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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 15
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Operum Nallisianorum Tomo tertio etiam extat, in qua modum tradit exprimendi
rationem subtangentis ad Ordinatam, in Terminis quos non ingreditur Ordinata
ubi si loco yd dy ipsarum valores vinculo inclusos posuisset, statim scopum
altigisset.
In Prima Epistola quae per Oldenburgum ad Leibnitium transmissa
est, Docuit Merotonus methodum qua quantitates inseries Infinibas reducndae
sint; ie. qua Quantitatum feuentium Incrementa exhiberi possunt; In ipso
enim initio, seriem ostendit, cujus termini haec Gncrementa representant. Sed
illa Dnum
Leibnitium proesus latebat ante visam nervtont Epistolam
qua exponitur.
Sit 0 Incrementum momentaneum Luantitatis feuentis X e m Index
dignitatis ejusdem, et si prox Scribatur X +0, X +20, X + 30, X + 40, etc. Et
Zuantitates X + d, X + 20 X+ 30 X + 40 ec in series Infinitas expandam
tur, habebimus totidem series quarum prima, haec est quae sequitur
m-n
ens
m. 2n n-2mmnt2mna
613
m.zn
O0OX
_e In omnibus seriebuus
primus terminus erit ipsa quantitas fluens x e Si prior qualibet series a poste
riore auferatur habebimus harum scrierum differentias pumas. In quibus omnibus
primus terminus, est seriei primae terminus primus quem ingreditur quantitas o
m-n
Scil. X  et evanescente 0 fit ille terminus differentiis hisce primis cequalis,
vel quod idem est erit quantitasn ox feuentis inerementum primum.
Praeteria si differentia, qualibet prior a posceriori auferatur; deveniemus
ad differentias secundas, quarum omnium terminus primus per 2 divisus, idem
est cum termino sccundo seriei primae quem ingreditur quantitas 0 B evanescente
ofiunt differentiae illae per binarium divisae singulae aequales termino illo
primo seriei, qui est mm-mn
2nn
m-2n
m-3n
(t
seriei terminum m= 2mmn +2mnn 900X  aequalem esse singulis differentijs
613
tertijs per sen divisis; d quilibet terminus ejus dem seriei ad differentias
respectivas semperhabebit datam rationem, seil. terminus primus quem ingredi-
tur o aequalis est differentiis primis, secundus est differentiarum secundarum pars
media tercius pars seacta differentiarum tertiarum, etc. Slasce series quarum
Termini differentias omnes in infinitum representant, Invenit neutonus, uti
Dini, ante annum 1665, sed illa ante visam Merotoni Epistolum in qua exponitur
Dnum
Leibnitium latebaat; nam ante illud Tempus agnoscit Leibnitius semper
ipri necesse fuisse, transmutare quantitatem irrationalem, in fractionem Ratio-
nalem, et deinde dividendo Mereatoris Methodo, Fractionem in seriem reducere.
Eninde et iam patet seriem hanc differentias continentem non habuisse Dominum
Leibnitium; quod poscqnam ipsi per Oldenburgum oscensa est rogat ut
Onus perotonus ipsius originem sibi pandat.
(a) vide Epistolam acconitis ad didenourgum 2Taug. 101