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# Title: LBr. 227 · Eckhard, A.
# Folio 42v, page id DE-611-HS-960119:0084
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 43r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-960119&page=84
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 97, 2026-09-09T22:09:11Z — 71 lines, status machine
# Lines: 71 recognised, mean confidence 0.86
# 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.

Quod ita demonstro: Postulat problema primo
ut area Ali rectanduli ABC sit numerus
quadhatui. tam duo sunt manofesta: peimo
non fieri numerum couadratum nisi ex dlactu
juodem numeri in semetipsum, et deinde au
lali rectanguli Aduri ex multiplicatione
dlimidii catheti seu dimidia altitudinie t 
B
in vasen
BC, aut vice versa dimidice baseos io
cathetum siu altitudinem. Quibust positi
area ali rectanouli
esse debet, altitudo ejui AD dupiliam este debet
baseas C
aut vice versa, hoc est su 
2, BC ehit 1.
B et
illa 4, hac 2): si illa
Et sic in infinitum. nam scimo casu dincidia 
Ghav
erit i, q duita in bC
Ad, quae est 2 ilecta i. B
3
serundo casu climidi
C
est est
merum cochadcatum. Een tertio casa dimidioo AC
qua est 3, ducta in BCV.
itidem est 3 praduris
numerum padratum g. et
sit ceincers
unde si BC est e AC necestario este alt 24
sact. sejui duplum, alioqui nunquam provenies
area quadrata, quemadmadum jam demonste
tum est. Unde jam intelligi potest
AB seosuerim 2 27 et B
∞Z
est natura problematis fier: aliter non potuit.
Roi enim
Eed si altitudo AB sumatur dupla vaseor ex
qudd ut ex demonstlati, patet, Brevestario fieri
debet, si area numerut este debet quadratur
tamen hypothenusa HC mungliam erit numerus ratic
 quod serundo nalis: quod ita demonstro: diconiam in trian
lac in sphoblema vule revangulo Aet
te regrcirebatur aequant, quadrato AC. Weultiplico 28 28
rimiliter multiplico LBC
X
per BC per 2
Nec ABper 2
product. 42
praduct. 22HB
12
CCH
imo etiam ex
ductu aliorum
numerorum,
v.g.. 16 ex 
2 et 8
36 ex 3 et 12
est enor.
Sequeretur pari
jure productum
ex duobus numeris
inaequalibus verki
grabia unum quodque
parallelogramum
rectangulum non
posse aequari
quadrato
falsum