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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 18
# Folio 17v, page id 00068089:0034
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sporantur instatione applicatarum vel potus parallelogmnorum
662 respondentum (h. figurae ACF ad exempositoe sentin
maecedentibus AH, X. A, B, y. M, F. spatium AHC (Quod pondis desirnat
scatena Ast B potentia constans in infimo puncto  A, aa au
evic ut do ad dy atus pondus catena ad aa erit pdy= andx et
as
y = aa (ax: p. si ACF recta et parallela Axi AE erit p = ax
et fit aadx: p = adx: X = du vel adx = Xdus quod ostendit
miva Oalenariam ABG esse requi thinicam cujus sublangentiralis
 nunc ACF linea rrectum angulum
facient in A, cum laxe AE, ratio AH ad He, ut a ad b proinde
sit a
1 C- bX: a. spatium AHC = IXx: a = p ideo aa ax+p =
203 dx: xX cujus summatio 24d: bx =y quod indicet
curvam nam Catenaria ABC, ese (frg. 11) esse Hyper
volam, sed ab altera parte positam ob quantitatem regativam
v quod scuper accidet, quolies, grre e ACF vertex est in A
curva enim aBG, una ex hyperbolaeidibus eut, sed ex anverso
ta uno est vertitalis, altera vero laorr fontatis
Cum autem aCF est ex Huperbolicarum Genere (rit atenaria
ABG curva cuius vertex in A. si ex. gr. _ eF est tali ut CH vel bsit
aa: Vax erit spatium a CHA vel p = 2a tax. proinde aa ap: p =
adx: 2Vax ejusque summatio, tax =y. inde iprva funitularia hoc easu est
narabola ABG cujus parameter a Problematis inversi solitio etiam
nullo negotie habetur si nempe ex cognita natune funicularia ABG
inveniendasit curva. _X CF. Nam quia p = aadx idus eorumque
= aa )(dx :dy): dx, ex
afferentia ap seu tax = aa dxidus ideo
quo itidem patet, quod existente ABG otgebraica, curva XCF etiam sittalis
Cixur. ABE parabo param. a, Erguu Tax et ius = adx . dax
ergo aacxidu= ratax ejusque diff aaax: sax: quae diorsa
ut ante
sit ABe 
per dx dat aa: Vax = f = CH
circulus radius  a. y =  ap x et dy= adx - fox, : ax A
Cut aadx: dy = aa 1 (2aX XX): a - x et ad dx: dy = cx
Qu. (( -X) Ea X - XX) proinde + seu HC = a .  (a - X) iux axx)