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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 209v, page id 00067993:0420
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cendens, inter alia habetur per aegrariones eradus indetinici, tactenus
2 nemine consideratas, uc R sic XX F. X Xe qral. 30, _ quaeratur X, rC.
Perietur ese 3, quia 3F faz eAt 271f3 Pirc 30: quales aegrationes
pro circulo dabimus suo loco. Algebraica expressio sic per numeros, li-
cet irracionales, rulsares, seu per radices aequacionum communium:
quae quidem pro gradratura generali circuli sectorisqs impossibilis est.
Superes Quadracura Prichmerica, quae Calcem per series Ac, exhibendo
ralorem circuli exactum prooressione terminorum, inprimis racio.
nalium, gralem hoclOcopTOPONAM.
Inveniisitur: vid. AB. 3.
Oradeato Diametri existente +
circuli aream fore: F fF3  18 et5 Fe dc.
nempe gradeacum Diamerri inceorum demea (ne nimius
hac valor) ejus cercia parce, addica rursus ( quia rimium
demsimus) qrinca, demeaqre icerum (quia nimiumre ad.
secimus) septima; de ita POrrO.
Ericgi valorjosto major 1
minor Z 5
errorecamen existente intra L
majoc 7 515
minorz 5L 5 B
ec.
ec
Toca ergo series continet omnes appropingrationes simul, sire ralores
iusto majores eejucto minores: prouc enim longe cotinuata incellisitur,
eric errorminor Fractione data, ac proindede minor daca quaris quanci-
tace. Orare cota Ceries exactum exprimit ralorem. Et licet uno numero
summa ejus seriei exprimi non possic, de Peries in infinitum producacur;
qroniam camen una lese progrestionis constat, toca latis mence perci.
vicur. Nam ligridem Circulus non est qradrato commensurabilis,
non porest uno numero exprimi, sed in rationalibus necellario pec
seriem exhiberi debet; quemadmodum de Dingonalis gradracis de se-
etio extremi es media ratione Facta, qram aliqui dirinam rocant,
alixque mulcae granticates, quae sune irrationales. Ecgridem (iLu
dolphus poruisset resulam dare, qra in infinitum concinvarentur nu-
meri 314159 ec, dedistet nobis quadracuram Drichmeticam exa-
etam in inceoris, quam nos extibemus in tractis.
Ne quis aurem in his parum verlacus puret, seriem ex infiricis
terminis conttancem non polle agrari Circulo, qui eAt grancirasE.
mita,