Nine geometricall exercises, for young sea-men and others that are studious in mathematicall practices: containing IX particular treatises, whose contents follow in the next pages. All which exercises are geometrically performed, by a line of chords and equal parts, by waies not usually known or practised. Unto which the analogies or proportions are added, whereby they may be applied to the chiliads of logarithms, and canons of artificiall sines and tangents. By William Leybourn, philomath.

By the Projection.

Lay a Ruler to P and k, it will cut the Meridian Cir∣cle in s: the distance S s, taken and measured upon your Line of Chords, will contain 56 degr. 50 min. the Sun's right Ascension.

I should here shew how the right Ascension and Declination of a Star might be found; but, the Calculation Trigonometricall being very laborious, I have therefore in this place omitted it, be∣cause I have in another Treatise, now speedily to be published, fra∣med Tables of the Longitude, Latitude, Right Ascension, De∣clination,

and Semidiurnall Arches, of the most eminent Fixed Stars in the Heavens, exactly calculated for the Year of our Lord 1670; and also other Tables of the Sun's right Ascension for every Degree of the Ecliptick and Day of the Year: by help of which Tables, the Hour of the Night, the Rising, Setting, and the time of their coming to the South, may be obtained by the Rules and Directions prescribed in the forementioned Treatise, which will contain (besides the Tables here mentioned) all such others as at any time the Sea-man shall have occasion for in his Practice, and divers other things too tedious here to enumerate. But in the mean time I shall request the Reader to be satisfied with these two Tables following: These Exercises being things onely Practicall.

A Table of the Sun's right Ascension for every De∣gree of the Ecliptick.

Degr.	♈	♉	♊	♋	♌	♍
0	0 0	27 54	57 48	90 0	122 12	152 6
1	0 55	28 51	58 51	91 5	123 14	153 3
2	1 50	29 49	59 53	92 11	124 16	154 1
3	2 45	30 46	60 56	93 16	125 19	154 58
4	3 40	31 44	61 59	94 22	126 20	155 54
5	4 35	32 42	63 2	95 27	127 22	156 51
6	5 30	33 40	64 6	96 32	128 24	157 48
7	6 25	34 38	65 9	97 38	129 25	158 44
8	7 21	35 37	66 13	98 43	130 26	159 40
9	8 16	36 36	67 17	99 48	131 27	160 37
10	9 11	37 34	68 21	100 53	132 28	161 33
11	10 6	38 33	69 25	101 58	133 28	162 29
12	11 1	39 33	70 29	103 3	134 29	163 25
13	11 57	40 32	71 34	104 8	135 29	164 20
14	12 52	41 31	72 38	105 13	136 29	165 16
15	13 48	42 31	73 43	106 17	137 29	166 12
16	14 44	43 31	74 47	107 22	138 29	167 7
17	15 40	44 31	75 52	108 26	139 28	168 3
18	16 35	45 31	76 57	109 31	140 27	168 58
19	17 31	46 32	78 1	110 35	141 27	169 54
20	18 27	47 32	79 7	111 39	142 26	170 49
21	19 23	48 33	80 12	112 43	143 24	171 44
22	20 20	49 34	81 17	113 47	144 23	172 39
23	21 16	50 35	82 22	114 51	145 22	173 35
24	22 12	51 36	83 28	115 54	146 21	174 30
25	23 9	52 38	84 33	116 57	147 18	175 25
26	24 6	53 40	85 38	118 1	148 16	176 20
27	25 2	54 41	86 44	119 4	149 14	177 15
28	25 59	55 44	87 49	120 7	150 11	178 10
29	26 56	56 46	88 55	121 9	151 9	179 5
30	27 54	57 48	90 0	122 12	152 6	180 1

A Table of the Sun's right Ascension for every De∣gree of the Ecliptick.

