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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 288, page id 867984570:0316
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28E
OR P FY R
neros aequales, altribuendosu alete souls deu
tonis: Inaequales rero, maquic. Sb al.
tem a Fundanis numeris, ca quae Comoaas
spectane, demonstrabant; oltendit Ludemus (in
primo Rrichmerica cractationis) dicens, (de ly
Chasoriis,) haec verbatim: Ad a l
Consonantiarum rationes, (iplius DIa- FCHaTOH,
e Dia pente, e Dia palon,) quod Contingi
est in primis novenis; (Nam 2, 3, 4, TunEnO
vem.) Causam autem, cur oporceat aequales
numeros aequitonis actribuere, reddit Pcolemaus.
iplam per se rationis cridenciam. Deinde LiC
Pergit.
Dolitis principiis; in Tonis, equicono; es, in
numeris, sequalitare: Deindeque in Ponis InX
quitonis, et inaqualibus racionibus; ucrisque
quam proxime, secundum ucriusque principium.
d pro cujusque ab eo propinguitate aur lon-
sinquitate, commenturandas esse inaequalium
difterentias: Perspicuum inquit eAle, quod, pro
Xime polt aequalicarem, ordine sequieur, in ra
cionibus, per numeros conlideratis, Pario dupla
in Sonis vero, Unisonum Dia Daton. Quoc
isitur Dia palon, est ab aequicono proximum,
teltatur Sensus; quod ratio Dupla elt aequali-
tati proxima, oltendie Racio. Sola enim dupla
ratio, excellum habet aequalem ei quod excedi-
cur, eundemque. (Multaque hac de re à nO-
bis ance dictâ Tinc.) Adeoque auribuenda cle
ratio dupla ipli Dia-paton: quoniam, Vnilono.
rum, unicitimum cst ec pulcherrimum Dia. p2.
Ton. Cumque dupla ratio ip(I Dia paTON aUTI
buitur; ipsi Dis dia pason, arcribuenda erie bis
dupla. Racio aurem bis dupla est Ouadrupla.
FL Similicer Si Sic, ue admilerune aliqui, Tril
dia paton; aue eciam Ouater. dia. paIOn; (ut
Plato, in PEehoronia Dnirersi, ulque ad Oua
cer dia Pason et dia penre et conum, producens
diastema; ob causas quas alibi danus;) menlu
renur haec contona, ipso Dia vaton, e rationi
erecrai raveeor cst co du5, en Fn 100
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apibucor EdECOBCTO, 2015 100τOIS = cov dE aviocOV,
3015 aVIODZOVOIS ZaCQUEZNZEOV, a ZCOV KeIErCV
ev do D007(015, 25 1002018 er de de Duois,  1oo
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ors on de x donasr ergos Dioernos, dcirvo-
si o neros. Nor 6 qd ò dconas O NoyO, ri
VdEeox 1ol Ex+ red r Epexoduco, C Ed au-
rus HoMd dE CC iuir ∞ Et r8TS éipn ceGrEPOV.
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VCOV EVEOTMLESTATV Z CC nam ISOV ∞ DI∞ XaSCOV. YZ
de dtnaois rn 3)a ascor dirododerros rn dis
dhae aocor dirovepsp + dis donasuer dis ded
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re15 d NaOCOV ESI, CdS ZIVES X apEd EZarro n naI
Ter CaNIS, cos HNCTCOV, EY FH VvXOYova τ8 X av-
205, eXet r8 terCans dha nascor nai dhe nev-
72 naI 2018, WeYCV ~ diasqo di a5 ev
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ra ra OPCVa, EE  dia XascoV Nat ∞ di-
Tonaoo
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Dnor, 2015 100701015 06cg(015 165 dE 163; 
av10DFoVOIS O2 gd, 3)9 ZcV ob WNC, 18. nat c
Tas ouuPcoraS nd civa, 3H Not LV C
rio necorco d api BS isoCa RV et
HODarPCiCOV, TOVH XaTa NEGWr En dE 60V tut
tcOV OOpDCoVICOV N6Y85, Z8 TE X(9 Z~ apCOV, H9)
nGCoroIS LapX 3015 civca B V,Y dgnctat
s D)a nErre, 3 8 _)a Xarcov, on oopbEBAHEV, Et
ErrEo Aiar ) o HTONCuO, 3 deiv 285 1085
deXS DeroVECN 2015 100FoVOIS, dinctduos 
avrodi S noys craertar FEs de encir.
CL prONSDoV roruw erros rn apxn, 3 C Xa5 Cy
numero.) Aiqualitatis vero, simpliciter, nu-
a Camque huic principio consentaneum sit, FN-
ee positas sonorum maequitonorunt differen-
rias, pro earum ad aequalitaten propin-
a quitate, invicem comparandas, esst. LLnC
statim manifestum est, Ni qualituli huic
ec proxime suecedere ratimem duplam; (ut
 quae excesum habet, illi quod Exceditur.
c aequalem eundemque:) Ontfonorum vero.
ce aptissima simplicitaris e omnium pul.
a cherrimum esse, Dia. pason: Ldeoque huic
a coneruere rationem Duplam; ipsique Dis
dia pason (verbi eratia) vis- dupam, b0c
 est, quadruplam;  sigua sant ana
e quae à Dia pason incerrano e dupla ia
eerione mensurentur.
Accribura aequalitatis ratione, quae in nume.
ris aequalibus compicitus, aqutonIS; e IX
qualibus, inaeguitons: Comeuaa CtIl
neas ZCV avioororcor DBoncor 2)aD-
e45, H C95 Ta5 Woous eygoryt  4
Y ero erieriav, repOnO eruiezsav. e sic aliquories. 2 MIF.. ris sed D. rois. a MF. DeeA rois - - ev 3 4) 17715.
NF.