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# Title: [Quo Continentur Claudii Ptolemaei, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunae, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Graece & Latine Edita, cum Notis ; Accedunt Epistolae nonnullae, rem Mathematicam spectantes; Et Opuscula quaedam Miscellanea] Quo Continentur Claudii Ptolemæi, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunæ, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Græce & Latine Edita, cum Notis ; Accedunt Epistolæ nonnullæ, rem Mathematicam spectantes; Et Opuscula quædam Miscellanea (shelfmark Leibn. Marg. 100:3)
# Folio 543, page id 867984570:0571
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=571
# Source image: https://digitale-sammlungen.gwlb.de/content/867984570/jpgs/default/00000571.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.81
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

i
DTMENSTO CTRCDLL
543
i an Xeds nY, Enaaova Negor Ex. i ep B7 Ta no FL propterea, an ad uy minorem rationem ha-
pos  X y  a y Xp0S  Yy ExaOOa 
na avra, pos rli by, Ena NOV NogoV EXCI, n ov
bet, quam 2OEr ad 780: ipsa vero ay ad yu
minorem quam 3013 = à (hoc est, 3013 4) ad
780.
Bitariam secetur angulus van recta aD. Pa-
riter igitur ostendetur, quod a ad Oy minorem
EINd LS rpos V X, n ov e coK Y reos isrationem habet, quam 5924 = = (b. c. 5924 3)
 i (’Exarepa qd Exarecor d oy.) (25 re  ar
reos rli y8, Enacora nogor Exe n ov   Co M
d 1d p05 6 
Es dixa n vno D a Y n X ∞. Kat n H a XpoC
lio X Y, EMae Keror Exet. n ov  Y ZE a
d 10 Xeo5 5 po i dv a  poS n G5. (N exe
repa id Exa rEpCOV + a po.) A a Y apa Xpo5 dl
VYH, EM NOVa Regov ExCt, n a d 5 poS E5.
Ert dtx A CO H a Y FH. N∞. H a N apat
ad 780; seu, quam 2823 ad 240; (nam VIra-
que urrorumque SuINE =.) Adeoque ay ac
20, minorem rationem habet, quam 18382
ad 240.
Bitariam Porro secetur Day angulus, recta
ona. Flabet isitur na ad uy, minorem rationem,
quam 366527 2d 240; seu 1007 2d66; (nam
Vtraque VErOTUmquE SUNE 2S.) LTabet erSO ay
ad 2n minorem racionem, quam (0095 ad 66.
Secetur denique bitariam angulus nay, re-
eoS r NY, Enaaora Negor exe n do 2a 135Cta n a. Flabet itaque an ad n y, MINOrEM PA-
B15 5 Xpo5 E5 i  ay ApOS YN, enao-
oiva, n ra B1C dreos E5.
AVaN  apa, y PX  reoS i ya e OVa
tionem quam 20165 2d66. Ipla vero a y ad
y a, minorem quam 2057 = ad 66.
Contra isitur, ay ad ya, majorem ratio.
Norer exl. hrce E5 orpos B+3 d. C aeiperpos nem habet, quamt 66 ad 20274: et avibicus
Polys-
ov Y 1Y Ld Xpo5 .
XXa y r0 Y an rn ab. H a apa, X
BPrON reDOBO D. à B. inpries id ingrieas. L B. aunn s aes ops. L SupPleo, yXca D su coes op n dr. m B
1.  B.  r g rd onarieas oicuai aiei co 3o rli netrui nozo1 ao5 coeds Lc. 0 B. a. P Suppeo ny ces rluo yar peil era
A0goo EXCt, H C5 oe95