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# Piece: https://leibnizlegible.com/api/records/62170/text
# Catalogue record: 62170 — Leibniz an Vitale Giordani
# Incipit: [...] Sed in universum in horum axiomatum de recta demonstrationibus
# Date: 1689-10
# Sender: Leibniz — Addressee: Giordani
# Akademie-Ausgabe: AA II,2 N. 071, AA III,4 N. 216, AA II,2 N. 71
# Other printings: Gerhardt: Mathematische Schriften, Bd. 1-7, 1849-1863, 1 S.195-196.
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=62170&katnr=45691
# AA II,2: its series at Leibniz-Forschungsstelle Münster (online after accepting its terms): https://www.uni-muenster.de/Leibniz/seite5.html
# AA III,4: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-iii/
# Work: https://leibnizlegible.com/work/DE-611-HS-974807
# Title: LBr. 452
# Folios: Bl. 5 (from the shelfmark LBr 452 Bl. 5): 2 pages, canvases 9–10, page ids DE-611-HS-974807:0009 to DE-611-HS-974807:0010
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-974807&page=9
# Lines: 98 recognised on 2 of 2 pages, mean confidence 0.83
# 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.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# 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 5r — DE-611-HS-974807:0009
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-974807/jpgs/default/00000009.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 244, 2026-09-10T12:31:57Z — 53 lines, status machine
Etsisibeus agno scamviris magnis qui
quaedam notiara tanquar concessa ed u
itsi
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an spernom
nonus ar quaedem nocra
adgrisere ut ed mairus progredeentur esse ignosenti rague con
inserim candenda est posttram maeceriet
13
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vir C.lme
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ia
percurri nonnulla d  Euclidis
cui restituti et magna pum voluptat
a
mnta
+
non panca
de feicitem supple
et Hec cum eis facii qui rigorosas ceponerationes ontlusunt
quae ed perfectiones ermentamium demonstra
tionum desiderabam. In primis circa paralletas
est rationum compositiones video te profunde medita
tum. Quidam Non ancurtius in Belgio libellum de
rationibus c peripsit, quem me videre memini
hajus methodum lanat et secutus est Arualdus scelebrus
apud Theologos sed idem in omni doctrinarum genere
excellens) br in secunda editione libri quem
inscripsit Gallici, quem inscripsit nova
geometriae Elementa. Ambo rationem
exprimunt per fractionem, cujqus numerator sit
aufecedens, d’no minator consequens, sed os
videbatur mihi de esse aliquid ad summum demonstrandi
Et fractio iste spby sest aliquid ioer detem pans quam ipsa ratio
arolem. veliu qu nosse quae tua sit cirea hoc argu
mentum de. sententia de posteumis Galilaei a Cl.
Viviano editis
quasdam
cirja demonstrationes quas ab aliis in Tuum haclidem
trans sumsisti nonnihil difficultatis repenio, sqis.
Nam in demonscundem in Thec demonstratione
Thaletis, quod dimne recta per centrum ducta circulum
n
dice ret aliquiss
Y pag. 21
bisecet unos casis negligitur cum ecilicet unum segmentum
A in alteram partem transtatum, partim intra
partim extia alterum segmentum cadere item
iDC

## Folio 5v — DE-611-HS-974807:0010
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-974807/jpgs/default/00000010.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 244, 2026-09-10T12:31:57Z — 45 lines, status machine
pay 122
23
 in demonstratioas ajoratum, quod ues
rectae non habeant partem communem nec
spatium
pon
inclodant; supponitur duo puncta E.R
pan 2C. et duo puncta Et nay. Z
quibqus uae recto a circul: secantur non coincidere
inter se quod tamen adruc monstrandum erat
et licel in de axiomalis posterioris demonstra
hode lavius hunc iustantiam removere
voluenit, attamen ipsemet in eandem denno
incidit supponendo novum circulum esveni
pribit ex centro  secare rectas A sum to
1t ep.p
in recta ACO secare rectas in punctis Eet F
in coincidentibus Sed in universum in istis
t Lorum axiomatum de recta demonstratio. Ibu
um difficultatem reperio, quod in eas nullo
panodo ingrevitur definitio ne
ste
nece ulla recta
ropriatus axiomate aliquo proimisendo contenta
e
prophietas recprocas prip vel proprietas definitio
m rectae a te assumta est. quod sit brevissima inter duo
puncta, sed quae pulchic
nteris pro parallelarum propri
haec aliud de recta axiomapo pamiltis
tate, sed hic eam non adhibes. Itaqu in emnibus istis vemon
e
lntionibus posset alia quaecunque linea pro recta assumi
vert gralia circules aras colculan. singendo
pioate arcus paraboli Ellint circulans. Pro (ireulo
Fassumendo novum lneam fictitium tatem. in qua omne
reene arens circuli anpentio ad circumferentiam ducri
sint equales qua generetur circum ductione plicuius arcu
crculcneole enim modo deinde demontuabitur quo
linita nale fieret. itaque videtur aliquis his demonstrationi deese
Et videtur diffilulter absolvi po demonstratio tisi quis assumat dotione
rectae, quaego uti solee, quod corpore aliquo duobi punctis immotis revol
+
loctis om itium punctorum qui scantim sit recta
e