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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 164, page id 1066518432:0192
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I64 DE V ERFBUS FF MIOTTBUS CORPORUM. L IB. II.
ram quaesitam reapse eam esse, cujus cunctxe perpendiculares in idem
punctum seu centrum rergant; non obstante, quod hoc idem pro-
blema jam supra (5. 202.) Tolutum sit, Sed diverla ratione ad illu.
Arationem generalis theorematis, quod infinita ejusmodi alia pro.
blemata solrit.
PROPOSTTTO ZVT PROBLEMA.
8. 69. 303. Dato tubo AB ex materia molli seu fexili clauso in B, aperto.
16 1o
que in a ad horizontem verticaliter erecto; es aquae aliusve liguoris
pleno, determinare ficuram, quam sectio quaelibet horizontalis in tubo à
liquoris pressuris acquiret.
Sit AZBZ figura quaesita, cui rectae Z X, AB ad angulos rectos
in R se inricem decustantes perpendiculariter occurrant in punctis
A, Z, B, X. Sint contigua currae elementa DC, DF. X L. Z, Aa
punctis Z, A adjacentia singula inter se aequalia, ducanturque 21
DI rectae Z X normales, ipsisque aequidistans FN, nec non per
puncta C e D rectX CM e DN ipsi Z X parallelae, ec per a li
neola ab eidem ZX aequidistans; ac denique AANE Dm =FN e
D8 =CM. Duibus postis, quia sectionis tubi Z AXB singula pun.
eta a liquoris superficie aequaliter distant, singula puncta xequalem
pressionem lubibunt, ex quodris ejus punctum D (5. 255.) prestio.
nem sustinebit aequalem ponderi tilamenti liquoris, cujus longitudo,
quam per lineam DEI currae perpendicularem in puncto D indica-
bimus, aequetur Auidi alticudini super sectione Z AXB, juxta di-
rectionem currae ubique normalem Dd; ergo singulae DIl, quae su-
muntur in lineis currae perpendicularibus, porentias eidem currae
applicatas repraesentabunt, atque adeo rec- lum DII. DC refere po.
centiam in totum elementum DC agentem. Verum potentia DII
(5. 39.) aequipollet lateralibus DF _ FFI, quarum haec ipSI Z X pa-
rallela, illa vero eidem perpendicularis est; ergo etiam potentia
agens in totum curra elementum CD, quae exponitur rec. lo DH.
DC aequipollet potentiis lateralibus CD. DF ex CD. FHI, vel quia
triangula similia CDM _ DHIE pEXbeNE CD. DE =OM. DHI e
CD. FHI = DM. DEI potentiis lateralibus per rectanoula OMT. DII
aC DM. DEI exponendis juxta directiones DF e FM vel huic pa-
Fallelam, agentibus.
Tam (5. 98.) est generaliter sFHI, hoc eA aggregatum porelta
rum juxta directiones LFI, seu juxta directiones rectae LX paralle.