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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 85, page id 799199311:0101
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HOROLOO. OSCILLATOR.
dem cunc haberi dictam rationem, qualecunque fuerit interval-tba
lum RL.
Ac Ci locus alia linea curra fuerir, diverla erie ratio v Z ad XT.
prour majus minulre Fuerit incerrallum K L. Inquirendum est au-
rem quaenam fucura sic ilta ratio, cum x L infinire parrum imagi-
namur, quoniam ec punctaB, E, proxima invicem poluimus. Si-
militer icaque de puneta r, T, linea currae minimam particulam
incercipere incellisendum est; unde recta vr, cum ca qua in x
curram continsit, coincidet. Sit ergo rangens illa Y Y; Porest
enim duci quoniam curra, ad quam luntpunctar, r, seomerri-
Caect. Ratio igitur Y K ad X Y data erir, adcoque _ V Z ad ZT.
ex qua etiam rationem L K ad e m dari olcendimus.
Ouaenam vero sic linea ad quam lunt puncta r, v, invenitur
ponendo certum punctum s in rectakL, a vocandOS K, X; K F,
y. Nam quia data eAt curra ABF, eique B n ad angulos rectos du-
cta, inrenietur inde quantitas linca i m, permethodum tangen-
cium a Carcelio traditam, qua ipsi K T, live y ae quabitur, e ex ca
aequatione, natura curra r v innorelcet, ad quam deinde tangens
ducenda est. Sed clariora omnia hene sequenti exemplo.
Sit A B F paraboloides illa, cui superius rectam aqualem inveni-
mus; in qua nempe cubi perpendicularium in rectam sH, Lintin-
ter se licur quadraca ex ipla s R abscilsarUM. FC OpOrcCat invenire
curram cDF cujus crolutione paraboloides sB F describatur.
Ilic primum racio B O ad B e Facile invenitur, quiarangencem
paraboloidis in puncto B duci scimus, Cumpra sH aquali : SR.
Cuitangenti cum Bm ad angulos rectos inliltat, dantur jam linca
MF, EIK, ac proinde earum incer le ratio, quae est cadem quae O B
ad B P.
Ve aurem ratio BP, sive R L ad m vinnorescat, ponantur ad KL
perpendiculare srectae XT, L V, aquales singulis R M, L N, Cicque
vZ parallela L K. lam quia ex duabus limulEL, L N, auterendo
M, relinquitur m N; hoc est, auterendo ex duabus XV, V L, live
Z V, Z X, iplam XT; hinc aurem relinqui apparCE V X _ Z T:
crunc isitur lx duae v Z, X Y ipti m e aequales, ac proinde ratio
KL ad m  eadem qua v x ad duas simulv Z, X r. Veaurem haec
racio innocelcar cum incerrallum r L est minimum; oporret le-
cundum praedicta inquirere quis sir locus, sire linea ad quam lune
puncta F, v. Ouod urtar sic lacus rectum paraboloidis AB F x a;
S EE D X; H T ∞ γ.
Duia iBicuE proporcionales TUnFKH, KB, Ku, elEquC H K V
CUIRVARUM
EYOLUTIONE.