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

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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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