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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 267v, page id 00067993:0536
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ge
3
369
1082
2
3
3 74
1088
Epto in Plo Rectengulo AB 3. BC. 4. AC5.
centrum gravitatis D.
Wideamus au recta ducta per D ut est EDF
etiam peripheriae momentam bisecet
esto cd. basi BC. parallela. exempei
guatia. Jam momentum BC est 44a-
4a. ducta EB in BC.
momentur e EB a por
porro FC est AC, ejus puncti medii
distantia ab EF es = EG. Ergo ejus momentum
5a
4 = Ea s
2a2a 4a
24 7a 442
4a2a- a
44 2a. +a a
2a C2a 447 3
2a a - 43
. 2
4a
e
Xa
ae a
64
a 2a- a. J 3at a-
=4a
Summa momentorum 3 hujus lateris.4a + a +5a: 9a + 5a = 54 + 10, 64) 16a
ab altro latere sisi prie
mum summum lineam omnium AE+ EF+AF 12 123
+
5
= _ 8a 2+ 858.
6
10. = 18 4 - 6 + 2 - 8.-
42 B 322 6(2
ducamus in distantiam, centri gravilatis  triaehnili AEF a recta EF. quasi istud
centrum Trianguli AEF etivi phipheriae ejus olincentium esset, distantia autem est
fiet _1ba ecce idem quod ante. Idem aliter proveniet, multipliando
2
A A per 1E = 2a a = 2a, et AF - 70 a a = 10 a jam 10 a + 6 a (a)
164
librationis AB.
= 95a2
2
Nure rem experiumur infigureo acctilinea compositae, se hypoleans
ut ABCD. F ita tamen ut facilioris calculi causa surdas radices evitem
ideo altitudo A AB = 6 + basis BC = B + 3. hypotemsa ADvd l
12
Investigemus nunc Centrum gravitatis Tilimei quexi orthoponi couexi
AB_CDA, ergo primum momentum ex AB. rectanguli
128 Bd momentum ex AB. est 3  8a 4a = 324, 44 = 129 a
64. DFC. = 4a 3a = 12a - 6a 9a = 5+ a.
24C
in AG4- 628-48 a 24a 8a = 64 a. Summa
4
64
Po
mentorum 128 +54 +64 = 246 a3. dividatur per
216 (360 = 4 - = a. = 246] (12 3a) - BH.
e
62
62
e
distantia centri gravitatis hrilinei cquexe a AB.
296 Similiter ex basi B axe aequili librationisposito BC. momentum
BDF erit 32a2a = 64 a. RFDC 6a 4a - 3a
R AGD. 244 4u  6a - 1440 Semma.
64 + 8 + 144 - 21647) (108a)
624
Ant fere somm
AYI
Nunc quaeramus et (entium gravitatis periphetae: ac primum exaxe f
C primum BC = 11a ia = 121 a. deinde DC 5  P+ 3. 40+ 1 (.
dividatur per 11+ 5+ 10 - 26a fiet 148 a 24 a comparetur haec distantia priori:
(23a (74) potet has duas ranis non esse candem. si dividas 148a addito sil. 10a =AB
26
3c
fiet 14y (74) (374) hoc ratio propius quidem aceda, sed non 36 gnen est praeise eadem
1 ∞
priori 123a. Ergo lentenus ex brachio DE. extra assumto. BC = 11 a 1a = 121 a
CD - 5 d = 15 a Ad = 10a 3+ 4 = + a. Summa: 24. 15 ar 140 a
276) 138169)(23
36
ad 23 adde 74
13
Addatu ad 123 + 23 2bu deberet fieri 11. quod
non facit, 31 X 3
nusus nihil. quid si 22 37 34f1+. ne sicquidem
3
X
patet lineas non nisi ex axe, qui inteo ipsas non sit, librari debere,
ut eorum centrum aequilibri habeatur
ea
1B3
29.
c
ui
1g
A0g2t
Smmm
Sumursa