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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 309, page id 1041163592:0343
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PRTNOTPTA MATFTEMAETCA.
Convexa erit versus cataractam, et propterca major COno cujus ba. L LVEN
sis es circellus ille P 9 de alcicudo CFL, ict est, Major FCFFIA PArtC SECVNDVS.
Cxlindri eadem base e alcicudine descripei. Sustince autem cir-
cellus ille pondus hujus columnae, id eAt, pondus quod pondere
Coni seu tertiae parris Cylindri illius majus eAt.
Corol. 8. Pondusaquae quam circellus ralde parvust  Fuctinet,
minor cst pondere duarum cerriarum parrium Cxlindri aquae cujus
Basis est circellus ille ex alticudo est FG. Nam Rancibus jam po-
Tieis, describi intelligacur dimidium Sphaeroidis cujus basis est cir-
cellus ille ec semiaxis sive alcictdo cA HEF. EF haec Agura aequalis
eric duabus certiis partibus Crlindri illius e comprehender colum-
nam aquae conselatae F   cujus pondus circellus ille lurtinct.
NIAM VE MOTUS aque sic maxime directus, columne illius (uPer-
ACIES CZECrHA CONCUERCE Cum B2EI F O) in angulo nonnihil aCULO,
propcerea quod aqua cadendo perpecuo accoleratUr _E PFOPTCr aC-
celerationem Ac cenvior; et cum ansulus ille sic recto minor, haec
columna ad inferiores ejus partes jacebit intra dimidium Sphaeroi
dis. Fadem rero Cursum acuta erit seu cuspidata, ne horizontalis
motus aquae 2d vercicem Sphaeroidis sic intinito relocior quam ejus
motus horizontem versus. Et quo minor cA circellus P  c0
ACuriOr CrIE vertex columnae; ex circello in infinicum diminuto, an-
Sulus PF in infinicum diminuetur, ec proprerca columna ja-
cebic inera dimidium Sphaeroidis. F.s isitur columna illa minor
dimidio Sphaeroidis, seu duabus tertiis parcibus Cylindri cujus basis
est circellus ille ec alcicudo CFV. Sultinet aurem circellus vim aquae
Donderi hujus columnae aequalem, cum pondus aquae ambientis in.
desturum ejus impendatur.
Corol. 9. Pondus agua quam circellus ralde parvus FO) sucti
nec, aequale cs ponderi Cylindri aquae cujus balis cAt circellus ille
ee alticudo est =GF quamproxime. Nam pondus hoccc cA me-
dium Arichmeticum incer pondera Coni ee Hlemisphaeroidis pexe-
dictae. AF S circellus ille non sIc valde parrus, sed augcatur doncc
RQUCE FOramen P F; hic sustinebic pondus aquae cotius sibi per-
Dendiculariter imminentis, id cst, pondus Cylindri aquae cujus ba-
sis eA circellus ille ec altitudo est ( II.
COrol. 1O. FF (quantum sentio) pondus quod circellus sustinet,
est semper ad pondus Cylindri aquae cujus balis ett circetlus ille et
altitudo eAt ZG FL, UE L Fg ad F Fg = Z P ~g. live ut circulus
E. F ad excessum circuli hujus supra semissem circelli P a quam-
DYCC.
L F. MML A
HIIHIII
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