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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 41r, page id 00068160:0081
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foc bone sed melius in alium schedam translata.
si trium punctorum aeque gravium quaeratur centrum gravitatis
nempe ipforum B, E, C. quoratur primum centr. gr. ipsorum
B et E, nempe L lut  in medio E B. junga
tur AC, et triens ipsius sit LM. erit  M punctum
gravitatis quaesitum. idem est si CE biseces in L) et
jungas(L) B, erit hiens ejus (L)M, idem M, quod ante
et rarsus si imigans CB idque diseces in () et
jungan((E eut rursus triens ((L)M. Patet hinc, ut
n
vel latera
obiter dicam omnes rectas L) BB, CL E(L)) quae angulos
Transi trianguli bisecant, concurrere in eodem puncto, M.
sed si puncta sint inaequalis gravitatis, et sit BL: EH : E:B et similiter
 C(1): E(6):: C: C et B B(L)): C(L)):: C: B erit  cumrursus
coincidant puncta M, erit BM  (L) M:: C+ P: D et CM: LM:: b + e: C
eshae rationes nuitate auctae sunt
e EM: L)) M d B, + C: C s rccipioce, ut b c, e.
taque it
 trianguli alicujus latera secentur BCE BEC latera tria
(,BL
quod fict.
ecentur BG in ratone in L, ratione BL: XEBL. EL (seu B
 quod fiet.
et EC in (L) ratione EIL): C(L) denique BC
EC EC
si et ratione CB C). BL))
B
CB
BE BE
CB in (L) quod
sitque ratio BLB: EL:: C: b et 8L): C(I) :: C: C et ((LV: AL : b: C
erit cmposita rato copositaratio rationis BL: LE et E(L): (LC erit C.
et similiter composita ratio E(L): (GC, et C(L): (L) B erit bC et
.Ri
denique composita ratio Cst: (1) B _ et BL: ( LE erit ece
pursus ilem ratio lationis. L BL ad rationem sE(L): C(L)
est b: C Ratio rationis CL) (L) E ad
vel rationes BL: EL, et E (L): (L) C et C((L): (L)) B
erunt inter se, ut , ec ee, bc itaque si trianguli
tria latera ita secentur ut rationes secantes ordine sumtae, sint
ut qu eC, Cb, bC, et colposilo ex ipsi binis eode
vel composita exbinis eodem mo ordme sumtis, ut ce bc, eb
rectae jungentes vertices cum puntis interfectionum concurrent in eodam punt
erit
Ansic iataratins EL: BL ad rat. 2(L) +C(L) est
13
2 C
M
C duobus lateribus,utcunque sectis
Ba Brevius si manguli B3, quo secabunt sese in M, d
ungantur (L) et CL
et
eum
in tungatur M qoqdae producatat si opus iphi Eoccurrat in Cpuncto (L)
devique
 ratioB (L)
P
in  L
i
u et
 composita rationis 1) rep e
EIL). Ct
quae pulchia est constructio, sed in
fuollor jam nota