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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 289, page id 867984570:0317
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=317
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 111 lines, status machine
# Lines: 111 recognised, mean confidence 0.79
# 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.

20
GOMM ENTARIOS.
Er. HeOGEDEtOnS SV ~ da XaSCOV, 2n dis X)a H
ccr, sxnaova deuor NyVouca 28 ad
Ouros de EsIr, o n rEOS X ev Ney dE TW Oistd
XNao Et DE ein CC TETGCNIS d nascor X
pcda naet S oxrco di Naorov, 215  zvE) et
naouo xmoneedco id n reis Xa ascor Oinso duxta. Supponatur enim Consonantia Fril dia-
palon; iplius utique Dia Palon numeri, TunE
ut 2 ad I: ipsius DiC. ca PaC numeri erunt
nE 4 ad c: Adda B alia d. PatoM, IPII
Dil. dia palon, numerum lumemus duplum ip
Eus 4. ATic autem est, ul 6 dd L; crieque in
est 16; eritque in racione sexdecup. Mla
laala utus an pla Consonano Ll1- a1a- Pa
~ pdi 2)a raocor nour axibuor ios r duo reo
x er b FyS) dis dio XasCV, ioS TOSaCQ EOS Y
NoyCo FC ExKGdENa Nao pcreSpdco En ret
dia ascv, i En dia aocor. RoEcer di Si apt
pSS TE CC NOGO des SMI KeOV. AWapet) 2
58or diua Xlasrra duva vor doudatret
pydco TaVTa.
roxeir ardeconco Hee d ZV FC quo pcrcor a
quam in ratione Oetupla. Si aurem Fuerie Oua-
cer dia palon; Cumemus, ipsius 8, duplum; hoc
o Cea Fato. Lo isesle ausere tum
numeros, tuim rationes, in immentum. Potencis
impoltibile aurem id homint contingere. De
Onisonancibus igicur haec dicta funto.
quidem postibile elt, canco dialtemare distare:
cTan E edi CoV. dexnaoiss Ne785, Zuoiv2
av ergoripa D ioonos, oi dlXa 28183
a D)aipSVrS TBreWo TE HutontS
o drerroS 20yd dixa era Ho
CC3 28 eis duoiva Mera dEC8D VS
Eecoro d T oouDcorcOV, oi Y dia naocor
dexa Erzisa DaIPSVTES ZBHEW O dia
CC pEVTE 3 6 dia ScOV 25C ∞ adi dia
ce perre nara  juiontor x de Nego
cC X dEdia Sdecor, Nar  DierroV REu
CC repot dE, oi naTa ou)oV EnaS T neCo-
et ZCOV pE S NGCOTS TcoV quoDcorcor 0 idi
 dia narcor i dia nerre, nar oudit
ec dépdvor Nogor ex r3 d ix NadIB , 1 poto E
CC X RCL NaorOV O de dia XaScV Na OI
ac reosapcor, nara t ouat toteret
CC 4Y dIXNaVIS I SareITS, Y X OUTC MGO
ec ra ria Ni ed Sder quas, 8r6 Odn
cor Sue, O in noman Kab, ddoconn
Metdo e dixnaoror Z Bquoe icor, e73
a Porro; (post rationes Duplas,) proxime ad
ec aequaliratem succedunt, quae illas bga
ce riam quam proxime dividunt: numil aist
Sesqur altera e Sesqui terria: (nant 
ec fariam proxime, est prope idem atque, 
ac duo aequalia:) Et (post Onisonos) Con-
ee sonorum Primarii sunt qui Dia pason di-
ec vidunt bisariam proxime; nimirum Dia-
ce pente eo Dia cessaron: Adeoque ponen-
a dum ilidem Dia pente in ratione desqui
ce altera; Dia tessaron, in Sesqui terruu
a Contonorum vero Secundarit; qui suunt
ac ex compositione, uiriusvis primariorum
c cum primo Ouijonorum; nempe, Dia-
ae pason e dia pente, in ratione quae con
ce ponitur ex dupla e sesqui altera, qua
c’est Tripla; atque Dia pason  Ma les
ec ron in ratione quae componitur ex dupia
e sesqui tertia, quae est Octonaru ac
ae Ternarium. Neque enim hos gulequant
 conturbabit, quod non sit Bab, det supet
e particularis, vel mulcipla, ut qui nibit
tale ante supposerumus.
Postrationem duplam; ex Tuper- Parciciatoo
Cune (inquic) proxima principio (qua elt aequall-
CaS,) quae duplam quatr in aequalia dividunt proxt.
me. Nam ue eam diridane in aequalia, non erae
Pollibile: cum ipla sint inaequalia, non in deGu
licate constitura. Oua rero diridune baltam-
rationem duplam in aGua CVIaUMEOatra
Proxime, TuInE Se (quI. alera  le GuLTeKLa. NVOI
enim magnus est excestus Selgut alleito, UPIa
Telqui certiam; quippe in ratione leses aVd.
Ouin bitariam. proxime, est prope he de,  ao
aequalia. A rationibus igitur, calem habCMBUS Or-
TOnOS, prOXimC d PLLICIIO, LCIMI COIVII. 10.
rum primarii lune, qui Dia pason dividunt bita-
riam proxime: sune aurem hi, Dia- Dente, ee Dia-
celtaron; eltq. Dia pente, major quam Dia reMaron;
od ponder zE 7018TO  cegimonDuerSS.
eier D deXnS, PHOW, Hne lu ioornS, ot Y d’EX Na
OIoV EYZSa ICOS eiS iO XICIPEVTES NINei per y
avror Ets loa, 3X oiev re lu orra T aviscor, a m
 ioor 6.  Oi de eyzsa dxa Xa ipEVrS, Ey-
305 av eier ~ Woonr  Eygos de eis ioa HaspSo
 diNaoror, d  u. G iG o re1 O Oi
d nom n rcEpoXi T8 ipIoNS, n 28 SireirE
in roceoxn zou enydo 9. 20 de erzsa dixa
XNgstoV es 23 Eis duo o Fcr SV Noycor roca
Eo ExoVECOVZaGWV, pera Cao S cov D0025
Noar de,  Cor ouopcorss, oi supPcavot eygos  dinem, transcundum in Sonos. Post aucem Vni-
dexus Av rGcorot, oi Eygisa rs dia nascor si
Xa X91eZrrS Fior de 3roI, oi dia Nevre, C ot
DIa TEOS APCOV NaL pEICCVO dI MEVTE, FSDI ZEO
Ocipcov, rorcs ArodorEor de nat F erzsa X).t nempe LOHO. O ete, (CatIII
Qua
Deonum, lunc prope ab aequaae.  AMLCH
BMP. decst a d dis. M
f1 oixnaoion e
cocim iis riovae cd 10 H. MC. urtut.  2.  oon s fBS. e ML.. B
e tte