Page:Cyclopaedia, Chambers - Volume 1.djvu/521

CYCLOID, in Geometry, one of the Mechanical, or, as others term 'em, the Tranſcendental Curves; called also the Trachoid. See Curve, and Trochoid.

It is describ'd by the Motion of a Point A, (Tab. Analysis, Fig. 55.) in the Periphery of a Circle, while the Circle makes a Revolution along the right Line A P.

Hence, the Properties of this Curve, viz. that the right Line A E is equal to the Periphery of the Circle A B C D ; and A C to the Semi-periphery; and in any Situation of the generating Circle, the right Line Ad is equal to the Arch D d.—Again, a d being parallel to A C; A D is equal to the Arch of the generating Circle d F.—Further, the whole length of the Cycloid is four times that of the Diameter of the generating Circle; and the Cycloidal Space comprehended between the Curve and the Subtense A E, triple the Area of the generating Circle.—Lastly, any Part estimated from the Vertex, as F I, is every where dou- ble the Chord of the Circle F; and the Tangent thereof GI, perpetually parallel to the same Chord F b.

The Genesis of the Cycloid, may be conceiv'd by imagining a Nail in the Circumference of a Wheel; the Line which the Nail describes in the Area, while the Wheel revolves in a right Line, is the Cycloid.

The Cycloid is reputed a modern Curve, and its Invention ascrib'd by some to Mersenne; by others to Galileo: but Dr. Wallis shews it of an older standing, and to have been known to Bovillus, about the Year 1500; and even consider'd by Cardinal Cusanus much earlier, viz. before the Year 1451.

M. Huygens has demonstrated, that from whatever Point, or Height, a heavy Body, oscillating on a fix'd Centre, (v.g. a Pendulum) begins to descend; while it continues to move in a Cycloid, the Times of its Falls, or Oscillations, will be equal to each other.

This Property M. Fontenelle states thus: The Nature of the Cycloid is such, that, if a Body which describes it, fall from a greater height, and by that means acquire a certain Augmentation of Velocity, as in Galileo's Theory, the greater Cycloidal Arch which it describes, takes up precisely that Excess of Velocity. So that the Body does not describe it, either sooner for its being accelerated, or later for having a greater Space to move: And hence arises an Equality in Time, notwithstanding the Inequality of Arches. On this Foundation it is, that the Pendulum-Clock is built on the Subject whereof, the same M. Huygens has wrote a large Volume, under the Title of Horologium Oscillatorium. See Pendulum; see also Oscillation.

CYCLOIDAL Space, the Space contained between the Cycloid, and the Subtense thereof. See CYCLOID.

CYCLOMETRY, the Art of measuring Cycles, or Circles. See CYCLE, and CIRCLE.

CYCLOPÆDIA, the Circle, or Compafs of Arts and Sciences; more ordinarily call'd Encyclopedia. See ENCYCLOPEDIA.

CYGNUS, the Swan, in Astronomy, a Constellation of the Northern Hemisphere. See CONSTELLATION.

Stars in the Constellation Cygnus, in Ptolemy's Catalogue ate 17; in Tycho's 19; in the Britannic Catalogue 107. The Order, Names, Longitudes, Latitudes, Magnitudes, &c. whereof, are as follow.

Stars in the Constellation CYGNUS.

