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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 431, page id 867984570:0459
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=459
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 97 lines, status machine
# Lines: 97 recognised, mean confidence 0.81
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IIA R NTO N TC A.
Cciass. Pario i Cooncipet en Hlaipcon ireo ratione, dilterendum estus secundum (qui divi-
pciconuctor revor 3∞ NML OESC. AIa ToCorEpOV
oEi D TCS  pa NONS EVEEVS n) Id x roIS
For je 6  pcNcodtas, 2 idi poxartNCy duco
duorcor, BaporCCaV Éxet Tin Nixavev Tcor 
00NOIct aCoT. C erSV oEvrEeqV o
EY 201S EM de Z HoCX.
Forapi Enddar ENCuESa C  16ISFOV ZEVOS 
prncodhas narareucir draipsodo XpcoTOV, 24 ZoC
pocipnuds esvnerres napnir, Tus v cls 28 G
rEpS Ta Xopd S 28 dAquS ZOVS, n201 rlv rn
Elos TEV VXGDSCNaICON, p nS aresocia, eis
OFC pEon Ioc à My NOIS Na noISEV Ts NIXarOY
avroc. nrot rs c Davr Fcor Vn Ep6oNoicoV, ioni
onnavrn i re ordeco puepet avrus. ios exdr avrtu
WeS CxCirW, NeyOr EXOYdOCV. ErTa HaNN cai
psuer, rus Quoduleo nexaior aurS, cis pecen enta
Ioc aMY NOIS n o1SuEV Y CVN Cr ∞. VrS, 4τO
ri riTs rcr V CPBONOIcoV. ion ean avrn  Y9
bdoc pepet avris cds excu avrio rpos enci-
vleo, Noyor EmEdoqcV.
Kct p ravra a PaiSu Aid YSEmESITS No-
28, or éxa n can aurs, iro n vier F duY
cducor, 20e95 o rios avrs. not  vius c
VnepConaicor, V cipad5 duo uoeis5 No-
785 n rot Y Cnoydoer, ov EZC y N1ZaioS airS 95
Els virlos ra Y Sedoor, ov exa n navonim
avrs woegs rlui Rixarer CC F nanopdvor et airs
Noger, dero 2 EES  DOrepcor Y eienuicon
Suoe icor 7cor, 47ot 2 Sro De door, 31971
vésonou aeOdS Cira LavarnS aisre Negor
dendus Cupponicur) conum Fypermixolydium.
t primo quidem de sectione generis Malaci en-
ton (seu mollis intensi.) licenim hoc melo.
diae genus, religuis duobus ance nominaris pene.
ribus, graviorem habet Lichanon; led, quam
reliqua, incensiorem; hoc est acuriorem: ut in
lequentibus oltendetur.
Ideoque, cum suscepimus hoc melodix se-
nus lecare; diridimus primo (opc praedicti
acuti cuspidis circini) Necen acurioris ceCra-
chordi jam expolici loni, (hoc elt Netenhy-
perbolaon,) cum omni accuracione, in octo
parces incer se aequales; facimulque ipsius Li-
chanon, (hoc elt Paranecen hyperbolaeon,) X
qualem ipli cori ejusque parti octara; ut ha-
beac haec 2d illam rationem Pe(qui octaram.
Deinde dividimus irem, sic factam Lichranon
ipliuS, in parces seprem incer le reguales; Faci-
musque iplius Parypaten, (hoc est Pricen hy-
Perbolaeon,) aequalem ipsi cori ejusque parti sep.
tume; uc habeac haec ad illam racionem selqus.
lepeimam.
Post aque autcrimus a ratione selqui certia,
quam habet iptius Fypace (hoc cl, Nece die.
ZCuemenon) ad Necen ejus (hoc clL, NeceN-
hyperbolcon) dictas duas rariones super parci.
culares; nempe selgui octaram (quam habet ejus
LichanoS ad NeTeN) de Sesqui lepemam (quam
habet ejus Parypate aet L. ichanon ;) 3) 8) 8 (37 (3
relicuanque ex ea rationem, (post ablacionem
dietarum duarum rationum Cuper. parcicularium)
nimirum sesqui rioclimam lepeimam, dignolei
uS accurate rationem eam esse quam habet
iplius Hypate ad Parypaten. Si enim d ra
eione selqui cercia auteramus rationem cum se(-
qui octaram, cum sesqui sepcimam; non alia
(ex luper- parciceularibus) ratio reliduum ex co
rcor x nanoudver et avrod  Dasquua ei dialtema continet, quam sola lesqui viselina
aro 101 d 2 re exoy door C ’enieb douor
Septima. Sicur (in exemplo) numerus ducenta
viginci quatuor, rationem habet ad cencum-
Texaginta octo, selqui cerriam; li ergo inde au-
teramus racionem lelqui octavam ee lelqui sepri.
20 drpe Ter exopdor r iaseuihoodts rovs.
Acurius Fecrachordum Fypermixolydii Foni.
Mananor evroror . .
o d. M.
raponru, n reirn.
racgviru, n arxaris.
Cenus Molle entonon.
virn stil coredicor.
reirn ras bonaicor.
racartira iitecraior.
mam;
43
ov EXC G05 XVI HpV  1D. K at Vd eiree a DENCo.
ad 2ot de enoydoor n) EnECdouor Nogor dio rS
CMTCIES NoyS, Sdes av N O Z empseicor No-
en uor  o enerodebdouos. Oior, Pri deir
uarOS, o Naxeora cirgortosoeq apibuos, nego
EXC NEOS F ExO rov EE yNOVTaOKECO, SITGITOV EaV SI
pra.
rirn Sncpbonaicor.
61ro ouans, sebono nanro, senlu poltulance.
Suppleo