Full text: Musschenbroek, Petrus: Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes

Diſtantia \\ pollicum \\ a contactu # Numerus \\ linearum \\ Aquæ elevatæ
9 # 1
6 # 2
4 {3/4} # 3
3 # 4 {3/4}
2 {1/2} # 6
2 # 7 {1/2}
1 {1/2} # 10
1 {1/4} # 12
1 # 15
{3/4} # 19
{1/2} # 28
{1/4} # 50

Tab. XIII. Fig. 2. Quotieſcunque angulus inter ambo ſpecula
comprehenſus eſt exiguus & linea juncturæ perpendicularisin Aquam
curva ab Aquâ deſcripta eſt Hyperbola inter aſymptotas ſuas con-
tenta, quarum una eſt ſuperficies Aquæ, altera, junctura ſpeculo-
rum. Ducantur enim duæ rectæ A C, B C quæ repræſentent ſe-
ctionem ſpeculorum junctorum in C. concipiatur B C diviſa in ali-
quot partes æquales & parvas, quales ſunt e g, im. & quia angulus
A C B eſt parvus, poſſunt concipi d f e g, h lim, ut parallelogram-
ma: quia autem poſitis ſpeculis a ſe diſtantibus & parallelis copia
aquæ adſcendentis eſtæqualis per Corol. 2. §. 3, erit inter d f e g,
æqualis Aquæ copia ac inter h i l m, adeoque erunt ea paralle-
lopipeda Aquæ æqualia, quorum altitudines ſunt reciproce ut ba-
ſes d e f g, h i l m. & quia hæ habent latus e g = i m, erunt
baſes uti de, ad hi, ſed ob triangula ſimilia d C e, h C i, eſt de,
h i: : e C, i C. quare erit altitudo Aquæ in e, ad eam in i, ut i C. ad e C ſive reciproce ut diſtantiæ â C. Quare ſi i C multiplicetur
in ſuam altitudinem, dabit productum æquale illi ex e C in ſuam; ve-
rum nota hæc eſt natura Hyperbolæ, ut parallelogramma vid.

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