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# Title: [Christiani Hugenii Zulichemii, Const. F. Horologium Oscillatorium. Sive De Motu Pendulorum Ad Horologia Aptato Demonstrationes Geometricae] Christiani Hvgenii Zvlichemii, Const. F. Horologivm Oscillatorivm. Sive De Motv Pendvlorvm Ad Horologia Aptato Demonstrationes Geometricæ (shelfmarks Leibn. Marg. 70; ZEN Leibn. Marg. 70)
# Folio 90, page id 799199311:0106
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CHRISFLAHL AVOENIS
generis hyperboloides existunt, quarum proprietatem lequens
cabella linculis aequarionibus exhribet, simulque rationem con-
struendi curram D C, cujus erolutione quaeque genCrCTuE.
X y X a
2 BM = +  BZ
BM + = B Z
+G  L, BM F = BZZ ∞ BD.
d
Xy ∞ a
a B M = + = BZ
L: BM + : BZ
Recta D BMZ curram a B, ut ancca quoque, sccacad anrulosre-
ctos, occurritque alymproris sI, Se, in m d 2. Si igitur exempli
pratia hyperbola Fuerit a B, cujus aquario est x y x a , lumCTUE
BD ∞ = BM F : BZ, quemadmodum cabella praecipic. Fricque pun-
ctum Din curra Dc quaelira, cujus alia quorlibet puncta lic inve-
niri pocerune, et porrio ejus qualibet rectae linex adaequari. FE
haec quidem eadem illa est curra, cujus relationem ad axem hyper-
bolx superius aequatione expresimus. Constructio aurem cabellae
hujus planc cadem est quae luperioris.
Caeterum, quoniam cum ad harum curvarum, cum ad carum
qua exparaboloidibus nalcuntur constructionem, ducendae lune
linca DBZ, Qua ad dacum punctum B ecene curras AB, live ipla-
rumtansentes BHI, ad ansulosrectos; dicemus in univertum quo-
modo ha tangentes inveniantur. In aquarione itaque, quae cujus-
que currae naturam explicar, quales aequariones duabus cabellis
praecedentibus exponuntur, considerare oportet quae lint expo-
nencesporeltatum x X y, d tacereur, licur exponens poreltatis x
ad erponencem poreltaris y, ita (IC S H ad H E. Juncta enim H B CUT-
ram in B concinset. Velur in cerria hyperboloide, cujus xquario
eAtxy x a: quia exponens porestaris x esti, poreltaris aurem y
exponensz; oporrer esseur ad2 ita si ad KHI. Ilorum aurem de-
monstrationem noverune analyricae arris periti, qui jam pridem
omnes has lincas contemplari caeperunt; e non lolum parabo.
loidum iltarum, sed e spatiorum quorundam intinitorum, inter
hyperboloides e asimproros interjectorum, plana solidaque di-
mensi lunc. Ouod quidem ee nos, facili arque univerlali metho-
do, expedire possemus, ex lola cangentium proprietare Cumpra
demonctracione. Sed illa non Cunchujus loci.
90
cuxrarum
orimranum linex s_, in alcicudinem x B ductum, hoc est, Colidum x x y, cub0
procurronn. Certo equabitur, qui rocetur a. Acque ica innumerx alix hujus
Si