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

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[11.] Theorema III.
Page: 17 (317)
[12.] Theorema IV.
Page: 18 (318)
[13.] Lemma.
Page: 19 (319)
[14.] Theorema V.
Page: 20 (320)
[15.] Theorema VI.
Page: 23 (323)
[16.] Theorema VII.
Page: 24 (324)
[17.] Theorema VIII.
Page: 29 (326)
[18.] ἘΞἘΤΑΣΙΣ CYCLOMETRIÆ CLARISSIMI VIRI, GREGORII à S. VINCENTIO, S. J. Editæ Anno D. cIↄ Iↄc XLVII.
Page: 34 (328)
[19.] FINIS.
Page: 49 (340)
[20.] CHRISTIANI HUGENII, Const. F. AD C. V. FRAN. XAVERIUM AINSCOM. S.I. EPISTOLA, Qua diluuntur ea quibus Ε’ξε{τα}{σι}ς Cyclometriæ Gregorii à Sto. Vincentio impugnata fuit.
Page: 53
[21.] CHRISTIANI HUGENII, Const. F. AD C. V. FRAN. XAVERIUM AINSCOM. S. I. EPISTOLA. Cl. Viro D°. XAVERIO AINSCOM CHRISTIANUS HUGENIUS S. D.
Page: 55
[22.] CHRISTIANI HUGENII, Const. F. DE CIRCULI MAGNITUDINE INVENTA. ACCEDUNT EJUSDEM Problematum quorundam illuſtrium Conſtructiones.
Page: 63
[23.] PRÆFATIO.
Page: 65
[24.] CHRISTIANI HUGENII, Const. f. DE CIRCULI MAGNITUDINE INVENTA. Theorema I. Propositio I.
Page: 69
[25.] Theor. II. Prop. II.
Page: 70 (358)
[26.] Theor. III. Prop. III.
Page: 70 (358)
[27.] Theor. IV. Prop. IV.
Page: 72 (360)
[28.] Theor. V. Prop. V.
Page: 73 (361)
[29.] Theor. VI. Prop. VI.
Page: 73 (361)
[30.] Theor. VII. Prop. VII.
Page: 74 (362)
[31.] Theor. VIII. Prop. VIII.
Page: 76 (364)
[32.] Theor. IX. Prop. IX.
Page: 77 (365)
[33.] Problema I. Prop. X. Peripheriæ ad diametrum rationem invenire quamlibet veræ propinquam.
Page: 78 (366)
[34.] Problema II. Prop. XI.
Page: 83 (368)
[35.] Aliter.
Page: 84 (369)
[36.] Aliter.
Page: 84 (369)
[37.] Problbma III. Prop. XII. Dato arcui cuicunque rectam æqualem ſumere.
Page: 85 (370)
[38.] Theor. X. Prop. XIII.
Page: 86 (371)
[39.] Lemma.
Page: 87 (372)
[40.] Theor. XI. Prop. XIV.
Page: 87 (372)
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17317HYPERB. ELLIPS. ET CIRC.
Data ſit portio A B C & triangulus D E F, baſibus A C,
11TAB. XXXIV
Fig, 2. D F æqualibus; & portionis diameter ſit B G, in trian-
gulo verò ducta à vertice in mediam baſin linea E H. Sint
autem utræque B G, E H vel ad baſes rectæ vel æqualiter
inclinatæ; & quam rationem habet B G ad E H, in eandem
dividatur ſpatium datum, ſintque partes K & L. Circumſcri-
batur jam ſicut antea portioni A B C figura ordinatè, quæ
portionem ſuperet exceſſu minore quàm ſit ſpatium K. Et
triangulo D E F circumſcribatur figura quæ totidem paral-
lelogrammis conſtet, quot ſunt in figura portioni A B C cir-
cumſcripta.
Quoniam igitur baſes portionis & trianguli æquales ſunt,
apparet quidem omnium parallelogrammorum eandem fore
latitudinem. Hinc quum parallelogrammum B M ſit ad E R
ut B G ad E H, id eſt ut K ad L, ſitque B M minus quam
K , erit quoque E R minus quam L . Verùm omnia 22Ex conſit.3314. 5.
Elem. gula quibus conſtat exceſſus figuræ circumſcriptæ ſupra trian-
gulum D E F, æqualia ſunt parallelogrammo E R, ergo
minor eſt idem exceſſus ſpatio L. Sed & exceſſus quo figu-
ra circumſcripta portionem A B C ſuperat, minor eſt ſpa-
tio K. Ergo utergue ſimul exceſſus minor erit ſpatio K L
dato. Et conſtat fieri poſſe quod proponebatur.
Theorema III.
SI portioni hyperboles, vel ellipſis vel circuli por-
tioni, dimidiâ ellipſi dimidiove circulo non majori,
circumſcribatur figur a or dinatè; ejus figuræ centrum
gravitatis erit in portionis diametro.
Sit portio quælibet iſtarum A B C, diameter ejus B D;
44TAB. XXXVI.
Fig. 3.& circumſcribatur ei ut ſupra figura ordinatè. Oſtenden-
dum eſt ejus figuræ centrum gravitatis fore in B D diametro.
Ducantur lineæ H K, N R, P S, conjungentes ſuprema
latera parallelogrammorum quæ à diametro portionis æqua-
liter utrinque diſtant.

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