Degr.	♎	♏	♐	♑	♒	♓
0	180 0	207 54	237 48	270 0	302 12	332 6
1	180 55	208 51	238 51	271 5	303 14	333 3
2	181 50	209 49	239 53	272 11	304 16	334 1
3	182 45	210 46	240 56	273 16	305 19	334 58
4	183 40	211 44	241 59	274 22	306 20	335 54
5	184 35	212 42	243 2	275 27	307 22	336 51
6	185 30	213 40	244 6	276 32	308 24	337 48
7	186 25	214 38	245 9	277 38	309 25	338 44
8	187 21	215 37	246 13	278 43	310 26	339 40
9	188 16	216 36	247 17	279 48	311 27	340 37
10	189 11	217 34	248 21	280 53	312 28	341 33
11	190 6	218 33	249 25	281 58	313 28	342 29
12	191 2	219 33	250 29	283 3	314 29	343 25
13	191 57	220 32	251 34	285 8	315 29	344 20
14	192 52	221 31	252 38	286 13	316 29	345 16
15	193 48	222 31	253 43	287 17	317 29	346 12
16	194 44	223 31	254 47	288 22	318 29	347 7
17	195 40	224 31	255 52	289 26	319 28	348 3
18	196 35	225 31	256 57	290 31	320 27	348 58
19	197 31	226 32	258 1	291 35	321 27	349 54
20	198 27	227 32	259 7	292 39	322 26	350 49
21	199 23	228 33	260 12	293 43	323 24	351 44
22	200 20	229 34	261 17	294 47	324 23	352 39
23	201 16	230 35	262 22	295 51	325 22	353 35
24	202 12	231 36	263 28	296 54	326 21	354 30
25	203 9	232 38	264 33	297 57	327 18	355 25
26	204 6	233 40	265 38	298 1	328 16	356 20
27	205 2	234 41	266 44	299 4	329 14	357 15
28	205 59	235 44	267 49	300 7	330 11	358 10
29	206 56	236 46	268 55	301 9	331 9	359 5
30	207 54	237 48	270 0	302 12	332 6	360 0

The right Ascension, Declination, and Ma∣gnitude of some principal Fixed Stars.

The Stars Names.	Right A∣scension.	Declina∣tion.		Magni∣tude.
	D. M.	D. M.
The Pole-Star	7 47	87 27	N	2
The Girdle of Andromeda	12 32	33 48	N	2
The former Horn of the Ram	23 38	17 37	N	4
Bright Star in the Ram's Head	26 56	21 48	N	3
The Whale's Jaw	41 3	2 42	N	2
The Head of Medusa	41 27	39 35	N	3
The Bull's Eye	64 0	15 46	N	1
The Goat	72 44	45 35	N	1
The former Shoulder of O∣rion	76 38	4 59	N	2
The latter Shoulder of O∣rion	84 7	7 18	N	2
The great Dog	97 27	16 13	S	1
The uppermost Head of the Twins	108 1	32 35	N	2
The little Dog	110 17	6 6	N	2
The lower Head of the Twins	111 0	28 49	N	2
The Crib	125 4	20 52	N	Neb.
Hydra's Heart	137 39	7 10	S	2
Lion's Heart	147 27	13 39	N	1
Lion's Loins	163 54	22 26	N	2
Lion's Tail	172 49	16 32	N	1
The Virgin's Girdle	189 32	5 20	N	3

The right Ascension, Declination, and Ma∣gnitude of some principal Fixed Stars.

The Stars Names.	Right A∣scension.	Declina∣tion.		Magni∣tude.
	D. M.	D. M.
Aliot	189 36	57 36	N	2
Vindemiatrix	191 15	12 51	N	3
The Virgin's Spike	196 44	9 17	S	1
Arcturus	209 56	21 4	N	1
The Southern Balance	217 56	14 32	S	2
The Northern Balance	224 31	8 2	S	2
In the Serpent's Neck	231 49	7 35	N	3
The Scorpion's Heart	242 4	25 34	S	1
Hercules Head	254 40	14 51	N	3
Ophiuchus Head	259 41	12 52	N	3
The Harp	276 17	38 30	N	1
The Vulture	293 27	8 1	N	2
The upper Horn of the Goat	299 30	13 32	S	3
Left Hand of Aquarius	307 10	10 43	S	4
Left Shoulder of Aquarius	318 18	7 2	S	3
Pegasus Mouth	321 49	8 18	N	3
Right Shoulder of Aquarius	326 59	1 58	S	3
Fomahant	339 29	31 23	S	1
Upper Wing of Pegasus	341 53	13 21	N	2
In the tip of Pegasus Wing	358 52	13 15	N	2