot affe&t any praétical calcula- 
The number of fides being found by this table, that which 
6 19° 20 5 follows will give the angle which each fide forms with a 
8 25 24 6 horizontal ftraight line, seam a and feconde, and : 
TO Bi 32 8 taking the neareft degree ater minieene s be re- 
2 38 - 36 9 quired, which will be (eldom, if pai neceflary, the calcula- 
14 44 44 II 1 y be carried out even to decimals of a fecond, by t 
16 50 52 13 rules already given. ‘The firft column contains the fides in 
18 57 60 15 e whole circle, and the fecond, thofe in the quadrant, cor- 
20 63 64 16 re{ponding : table he remai col num- 
ae 69 72 18 bered from 1 to 26, give ‘the a aa . the fucceflive angles. 
24 "5 76 19 By the peeangie a always at ne the hori- 
26 82 84 21 zontal diameter of the circle, as AB 1, fig. 17. Plate V. up to 
28 88 ’ $8 22 a polygon of 100 fides, the whole angles in the quadrant are 
30 04. 96 24. iven; above that, they are only carried to the oftant, or 
32 100 100 25 ill, however, be obferved,. that the angles 
36 113 116 29 omitted are the exact complements | of thofe given, the ex- 
40 126 128 32 sn angles forming together 90°, and fo of the others 
44. 138 140 35 verging towards the ‘midée. Thus, in the laft line, 
48 152 152 38 mies 5t angles are required to complete the ss 26 
52 163 164 41 only arc given, and the 26th is the mean angle, or 45°. 
56 Ry6 170. 44 The firft angle is 89°, whofe complement being 1°, that is 
60 188 188 47 the meafure of the 51 The fecond being 87°, its com- 
64 201 204. 5 plement of 3° gives the ome and fo of all the others.: 
Tasve III. 
Polygon. {Quadrant 1 | 2) 3 ] 4/5 6|7 18 ]g {10 11 [39 13 |14| 15 | 16 17| 18] 19 | 20] 21 |22 |23 124 | 25 126 
20 5 (84°1634145°5]27°| 9° 
24 6 —|83 (68 153 137 j22 1-7° : 
32 8 184. 173 192 15 r 139 28 |17] 6° 
36 9 [85 175 195 [55 [RS [35 [25 [45 | 5° 
44 11 (86 178 |70 |62 {54 |45 |36 |28 |20 |12% 4° 
52 13 (86 79 |72 165 155 51 l45 139 [32 ]25 [tS jtr9 4° 
60 15 © {8-7 |Sr 175 [69 163 157 |5¢ [45 129 133 [27 [22 [£5 | 9°} 3° 
64 16 187 181 |76 170 [55 159 153 48 142 137 132 [25 |20 114} 9 | 3° 
92 18 187 (82 [77 [72 167 |62 157 152 147 [43 [38 133 [28 [23 [r8 |13 | 8°) 3° 
76 19 {88 183 178 173 |99 164 159 |54 |49 145 [41 [36 jaz [26 [ae j47 [12] 7 | 2° 
84 21 38 184 j80 175 171 |67 |62 158 [54 |49 145 lat 136 132 [28 Jag |rg [ts [10 | 6% 2% fF 
88 22 38 184 |80 176 |72 168 64 |50 156 |52 147 143 138 134 130 126 |22 [18 |r4 jro | O | 2° 
96 24.  |88 |84 [80 |77 |73 |69 |66 162 |58 15 4150 |47 143 140 [36132 28 [24 jar ]17 [15 [10 | 6% 2° 
100 25 38 184. 181 177 173 170 66 152 189 155 151 148 145 142 [39 [35 [34 [28 |24 120 [17 113 | 9 | 6 | 2° 
116 29 (88 |35 }32 79 |76 173 |7° 197 |O4 jor |58 |55 [52 [49 45 ; 
128 32 39 [86 ]83 |80 |78 175 |72 |6g j67 [64 JOr 158 155 152 |49 [46 
149 35 — |8Q |S6 [84 181 178 |75 |73 [70 JO8 [65 ]O2 |50 |57 |54 152 149 147 145 
152 38 — [89 |86 |84 [8x I79 |76 174 |71 |69 |67 [65 |52 |60 157 [55 |52 150 [48 [46 
164. 41 {89 |87 |85 [83 [80 178 176 [74 |71 j59 [67 |O5 [62 |60 [58 156 153 |5z 49 147 [45 
176 44 [89 |87 |85 [83 |8z 179 177 |75 |72 |7° 68 166 |64 |62 [50 |58 156 I54 152 150 [48 |46 
188 47 [89 [87 |35 [83 [54 179 177 [79 |74 [72 79 JO8 |66 164 162 {50 [59 157 155 |53 151 149 147 [45 
204 51 [89 [87 185 [83 [82 [80 Fer | 75 173 {74 [69 [68 166 |54 163 |61 159 |57 156 [54 152 [50 148 [47°145° 
A fingle example will probably be fufficient to elucidate 3d - Angle - o2° 
' the ufe of all the three tables, after the previous defcriptions. 4th ~ ditto - 65 
et it be required to form a circle eans neryy 5th “ ditto - 58 
the diameter of which fhall be half an i s 7, is the 6th + ditto - 51 
ee of unity, the diameter will be reprefented by 16 in “th - ditto - 45 | 
able II, By infpecting the table it will appear, that th Sth - ditto = . 39 
canines is 5° ee neareft polygon 52, and the fides oth - ditto - 32 
contained in one qua roth ss ditto © 25°) 
By table III. we fin, eee the ane quoted, for the 1ith . ditto “ 18 
ft Angle 86° 12th - ditto - Ir 
a “ ‘ditto = 7 ith - ditto = 4 
x Let 
