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# Title: LBr. 396 · Hermann
# Folio 86r, page id DE-611-HS-973581:0171
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 85v); this page is its right half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 323, 2026-09-10T22:39:27Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.86
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9.
Ridicula plane ut P. Grandi aBACVia existimantio infinita nihila
atdoluta aggregare porse quantitatem ditam cujus paralogiomum notasti
cnita eleus eniti pniusmntia solutione. Ab andico rogaus statimi ist Marcattian
existoles putlicationem. Grandipni erroris fontum detexi, ortendens Grandium perperam sirium suum
6V - bV, + b1 - 5V, + bV - bY X. inster seriei enorrgenin haceasie cujnmodi siriu  qus in Drop. VII
extut ex qua lexidum ha suum locollarium deduxit. Nam in figura cjas bia (fig. 2.) remonta, existente
2
curos 145 ordinata DD = GK, et abscissa GD = kP = Ls = k13: GI, que in seriem exporrsa fit
= GY- G1, + G2 - G3, + G4=G5, + (G5. KI: GY). dam si sirico monngeni est quod fit cum Gk mimor quam
Vk, frartio G5. Rs: G1 abjici potest propler aliquam ut G5 quavis data miiorem et habibilus prscire serice
quam Prop. VII dedit; sed coincidente XG cum bV et G1 cum VI, tantum abest, ut fractio G5. RP: Gi cratumno
debent ut potrus tota series egualis fiat Biic fraicioni, qus tunc erit bV. Rs: VI = = bV = V5. eliaentibus
se mutuo omnibus lerminis ippan grgudentibus 60 - bV, + bV - bv _. iporum numero existente pari; sed so
impar suirit adjecto ad huc termino G6, seriei summa iia = bV - (6D. RS: V12) = = bV, ut prims, dutrum
tibur se mutuo omnibus torminis qui 6V - (bV. KI2: V12) igudun. Certe ejumodi ridiculum eoralaria
aptius ut ad labes naerudam mysteriorum fidem et prostilumdam profundiorum Guometriam, quam ad
easdim illustrandas.
Analylia men Currarum Paracemtvicarum ita habet in compendimni redacta. Frg. 3. Dine SA N Papucen
trica AR oirctio jactus et D A ipsi perpendicularis ex cnero sollivitatio num D, sineque _R = b, Celeritas jactus
serundum AR = C, Crordinalis curos DQ = X, 2N = y, D N = E = V + ju. Sollititatio inerros prncto N, = f
et in eodim mobilis velocitar = u, aq perpendicularis ad tgenem movs Nq = p, avem DD = B, qunque radius
veu
seu Nn
prgtunt dd =- prae: ZV_- ; verum est Cel. im AR (C): Cdl. im N (n) = D9 (p): DR (6), uonde p = bc: u, quod
in prrec. gqu. substilutum dat db = - bc rae: EVnu -bocc quod nono = do:n existente n quolibesmumero
1
potitivo rationali, hinc do = do: n, et D = g = 0:n. Idiirco quotie  est arcus circuli timilis euidum
avaii TDO, ejurque radim ad hucjum radium, ut 1 ad on id irt ut ommurur ad ounurum Droblema est Algctonicum.
Dono igitur do :n = - rat: nVrr- H, ubi t = = e = A, et e constans A vero quamtitas quy libet data in d et
conitantibur, unde equalio (1) Pict berde: ZVm-bbcc = rde: nVrr- EE; atque hinc plicitur seguens
quae est sine diffeentialibus
nu = bbcc : 32, + (1 = 2es - A) nnbbec: B Et existente ss = rr ee et B = det: dh: Differintiando diinde
(2)
iu ore apii pn eoe 201