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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 189v, page id 00068193:0384
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Sect. V. Cap. 2. De Motus directione et.
um ABC describens soledum BA, C2C3CAB, ejusque centrum mum
gravitatis describat arcum circularem 1G2G3G; Patet solidu seu
generatum factum etse motu trilinei in se non succedente, nul punet
lum enim punctum alteri succedit, (ut fieret si trilineum hocp quod
num per unum idemgi planum duceretur) et cujuslibet punch ut L
motum este aequidirectum, tangentes enim circulorum in locit
non e
ubi puncta sunt eodem tempore, sunt parallelae. Datet et mt pante
tum este aequiangulum ad mobile, quilibet enim arcus circul
a quocunqi descriptus, id ert ejus tangens semper facit ad mota
angulum rectum. Itaqi solidum ductum ratatione genitum d
I
quatur facto ea trilineo ABC m viam centri gravitatis, ti
m 1G2G3G normaliter ducto, id est solido cylindriformi, cujus
baris est planum trilineum (A) (B) (C) priori aequale, altitutu
vero est recta (A) H aequalis arcui 1G2G3G, normaliter duc
in hanc figuram (A) (B) (6) sacentem.
Si C fuisset een
trum gravitatis non trilinei, sed linea AC, tunc eodem ar
gumento superficies solidi dieti rotatione hujus lineae genu
aequaretur superficier cylindriformi (A) AK (C) factae ex recta
id ett 1G2G3G mrectam eatens a) normaliter ducta m lineu
A) (C) ipsi AC aequalem. Sed et nostris demonstrationibus
ampliari potest haec doctrina. Exempli caura in plano pagria
Fig. 24) evolvatur linea ABE (secundum moentr Hugen
ana) seu filum lineae huic rigidae cir cumplicatum, ita ut par
L
quaevis Ac extendatur in filum BC curvam ABE tangent
pars vero residua Be restet in linea eurva; et eatremo fil
C describatur linea ACF quaeratur via centri gravitatis Zr
Nempe primum ejus punctum Q est centrum gravitatis fu
m primo situ L, nempe centrum gravitatis curvae ABE; ut
mu
2GS
parte
et c
one
cedum
cedo.
hoc
gula
pro
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mo
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UM
adt
qua
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pro
yde