Huygens, Christiaan - Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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102384CHRISTIANI HUGENII

Problema IV. Propos. XX.

CIrcumferentiæ ad diametrum rationem inve-
ſtigare; & ex datis inſcriptis in dato circulo
invenire longitudinem arcuum quibus illæ ſubtendun-
tur.

Eſto circulus centro D, cujus diameter C B, & ſit arcus
11TAB. XL.
Fig. 6. B A ſextans circumferentiæ, cui ſubtenſa ducatur A B,
itemque ſinus A M. Poſitâ igitur D B ſemidiametro par-
tium 100000, totidem quoque erit ſubtenſa B A. A M ve-
rò partium 86603 non unâ minus, hoc eſt, ſi una pars ſi-
ve unitas auferatur ab 86603 fiet minor debito. quippe ſe-
miſſis lateris trianguli æquilateri circulo inſcripti.

Hinc exceſſus A B ſupra A M fit 13397 vero minor.
Cujus triens 4465 {2/3} additus ipſi A B 100000, fiunt partes
104465 {2/3} minores arcu A B. Et hic primus eſt minor termi-
nus, quo poſtea alium vero propiorem inveniemus. Prius
autem major quoque terminus ſecundum Theorema præce-
dens inquirendus eſt.

Tres nimirum ſunt numeri quibus quartum proportiona-
lem invenire oportet. Primus eſt partium duplæ A B & tri-
plæ A M qui erit 459807, vero minor, (nam hoc quoque
obſervandum ut minor ſit, idemque in cæteris prout dicetur)
ſecundus quadruplæ A B & ſimplæ A M qui 486603 vero
maj. Et tertius triens exceſſus A B ſupra A M, 4466 vero
major. Itaque quartus proportionalis erit 4727 vero maj.
quo addito ad A B 100000 fit 104727, major numero par-
tium, quas continet arcus A B, peripheriæ ſextans. 22per præced. igitur invenimus longitudinem arcus A B ſecundum mino-
rem majoremque terminum, quorum hic quidem longe pro-
pior vero eſt, cum vero proximus ſit 104719.

Sed ex utroque iſtorum alius minor terminus habebi-
tur priore accuratior ſi@ utamur præcepto ſequenti, quod
à diligentiori centrorum gravitatis inſpectione dependet.

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110	389
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Scan	Original
101	383
102	384
103	385
104	386
105
106	386
107
108	387
109
110	389
111	390
112	391
113	392
114	393
115	394
116	395
117	396
118	397
119	398
120
121
122
123	399
124	400
125	401
126	402
127	403
128	404
129
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