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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 13
# Folio 9r, page id 00068166:0017
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sclatio
solutione del problema del R. P. Vanni
solutio problematis R. p. VannRS. 1.
orax  o c, s
parmensis a Leibnitio Missa
dum intermaniam redep inl per otium
in itinere Vannianum problema, expendi et
pondus cujus centrum ravitatis e solutionet vobis
Globus (homo geneus) cujus centrum ponderis
figurae, et gravitatis idem (G) incumbast,
sa
solutionem vobis per inclytum
mostum mitto
lumaue lasis restaee ateusi memiriam in
oisse
ligatis. R. P Vannius proponit globum de
gravemi G. incumbentem simul duobus
vel regulis.
planis, iclinatis angelum AB Cd
angulum inter se rectum facitalibus
si continuentur facientibus es quaeritque
Quantum prematur unumquodque planum
grave
go problema generalius concipiam, sit corpus quodcunque
cujuscunque figurae, cujus centrum gravitatis G incumbens
incumbens regulis de e nus AB, cd angulum inter
id corpus incumbat,
se facrentibus quemcunt quaeritur quae sit proportio
a punctaG
Aidem ma
pzcaliisglb
et resistentiae planolum. e punctas per punctum G
ducatur recta EGF perpendicularis ad homizontem
et ex punctis ceet A et C educantur rectae AHE et CFH
normales ad plana AB Cd. hae tres rectae ses
secalien sese in punctis E, F, H: et atera trianguli
pordine
EFH latera EF FH, HE erunt proportionalia tribus
potentiis propositis, nempe ponderi G, et resistentiis
planorum  CD,
tria latera FE
tribus potentiis
erunt ordine proportionalia propositis tribuspotentiis
ponderi 
resistentae plani
plam ABCO
idem est si rectis ductis quae sibstasis hispavallelae, fiat hiangulum
od, qu
Veri
8
eorma ipsi Fex simile, quo d utile
erit eo casu) quo coincidunt puncta
agifestum dd E et F et H. ut in gohseneo
ut si pondus cAAtylob homogeneque
nem
proli est theorematis demonstratio quam ut hic
Theorematis non inelegantis demonstrationem
quaeeut viri docti ala dabimus in dynamicis nos nostris
interim qui volet poterit veritatem  ejus discere experi
mento, sit reguba AB mobilis circa centrum
ap
librationis B
eleuueumabel
et c oppositum brachium aequales ho horizontate sit
JL pontuys
similiter regula cd sit mobilis circa centrum librationis D, cur
et oppositum brachium horizontale sit dm aperum habens pondus in M
seut autem rectae AB, BL, Cd, dM, aequales; ajo u ut omnia sint in
alioqui si G propenderet
n alterima aliomnam
partem, t
eversum in ea
partem cadere
corpus
un
resistentiae