Names and Situations of the Stars.	Signs	Longitude	Latitude	Magn.
Preced. of two towards the Harp		20	54	46	66	13	6	5
Subseq. and more North.		25	41	28	68	49	57	6
In the Extremity of the North Wing		10	38	18	73	50	11	4
That preced, the Bill towards the So.		23	47	46	47	44	20	5
Preced, the Bill towards the South		25	18	47	50	57	30	5
5.
		24	16	45	46	25	40	6
		28	51	20	57	20	44	6
That below the Bill		25	12	34	45	54	20	6
		25	16	24	45	59	22	6
In the Bill		26	55	37	49	0	31	3,4
10.
Middle of 3 in the North Wing		13	40	9	72	10	51	6
		29	55	52	55	14	20	6
		13	42	43	71	28	38	4
		2	38	16	57	23	36	6
In the Head,		0	36	19	50	39	38	5
15
South of 3 in the North Wing		14	22	42	69	37	56	4
		7	54	44	63	42	5	6
		0	18	38	46	10	32	6
		5	50	43	57	15	9	6
Preced, in the Inside of the No. Wing		17	1	8	69	30	50	6
20
Preced. in the Neck		4	36	37	53	42	33	5
In the Angle of the North Wing		11 57 17 64 27 14 3 4
		1	28	49	42	41	50	4 5
		8	53	22	58	7	12	6
		2	43	29	43	58	26	4 5
25
North of the middle Stars in the Wing		24	13	58	70	13	46	5 6
In the middle of the Neck		37	28	54	18	48	4
		10	31	20	57	31	4	6
		4	7	19	42	40	56	5
		25	11	36	74	10	15	6 7
30	South of the middle Stars in the Wing		25 9 41 69 59 55 6 31 37 47 1 43 4 5 10 58 10 55 54 29 6 5 39 1 44 15 50 5	Last of those in the North Wing		23 44 12 67 33 40 6
35	6 36 40 42 41 12 4 5	Preced. in the Rife of the Neck	12 30 29 54 28 16 5	9 3 51 45 34 54 6 5	Middle of 3 in the Rife of the Neck	13 57 43 55 1 40 5	9 14 14 45 24 28 6
40	9 19 24 45 4 48 5 6 10 59 28 47 2 8 5 6 9 7 46 42 0 27 5	Subseq. in the Rise of the Neck	15 34 43 54 36 33 6 11 3 12 46 5 20 4 5
45
9 58 47 43 1 53 5	Preced. in the Foot, which is double		23 46 19 63 43 29 5	"	23 47 55 63 38 3 4	Subseq. in the same Foot	25 31 58 64 18 13 5 6	A new one of the Breast, Anno 1600		17 29 12 55 29 20 6
50
South of two under the new one	15	44	13	52	36	15	6	North of the same		17	2	13	54	33	16	6			11 26 23 42 26 36 6	In the Breast (of the N. Wing	20	32	51	57	9	20	3
Middle of 3 Informes preced.the Angle		15	42	22	49	36	33	4
55
20	51	58	55	4	46	6	South of the same		16 24 20 47 28 53 4			20	0	57	53	7	6	4			1	22	17	64	41	46	5	6			20	57	9	53	23	53	4
60
Middle and brighter agst, the No.Knee		1	46	7	64	3	51	5
Subseq. at the Knee		2	31	4	64	10	7	5 6
North of those preced. the Angle		20	37	18	51	38	16	5
		16	10	4	42	45	11	6
Preced of the Informes in the Triangle near the Tropic	16	42	41	43	13	32	5 6
65	South, in that Triangle	16	2	55	40	54	36	5 6
		14	56	59	38	7	7	5		Bright Star in the Tail		1	1	32	59	56	37	2
70
Subseq. of the faid Triangle		18	22	34	41	30	54	6
Inform under the Angle of the S. Wing		21	21	29	46	30	26	5
In the Angle or Elbow of the So. Wing		23	22	52	49	26	21	3
In the middle of the same Wing		25	26	47	51	38	37	4
75
	4	8	54	49	57	10	5
South of those preced. the Extreme of the 2 Informes of the S. Wings		21	18	12	42	37	9	6
South of those preced. the Extreme of the 2 Informes of the S. Wings		3	39	19	58	5	13	6
North of those prec. the Extrem.of the Wing		22	45	37	43	13	58	5
80
	20	45	4	37	39	42
In the South Foot		1	51	21	54	56	25	4
Foremost of 3 in the North Part of the Tail		8	49	9	60	6	19	5 6
South of the same	7	42	10	58	50	19	6 7
85		Against the South Knee		6	32	3	56	5	4
Subseq. in the North Part of the Knee		10	50	42	59	33	35	5 6
		24	51	36	37	59	50	6
In the Extrem. of the South Wing		28	44	36	43	43	13	3
Middle of those in the South Wing		4	16	38	50	32	40	4
That under the Extrem.of the S. Wing		28	44	36	43	43	13	3
90
South of 3 in the Wing		2	57	29	47	29	30	5
North of the same		6	3	49	51	30	45	4
A small one following the South Knee		10	14	21	55	20	9	6
		6	1	38	48	25	8	6
That the under the Extrem. of the S. Wing			1	14	9	40	0	20	6 5
95
		7	1	15	48	34	55	6
North of 2 in the Extrem. of the Tail			15	39	47	56	25	37	6
		9	59	28	49	7	0	6
South in the Extremity of the Tail			15	53	18	55	12	21	4 5
		12	1	23	50	32	2	6
100
		15	15	52	52	39	30	6
		13	31	55	50	25	21	6
		13	56	49	50	34	26	6
Under the South Wing, towards the Foot of Pegasus		6	8	0	39	32	16	3 4
Under the South Wing, towards the Foot of Pegasus		12	3	43	48	3	34	6
105
N. of the Informes following the Tail		14	1	45	58	52	37	4 5
South of those following the Tail		13	17	18	57	12	6	5

CYLIN-