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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 317, page id 867984570:0345
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=345
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 102 lines, status machine
# Lines: 102 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.
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E OMI MI F N F A R IY S
V
que ab his, ita ut sensous sarispat, di-
ac Ae vero jam (inquie,) Duan doquidem ne
cvisa fuerint Petrachordorum prima Gc-
ec sit tum concrnnlatum hypothesibus, tunt
ae phaenomemis, consentaneum: Primis, e
ac divisionum naturae concruis, sue eestioni
a bao, dostts. t extera.
ce mera: Conemur ipsi  hic servare, quod
depe roivuo, Onoir, entdn  BdE FSTOIS quo-
noysucos F aidgocor, dmen) a eco
ra son reor rereaxepdcr ucreqdiodt
auroNarEaVDa BSCIAI Y SE TCV e
MENCCOVELODEOCO, i Y roIS aOIS
2n o N S)oN Enop dvot  M, NoTa D
Om X pce 1OpucoV, B 6ONaIS. I, TC NoVe
Rodeiset SV, Ta necorae ion rV tel d. XBE
dcoV, d dso TE ACAGdhErS GAXO
5X OuONOYCOS E TCOV pBONCOTE DEO naI
co e 5 Deots n rahes Tar casnparcor avrois
cocidvasi nai ooc Wet atCOV CIEHHE. HetCG
monstrabic igitur, Prima recrachordorum
Genera, (prouc sunc cum ab Aristoxeno, tum
ab ArCHsa dirisa,) non congruenter tieri cum
Mulicorum senSibuS; ee quidem, contra poti
riones d Consticutiones Dialtematum ab ip(Is
luppolitas: guaeque de eis dixerat. COnacur
etiam hric conserrare, cum id quod consenta-
neum. lic concinnicatum hypochesibus, (in po-
lirione et ordine rationum super. parcicula-
rium; ). cum id quod, per phaenomena modo-
rum in melodiis recepcorum, est in contecto:
quodque consentaneum sit primis, de divilio.
num nacurx concruIs, Sugpeltionibus; qua5 2d-
Ycor, B F o0uPcoricr Seoor 1p0 abar hibet 2d Taniorem Racionum in Contonanciis
Des eis Déods ai raS T yNMOTECOV 287eSI decerminationem. Alumit aucem (ut Zemma-)
nara TOS oupPcoraS avrd Wege r)dnS, C e
N5yS. NOWOV VTCON TCV ucr ∞, n St ECoV T
reaxopdcor cor eDeEys PBo7 (85, eei coe95 a M
185 OC 18S noIC NoY8S GOV EXeL TCON eiS
duo XaejosS, n recis e 1585, TOUCOV EnEt un
duva ror eis io rEIVW EqpoPIOV Négor, n dhcona
oror aM eis IO cds X X)a NaSCoV, Ev dcona
orovt Noyco WWY X avoV, eis  axioc diyen), ∞ de 20
nevre nai 7) a TcOScpcoV NaTC TE Y nutexter Nogo
y  Biicerro recor erraida Quocor VnEZ cor
Ir gd ∞ SCoroV ∞ C iobrOVOV, EV n Ev Eirae dio 
ioornoS, DqVEnoecos Qodions r Erépco pova
dO, EVEro rap ioerysa N078, o 8 Xa nacor, E
dronaoio Norco, rcr duo weg5 x er MErO de r c
conétoror Nogev. egDun peraidos,  iu quodvos
o retCoNdorS NigoS, o Y ria de9s er opoicos de
 airs Quous ent r8 rsconaois, regover d rerea
2)d0 O, d WeS EV CoGEVNEPOX45 28E15 Eivai
(C a et  DaVEHoECOS ZwoWnS, 28TE51 W CBGC DetonS
rE Ereeco F oecor povad (O, pet  cor o Negos esiv.
ev vrepoxi porad O) ErEpCO aUTCV opcOV. FaNW, 
 chronaoror négor, Y rcor duo vees er, woe dunr
povadOS ExaTEpCO FCV opcor,) iu QuovoS o uio-
ad pertiones ee Oes ana (HOC MM,
Doluerat,) cum Ratione; hoc, omnium Gene-
rum commune: Nimirum, quod soni, etian
in cerrachordis continue politi, rationes semper
inter le Faciane super particulares: quae nempe
Spectane ad torius sectiones sire in duas rationes
prope aequales, sire in tres prope aequales; (eum
tieri non poltic, uc in aequalia dividatur ratio vel
Tuper Parcicularis, vel dupla; sed in Prope a-
qualia:) Or Dia palon (in ratione dupla con-
listens) diriditur in proxe aequalia, Dia. Pente et
Dia cellaron; ee in ratione sesqui altera, ee lel-
qui cercia; cribus ibi tactis exceslibus. P. rac enim,
primo, Agniconum; unum ec unum. Deinde,
ab aqualicare recessum est, tacto incremento uni-
caris alceri terminorum, tuque (Polt aequalicacem
rationis) Dia pason in ratione dupla, 2 ad c.
Post rationem duplam, accectione Vnitacis, (Fa
eta est ratio triplam 3 ad 1. Dimqua eo-
dem facto in cripla, facta est ratio quadrupla
4 adt T; Ut fiatt HE EAbC)aS. Lt. Sic sem
per, incremento facto, hoc est, unitate ad
alta aler Torminorum, Ratio fit major, in ex
cessu Oncacis dit terminorum fucto. Ra
NOS Nogos, oECV ia NGOS Za duc ouoicos des e0 Selqaa, 3 del 2. Similiterque, eodem
S airs Quocdis em FS iutoniS, regover eniretros facto in selqui alcera, fit selqui cereia; Wc Fianc
tres
dimpr
I NavraV)a daCoC je X aNeNS)or E ZCoN Ep-
MENCICOV DSEOCOI, et 1E Tn Deod n, 2n ZaZCI
Phchonsorum;) cum ex Hypochesi primicus
Polica, (quam ipse de Contonantiis ance pro-
rcr empoetor NoycOV  X nEOS Fà Pairoda
2cor nd cr er F pencochais ouonoysidvor anons
dcos F RECOS, 3 NaTO DuoW TCOV pceLO pcOV
Em 6oNCtS, ais h Ln) MOS OHEGEPOV ZCOV No-
fas. post runora caplatm L. id L; additione
DBogcor naea di D apXnder DEoS, 
unitatis facta utrique mandeum,) sic ra
CAP. 15. a Pro rvoncauhian reponO- ras. B PrO aiadios. LCH saV. LL1O oaoB CDOHO verere. d Sup
e Pro
pleo, quod excidiste videcur, (Talcem ad huinc sensum) in quoct e eC. ulque ad alcerum in gloiptuo.