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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 380, page id 1066518432:0408
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380
A P P F N D I X.
TIT. Circa regulam Guldini, cujus demonstratio supra (5. 47.) al.
lata Cst, duo notanda TunE. P. Fam non solum in Rouris aut soli-
dis rotundis obtinere, sed generaliter in omnibus aliis, quae genera-
ri possunt fgurxe genitricis motu hac lese facto, ut Rgurae planum
Lemper perpendiculare mancat linex, quam centrum gravitatis Egu-
exe genitricis motu ejus describit. Iloc enim catu solidum fieurae
motu genitum semper aequale est facto ex ficura in viam centri cravi-
tatis ejusdem.
6. ISl. NNam si Ponatur centrum graritatis C figurxe cujuslibet AB ince
denS in CUEra DEF, cui figura ubique normalis siE, delcripsise arcu-
lum currae CC, atque ex situ B A venisse in litum ba priori indetini
to ricinum, adeo ut rectae CO e cO, quae sint in planis Rgurarum
AB, 8 ab, e in planO CUIEVA DEF, eritque Ocontrum circuli
osculatoris currae datae DF in ejus puncto C vel ejus proximo c.
Adeoque solidum, quod figura AB describit cum ejus centrum C
Dercurrit arculum C6, Per 5. 47. aequatur Facto ex figura AB in ar -
culum CC, ergo omnia ejusmodi Colida rel solidum, aut Agura, qux
producitur incessu Agura AB per totam curram DEF, aequabitue
facto ex eadem AB in omnes arculos, qui in curraDF continentur,
id eAt, Facto ex figura AB in currae DE F lonsitudinem. Ouod erat
demonstrandum.
2. Notandum, haec tantum ita se habere, (i fgura genetrix gra-
vitatis sic uniformis, et fallere Culdini regulam, Egura genitrice exi-
Sente disformiter grari.
TV. ProDOTitio VTIT. L Ib. T. (5. 59.) etiam deduci potest vel fal-
tem ips aequiralens ex proprietate univertali rectis recti in singu-
lis punctis a pocentiis obliguis impuls, quam hoc loco explicare
FiB. r52. Placet. Sit linea recta inflexilis AC, quae in singulis punctis C, C,
exC. urgeatur potentiis CD, CD unitormi lese ad iplam inclinatis,
ec circa cam tanquam axem constitutae intelligantur tigurae ACCIP,
SE AOTTKA, ea conditione, ut ordinata quaelibet C6 (CI) St ad
homolosam potentiam CD in duplicata proportione sinus anguli
respectiri BCA ad SInUm EOtuM; ac ordinata CII (CH) alterius
AGUITX ACFI Sc habeat ad ordinatam CC (OI) priMX ACOP, ut
sinus complementi anguli BC A ad ejusdem sinum rectum, et sic
ubique, positis hisce, per centrum graritatis arca ACOP agatur
RS axi AC recta huic lincae AC OCCurrenS in R, critque lincaR I
cum RS angulum TRS continens, cujus sinus est ad sinum com-
plemenca, uc area ALLC ad aream AC. CrP, media directio omnium
P0.