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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 44r, page id 00068207:0085
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adhuc determinari posse, ut contrahatur calculus, vel assumi pt quoee nova
determinio apta. Sed hoc jum dissimulato, sufficit nes habere jamo aequ. 15.
cujus ope habet, f ex a, c; b, q; unde ex lege jurtitia similiter habltur (16)
K per b,g; a, C; Ita ut aegu. 15. et 16. non differant nin hâc tansporiti-
one. Astamta ergo relatione aliqua inter a, c; b, g, que et ipsa legem juni-
tiae servet, qua contrahat, alterutra ag. 15. vel 16. Contrahetur et alter similiz.
Et fd. inventi valores subitituens, in O et D et P, et portumo mstituat com
prolutio, ce subrtitutis valoritus in O0 + ab DD= et explorabit, an omnia
succedant, q erit finis finalis. Quod si res succederet, nec forte occulto nature
eludentis artificio mconerur emergant, quae hypothetin 4 non pmittendam orten
dant, vel etiam tine hypotheti 4, si saltem solvi possent aegu. 1, 2,3, licet pro-
sixins, haberet res maximi port quadraturam Circ: et Hyxb. in Geometira de
tragonistica s. sublimiore momenti, nin mo oia fallunt. Vanncs habe mittal
gefunden, das die applicatio Calculi Diophantei ad Geometuam tressense
bisthare unbactondta a ortseil brachte; P. ist beru dies applicatione exlarli
Diophanter dia bezvamlisonit, daso mom quoad valorem quantitatum deter–
minatarum alt c, e, etc. om rationales mist gabunde, d. nove su grinde,
ob moru sie pson in surdis erlonget,  nun die indeterminata, orlb X, y,
B. similes eatras vincula od irrationalitates blnibas si ist im effectu doo
semige, Wort, ich siere fuche mihte anderes, oilo 0 et D ita explicare per X,
ut 03 + abDD aequetur quadrato-quadrato. Dbanmastis newaen folgandet
problemo fehae uuteris, nnum es dicto modo su solvire. Ipsi X talem dave
vatorem rationalem per y, ut X alxx + ac requetur quadrato. Ex gr. fiat
et hic valor subrtitnatur in X1 abra + ac; detideratur
ut retuctis omnibus ad comunem denominatoum, qui est quadentus ab yy
py +aq, fint et numerator quadratus; Ed est, atsumtitia m,n, q, sic expli-
canda sunt, ut hec succedat. Nam unam ut p omitto, quia non auget liber
tatem, sed tantum ad hibita ett aequilibris causa. Quod a valor athuntus non
sufficiret, adtar ginoum esset ad X = ry + amy + an. Hec si haberi possent,
hytaqys taar
etsent maa momenti inter oia, quae hactenu in negotio retrayonituo
quatvi; a numpe semper su applicari posset methodus quati Diophantea;
et haberemus novum plane Analyseos sat sic dieam) genus ad determinandum
quae in quadraturco sunt, possibilia. nam Diophantea Methodi ad geometio
am applicatiosem coli inprimis optarem Quaeruntur autem siu temper
solutiones mosina, sed vicissim m iptis definitis literis non moramur
aut refrgimus nrationalitates, quod seurs est apud Diophantum.
ga ntan intessa inon polgaudet: p. sequ.
Lilloro
d amgean
tpy +aq