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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 161, page id 175905688X:0183
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=183
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.83
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

lae desion
Se line
corum line
lan
1
ieuune, de
dii
IOnIS
1d
EC) ad
que adeo
uc 82d1+
c, C
Id quode
demo
eteem
pol
l
Iua 
Ret
COMMENTAREE EN LTDRUM I.
cc
T6T
 D f: licebitgne pro ac C = a CC
ed ca seponere . Ubide
mum SiFat ut d adf, ita a ad quartam, quae vocetur b, Rec rurIUS, uE
Tupra, Z ∞b. Ouod limilicer pluribus modis expedire licet. Atque
Ita de catetIS.
P quibus constat, quantiratem incognitam Z. post hujusmodi
Operationes atque cognitarum linearum requilicas praeparationes.
ed reduci posse, ut subuna semper specie efferatur, de alteri co-
onitxe dicatur aequalis.
Norandum autem, huc quoque referendas else aequationes in
quibus guanticaris incognitae quadratuim, auE cubuS, auE quadea
c0 quadratum, ac. aequatur quancicati alicui cognita, ab(que
auditione vel subductione aliarum quantitatum, quae componun-
cur ex quibuldam mediis proportionalibus inter unicatem et di-
ctum quadracum, aut cubum, aue quadrato-quadratum _ C. mul-
ciplicatis per alias cognitas. Ubi incognita quantieas, extrahien-
docancum aliquam radicem, inveniri porest. IIc cum ZZ aequa-
Tur aq. Suppolta linea a prounitare, exit radix quadrata extra-
eta ex lineaq, ut superius est ostensum, (nimirum inreniendo
inter lineas a d q mediam proportionalem,) aequalis quae sica li-
nex Z, gua hoc modo denotatur: Z ∞ V a g. Ubi apparet,
quaectionem per hanc extractionem, dum planum aq transinuFa
tur inquadratum bb, cujus latus estb, eo esse reductam, ut inco-
onita quantitas alteri cogniea dicatur ae qualis.
Eodem modo si Z3 RguetI a aG, eC quXeratUFZ. ANUMPEa
rurtus a prounieate, erit extracta ex g radixcubica, hoc est, in-
ventarum inter a primam ec q quarcam duarum mediarum pro-
portionalium (ut certio libro oltenditur) prior, radici quae sItx
aequalis. Delignabitur autem hoc pacto: Z∞ V C. aag. VIbI
limilicer constat, quod, dum hac operatione solidum aliquod,
uepore aaq, relolritur in cubum b3, ee utrobique deinde extra-
hicur radix cubica, Z rursus frat ip( b aequalis.
Nec alicer erenit cum Z+ ∞ aagg. Ficenim dum extratutur
utrinque radis quadrato- quadrata eu bi- quadrata, hoc eA,
Poltquam rodix lemel extracta, dat 77 ∞ a g cadem adhuc semel
repetitaradicis extractio, dabic Z ∞ V ag, live, Supponendo a g
in quadracum bbesse conversum, Z ∞ b. Regue ica ulcerius in in-
Finieum.
POEre