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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 251r, page id 00068200:0503
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O. adde pag. versae finem ibique inspice fig. 4.
Ut jam problemm illud iltypabo, de differents
Hipperbolae homogeneis solvere saltem tentemus, esto 
NL-y
NZ 2. CL = Gq - X. GC - ZL = _ y - a.
et Y quia E2 pn= = L R = B. erit P = YX = LR.
NZ
a
ANL-y
ductaque ed curvat perpendiculari Nlo et quoniam NL.y
media proportionalis inter P et e, fiet Z = C = 2 -
et WN -v. NL + LW Setr,-ra+ q a
v
va
et W = Y a + y, eritque - vel W0 x = 5 a + yX
a
vel 1X - 7 2 = 0 in qua aequatione
e
duae sunt ve
quantitates incognitae vel in determinatae, nec
p altua in alterius locum substitur potest, cum aequatio
de illa, quae relationem ipsius X ad y. exprimat, quarat
quaeratur. 28
X a = XaCFC. X = Xa = CL N quae siup
e
at P
plicato ad ipsam unitatem constrntionis in
telligantur, fiet= ax cromenta
4 posita D et
Testrali CB NZC ex CZ maxiuma
momentum vero rectanguli CL NZ, tiet Xy.
ad qua si anferatur Momentam figurae ipsius CL NBC, resabit
ulius monentum Trilinei quod srpra. Momentum autem
eat
xvariab.y
e
fiet Xy = summa omnime XY = aX at
c
fignum talem imenire diffaillimum hand dubie problema
est, non minus quam propositum, quodque etiou
pendet ex Hyperbolae quadratura. Et memorabilia
sunt ejusmodi problemata quoniam iis similia nunqua
hactenus proposita sunt. Sed si y. per suum valorem
expromemque vereor ne aequatio fiat ejusdem cum eodem, tentan
dum tomen y= a + Y y d +  Y - a + differento
inter Xy et XY - Y seu Ya + XY XY +.
2
X2
 summa omnum
per Ergo aX - (∞ Y = 7X - ax + Xy - Xy +X7
2
2xy - ax
Atque ta habenus problema quae in quadraturis fundantum
qseu quae magnitudinet quorundam spatiooum locum det
terminant, uti  communica magnitudine rectarum.
ditfiae in absissas ductae opconflant spatium, ut N7CBN
id ergo spatium, hoc loco aequatur, et in C.
ducto fm
rectanguta MB, (quia QN et qM non differunt) aequetur
rectingulo  NM. applicitae ergo complementi
hujus geB N, ipsi 3C parallelo seu complementa
ipsau Vt ad basim sunt. differentiae inter duo
i 4 at proxina  ea autem est aX + a - ax
in partes aequales infini
  as Ergo interantes it area f ejus semper
haec
est a si si
tas divisa, naturo figuri
aquetur rectae datae a
in applicatam ductae.
a a + b. = ba, ul a + ba = ba, vel 1rb - b
a vel 1 = ba - b vel b = 9
ergo ternims hujus fenei prinus est 1). secundus a =1) tertius C, et erit
+  + c = Ca. Erqu 1+ = = 5
=  C n
-1
sit cum. Juries applicatalum haec: (B (2.) d (+
Nam pro a- 1. puto substitui tuto posse a
per a divisis. imo ale