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# Piece: https://leibnizlegible.com/api/records/496/text
# Catalogue record: 496 — [Aufz. zur Zahlentheorie]
# Incipit: Inventa Fermatii Analytica inserta postremo Editioni Diophanti
# Date: 1679
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=496&katnr=58073
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 82 (from the shelfmark LH 35, 8, 30 Bl. 82): 2 pages, canvases 163–164, page ids 00068124:0163 to 00068124:0164
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=163
# Lines: 96 recognised on 2 of 2 pages, mean confidence 0.89
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 82r — 00068124:0163
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000163.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 84 lines, status machine
rC
denbersu
er mati, quod Aantus kE7
inserta postremo Editioni dioganti Ia chetianae ed
Colosae 1670. Jac. de Billus collegerit ex Fermatii literis
Tres sunt inventiones Mlae. princa regula constendit invennis
innumeros valores afformativus radicis, quaesilae in duplicata
aequalitate. Prinam vulgari Methodo divesanti quaeritir valori
nec quant refert sitne iffirmativus an neque ubivus. Huic adjum
gitur +a etunima sumitur pro radice nova et secundu
hanc nova radice, nova duplicata aequalitas deducitur
ex prima, et rursus valor quaeritur vulgari Methodo,
Hunc novu ipsius a vatorem connecte pricri invento
etiam
et habes novum valore radicis. Hac nc thodo suantatim
a
negativis radicibus devenitur tandem ad affirma
i secunda fermatii inventio concenit
as
Ejus Earum nec
fitas
riplicas aequalitates.
duo fatium genera
Meminit diocantus
prius genus est
resolvit Fermatius unum
cum tres quantitates aequantur quadrato, quarum
quaelibet est composila certo numero ipsiqus a (affirma
fivo vel negativo) et eidem quantitati affirmativa
Alterum genus
cum tres numeri aquand
numero quadrato affirmativo
sut quaelibet, sit copo oposita
triplicatae aequalitatis e
∞
ito tales sunt
ex numer affirmativo ipsius aa
alequo= Y
etnumero ipsius a
firmativo vel ne gabivo; sine numero ab soluto
2
aquare quadrato
quar
eodem,
quantitatem copositam ex Terminis quinue fa ba+caa ate
vantitatem Termi
Certia inventio
Et aequare quadrato vel subo vel fat +ba+ ca tda
cum quadrato
biquadralum aut altirum
d
a
alter ex lumoram tebet esse
fa + ba + ca +
otd quant las 5 terminorum oportet aut prinum temitaum ee
rebet esse cubus si quantilas sposila ex sterminis
dsrum quatur
aaequanda qnto et primus Temulums sit biquadhatus sed absilutus teu altimus non habeat verdicem
esse cntur. Si formula quatuvo terminorum aequetur qoto
daxalem; talus quatiati ta fingendum est ut in qto side sint nuneri, qui in terminis a, a, a, et
ita hievanescant et fiat a, aequ. absituto. Nempe si LC exceditB Gbb, eut latus
aa + ba +  C - bb. sin cotra mutanda eruat horum signa pro habendo lntere funon video
Hic popitur summus terminus esse a
i mmnus terminus se si formula habeat non ultimum lenmmum beiquadratum sed primum quadratum, tunc
ita enm restant
lanone si sit
quadintum ita fingendum est ut evanes cant aa, a, eq absolutus
itaque pro
quid hc referat proquadnto
(a + ba = caa + da + rr = Ito et 4 crr excedit dd siat latus terr - d aa + a +Y
BY
tantu a) et a, adeoque A = 0. adeoque habetur a
dd= Terr aa (+ pulo ec errore  in signis
si siuunt sit o Inanius terminus ad, et mini utem primu terminus a et altimus YY, tunc
sin do excedit 4 CYY fiei Y + a-
QY.
ploter duoes praecedentes canones ad hac quatur locum habent non latus pt est esse aa + a + Y
Nota interdum prodit absundum
e pa vel Y + d a - aa; vel aa + 1b a +Y vel aa + ba = Y.
invento valore
mithodo, Eri, mineru aequalis artulo et tuns non liet adhibere
rudicis primitivo possunt indeniri deriativi, methodo primae inventionis, ut si radiae
la
inenta =3. senternus ad pro a. et procedemus et prus spro puru ato

## Folio 82v — 00068124:0164
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000164.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 12 lines, status machine
similis methodus i pro 4 terminis si
f  +bg+ ca+ dd aeg. quadrato
Hicit effici, ut termini ultimi evanescant obfictum contum. si 
e aba + ca +d oss ita finuendumgtum, ut duo summi tenmimi ava
res aant que sunt facilica. Quantitas composita ex termini
e
vantilas composita eus seminis 4 aequali ptlcibo, si vel surmur
icmmus vel ultimus terminus sit cubus ffici enim p ut duo
primi vel duo altimi termini evanescant
Non hbebal erat opus duplicibus praeceptis
nam faciendo e = 1. a transit unus casus in alium
et ex termino primo sit ulbimus