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

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

Table of contents

[21.] CHRISTIANI HUGENII, Const. F. AD C. V. FRAN. XAVERIUM AINSCOM. S. I. EPISTOLA. Cl. Viro D°. XAVERIO AINSCOM CHRISTIANUS HUGENIUS S. D.

[22.] CHRISTIANI HUGENII, Const. F. DE CIRCULI MAGNITUDINE INVENTA. ACCEDUNT EJUSDEM Problematum quorundam illuſtrium Conſtructiones.

[23.] PRÆFATIO.

[24.] CHRISTIANI HUGENII, Const. f. DE CIRCULI MAGNITUDINE INVENTA. Theorema I. Propositio I.

[25.] Theor. II. Prop. II.

[26.] Theor. III. Prop. III.

[27.] Theor. IV. Prop. IV.

[28.] Theor. V. Prop. V.

[29.] Theor. VI. Prop. VI.

[30.] Theor. VII. Prop. VII.

[31.] Theor. VIII. Prop. VIII.

[32.] Theor. IX. Prop. IX.

[33.] Problema I. Prop. X. Peripheriæ ad diametrum rationem invenire quamlibet veræ propinquam.

[34.] Problema II. Prop. XI.

[35.] Aliter.

[36.] Aliter.

[37.] Problbma III. Prop. XII. Dato arcui cuicunque rectam æqualem ſumere.

[38.] Theor. X. Prop. XIII.

[39.] Lemma.

[40.] Theor. XI. Prop. XIV.

[41.] Theor. XII. Prop. XV.

[42.] Theor. XIII. Prop. XVI.

[43.] Theorema XIV. Propos. XVII.

[44.] Theor. XV. Propos. XVIII.

[45.] Theor. XVI. Propos. XIX.

Page: 100 (382)

[46.] Problema IV. Propos. XX.

Page: 102 (384)

[47.] Christiani Hugenii C. F. ILLVSTRIVM QVORVNDAM PROBLEMATVM CONSTRVCTIONES. Probl. I. Datam ſphæram plano ſecare, ut portiones inter ſe rationem habeant datam.

[48.] LEMMA.

Page: 111 (390)

[49.] Probl. II. Cubum invenire dati cubi duplum.

Page: 112 (391)

[50.] Probl. III. Datis duabus rectis duas medias propor-tionales invenire.

Page: 114 (393)

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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