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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 378r, page id 00068196:0751
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sit Trilineum orthogonium ABCA cujus certrum gravitatis. G augeatur nova
B2BrC
hona basi parallela B(B) ()C. Cuius centrum gravitatis, sit 19 jungatur G9
et secetur 1G19 in 2G sic ut reciproce secundum a ut ABCA, et B B, (C) B, erit G
centrum grabitatis totius A, B2CA. Eodem modo trilineum A2B+ A
AP ALB2C A ad datudm B3B, C=CZgna 2B3B3C2C, cujus centrum 29,
junctaque 292G rursus secando quaeratur centum commune 3G, patet curvae
 intero alla 1B2B, 203B sint infinite parva, esse gG rectas gG, tantes ex 
dio medio puncto ipsius BC e ductas, esse tangentes curvae centrorum GG
Hinc si sit trilineum ABC A, et in eolinea centrorum pavitalis
AG, transiens per omnia centra trilineorum praecedentium ad eandem curvam
et Axem et ex M puncto medio basis ducatur recta  ad  MG
ad centrum trilinei, ea recta curvam AG fanget,
videamus an hoc generali calcuo m etiam calculo Einfinite simali
perdraliter inveniri possit sit cueo AB, X et BC, y. fiet Area
C du cendoad
momentum ex axcerit Z Syydx. itaque ex
axem normalem FG erit ea v 2 syyix: Sydx. Quaeramus et momentum ex
ydx et
normali per verticem, quod est Sxydx. Et fiet AF = sxydx: sydx =Z sit
AF, Z et FG, v, fi
ob 3
28 = sygdx: sydx et Q = sxydx: sydx. Et fiet
2a∞sydx + 9G 2B9 x = gyax. seu fiet
yda
pydda fit
2d7 = 2dQ sydx + y dx(syydx: sydx) = yydx. seu fiet dD-
n. Z Z. v = sju ax. sxydx 
yyde = ydx (By, ex. sa ), . 1
rursus fs Xsgax = (Xydx fint dx syax + By ax = xy dx seu de sydex + yda (Serexi be h) ey
seu Ex = Xydx = ydx (sxydx: Sydx): sydx. Ergo fiet do: X
re x (srgix sylX): ali x sstX) (sygax. fu (X) = BM - FG,: FB
d
FG = V = Esyydx. sy dx
X = ( sXyax: Sydx. Ergo dv: dx = 4y -
FB =  AB - ex t AF = x -
Syydx. Sydx
2x) ax -2) dx (Spy ex sy 
(Xydx: Sisdx, : , 2X
ut ante. itaque idem theorema calculo obtinetur, quod ex inspectione
y
+
BM =
figurae duximus. sed hoc interest, quod ex calculo aliuo facile animad
pertisset