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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 458, page id 867984570:0486
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4.5E
MI AN D E B ES BR Y R N NI
smilicer per conjunctionem continetur racio.
nis selqui decimae- quartae e lelqui quinta, in
ratione sc(qui. sexagelima nOna, 3) 33 (85
V
clare oltenditur in lubjecto s calt
Elypodismate.
quotcos nara orra plio ZIasiuuarOS, L  To
ExioapCoaidenarZ Noys nai rod EninEunS
Ex  E AEEHNOGEaTC Noyco, id5 EtapB et ta
onddce TNV 2018r8 ouSipat05 2c 
dcnrvca
SECTTO DECTMA-OVINTA.
De sectione generis Ditonici.
TOM generis item Enarmonici sectionem,
Laccurare jam (prour de ca poltularit con-
Cila oratio) peregimus: incumbit denique (se
cundum cum quem diridendum propoluimus
tonum Lly permixolydium) melodix genus quod
Diconicum dicitur diridere; prour ante sumus
vollicici. Postremo autem loco de eo dicen-
dum putarimus; (gnamvis species prima CI.
e, prae aliis speciebus harmonici ConCentUS.
nocior e magis ulitata;) Ouoniam, quantum
ad hypocheles Hlarmonicas, ommino necesse cst
genus hoc ab harmonici concentus idea proseri.
bere. Ouamris enim habeat hoc Cystema ejus
dem duo diastemata (maximum, e majus,
concinna; minimum tamen, non iten. Non
pocelt enim hocce diastema aur ab ulla enu-
meratarum quindecim rationum super-partieu-
larium contineri; aue quaris alia ettabili ra-
tione; cum sic natura Pua (uc ostentum est
omnino irrationale (intellise, quoad ratio
nem multipticem aut super particularem.) Om
ne aurem vocis diastema simplex, quod 
nulla praedictarum quindecim rationum super-
parricularium contineri conspicitur, illud om-
nino uc inconcinnum es prortus ineprum ad
ullam harmonici concentus speciem exictens, a
concinnitacum contiaeratione (ut par elt) ex
terminatur. Sed quoniam Auditus (cujus ope
Tolet Rario, omne illud quod concinnum cll.
aut non est, dijudicare,) neuriquam porest (ut
prius dictum est) hujus inconcinnitatis diver.
lirarem persentilcere, led omnino tanquam con-
cinnum admitric: idcireo, d receribus, etiam
hoc melodix genus (non inepre) dictis har.
moniei concencus speciebus (quasi esset ex
concinnis omnibus compolicum) connumera
TUF.
Cut BBICIL CTTaI AOC POPOImImUS, SCCUN-
dum conum Nlixoludium (aue alium quem
vis) secare; Primo diridimus, cum omni ac.
curatione (ope Expius ante dicti acuri cuspi
dis circini) acurioris ejus cetrachordi Neten,
hoc est HccnMlon, in parres octo in
cer se aequales; facimusque ipsius Lichanon,
hoc elt Paranecen hyperbolxon, aequalem ipl
cori ejusque parti octarae; ut habeat h_eC aC
illam rarionem sesqui octaram.
Rec. Mo bdp 56 cbt bbcr 36h.
Hei i Tln 8 erappovis Qvs5 nataroulio, 
chaipeon, dyne sOcopdiicos idn. na danre o w et
avrus oorrerunedi (9 negos a urd. Croinocueda
avaernajer nornor, nara F eis Ilaspcom inoncipdvor
inepprEoNuctor rovor, nai x nansidvor chroviaron
Quos x pesacechas nararociv, na dunce du enry-
NeuCa Weerepor. Tendrajor de ei aurs egon
NOV EirEr ignoc C)a NaL HEC OVTOS NECÖZS Z na
qucoepp  oorn decor cidcor  iepo-
ouo enddince, osco ud nara raS appoVINaS
oDeods, no z avoyun avro ~ 8 ipuco d
E Der idEas. Kat qd ci n, ra duo airs X)
Suola ~. T0ISTOV SUSIUa, TD FE plE 71GOV X, Y pet
GCV3 EAPIEN MEVTAO VEHTH), a  e rot je 28-
XaxISoV Sdapuos. Kat qd Sd W∞ evos SrVoSSV Y
EEne nucor erNaena Suoe cor noycor 
501STOV 2I_Sua OiOV ZE EnEXCD Sd un amSois
dn r9 Noy3 en2S ànogor Quod na dons nap
Xor, cos dedem). AXar dE PcrnS o SVSa
a once  SdEVOS Y WegKarNCY CON NEVTE
XaIdEHa EmOCICOV NoyCON EM EXouVor rEdCpNC
CKEIVO HEVTCOS CoS CNMIENES ngy KaT SdEra rOOV
emridcor ees n s ipuospds cidos LaXOV
 Y EpGpEACICOV id EaS CK TOMCE, 1d5 cino5. 11 d
de n aron. Si y5 o negos arar, e jpuoidiior e
in, nerer ercoder, sd aucos  gmarus 
expeneias avrs, na dur ee eoeder eion), d
Dareado duvan a ios EupCHeS oNcoS avr
adexem De T0t ZE TYTO, uno F aNaicor
n9 ∞ F01STOV VEr 6) F uEncodhas Cd andnoTCS
rois 28 ipuosius cipnudvois eidcon, ids et ana
SEOV EILNIENCIION oOYKCdVON, WOYKaTEINEK)
Torzaper enddar n 28r0 coegaipeden nari
F ixepurEoNctor rover, n KaY aMor eroiordia
nararuur necorov duccpod, ud ons 
Geraes, 2)a τ8 WCcdon S noManIS o vErrES Kap
nirs, ru virlus r8 oEurips rr ea xopd X avrS, yr05
ru ta  CadEBBKAICOV, EIS OHTC pUCPn 102 a Kn-
Loi5 Kat o ta nkutoi adio, niot Elo
Drylus F epbonaicor, ion onn avrn Ce r
cbbcd ppet abts s Exett avitio coess exerta
TMHAA AEALERATACKAIOA.
isoi cadsboodo
B LlO mimdosunes i repono imiconormmur. calculo postulane. a AB. ipurrims. II. enprdiam
F 1