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# Title: Leibniz-Handschriften zur Physica LH 37, 3
# Folio 75r, page id 00068532:0145
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de rotu fignus dent
de vectibus conjugatis et figuris
dentism in rotis, resumtae priores
cogitationes
25 octob 1679
scheda jma
Brevior vectis potentior
sit Tirangulum isosceles
in recta BD producta alio puncto A. junctaque
sumtaque
In Triangulo BCD sint latera BC, Bd aequalia, producatur
BD usque in A junctaeque AC, sumatur in AB aequalis AE
 ita ut juncta CE fiat aliud triangulum isosceles
ACE, quaeritur ratio inter CD. et  CE.
Aerit a. CEsit e CG erit E. AG erit a - C vel 4a = e
AE)
et area Trianguli ACE erit. eraa- et eadem
est A AE in CF, seu a in CF ergo erit
CF aequ. er4 a et
a
Eodem modo qud ponendo. BCt esse b et CD esse d
BD
quaerendoque similiter perpendicularem CFe altitudinem
CF in Triangulo. BCD uti quaesiveramus in Triangulo AC5
fiet CF aequ. d sabr-d2
quos duos valores aequando, fiet:  besta- e ad ab 
sivc 4abe - bet  4 a6d - aed4
qua
qua aequatione satis exprimitur relatio inter
a. b. e. d.
Donamus jam d et e esse infinite parvas, tunc
utique evanescent termini bre
et restabit
4ab e  p 4aeb. dr
sive fier de e
se
composit
recipivea
conjugatos in directum sitos qualipotentia uea descendente
aequali potentia se prementes en aequilibrio esse. Siveciproca
si sint duo vectes AE BD. mobiles circa centra A. B
quorum ille deprimitur a ponder
a pondere M attollitur
t
t
et si pondera sint aequalia et aequali centro A distantia suspensa et in linea recta descendant
ita ut discrimen sit tantum invectium longitudine AE B d. inaequali
inequuli ajo hac non obstante aequilibrium fore; nam ont t vinces pondus, quod manis pe
brachium lonctus vincat debet extremitas ejus D majorem cuculus ercum  troch leae ad
describere e, quam est averis (C, quem describit extremitas E majorem ercum
se
teres
pondus u sed intio positus DC. EC. infinite parvis calculus
octendit eas esse aequales (quod alioqui ut in sequentibus
ssend oo sabenenturibe srarvis fire
aequalis est ub imtiu nisus sive descendendi potentia utrinque reciproca, quare
quare duo vectes conjugati in direcstum posit;
utcunque longitudine inaequales si modo aequali utrinque
ecta descendentis
diagantur in cntra si i ponderis graviatione
sibi contranitantur, in aequilibrio manebumf potentiam shabebunt in reciproca longinnum
autem
vectes per se hic ipondere, semper carere ponuntur vel ab eotum
pondere animut abstrahitur
inter
bs
Ergo a
n ba
 bA EC
ae 
Ergo anguli adbi interse, in ratione
o rect
ua
arcrefsupei
jorem
x
ititer
cr
est quod majorem
erolvit fili partem. Sunt
autem anguli in R. B. inter se
in ratione composi
cenum et rec
cta
ratione