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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 303, page id 867984570:0331
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C OMI MI E N T AR IVS
ae de n Y a d exarceco F C a YB, ioor) ra
et  apa à eg r C a  d y ( βC 10 aN
et HAOIS EEW ma x CC r) X)a HEVTC
 Daot toteir oupPcorar (CK THEHOECOS N
(C XW NaTANaUCaVOVTES, on oi CE 6007(oI
Cc =ls 3) a E oouPcoriar ISOIV I SISC ENEt
 ∞ pdi a B X)a r apcor Est, ∞ i) CE D
PEVrE, oceoxn DE aorcor est rov O, (co3
Beiher  Lcooiden nai avroi nersor
a C et GB C’ae ouvauPore na Ne
LNE) FOVS EveS EKaSEpeV dE aUTEIN, T8TESI
Exe repor 7 à d i Y B, iurrors aior de
15t 3 X a Y conE  ∞ a β, dha masaecoV
1s 800 (C ipuo 85 out staas Fovcor.
(C a 7D pt 0 03 dyNOVOM W C9S F TCOV
a DN 5 NogoV EZ C drovS ES den
e SirreiroS 8 a  N5, OFB pn X3
’aea Kerppa er Neyco e TW TC
a rd d. AMa Ea
(L(C 78F COV a 2d p d, Y enoydoor na
Capd, Eouer api Duov Y Y BC  C
t n E5IV p cor o negos o 2 BPXG.
t voeos dd β p n, (NaN SvOS ditoTO.
un:) 7 B p H, coC95 Ta a r p 8
a Ta  a BC X C, Y βpo 7,  
c edo unceoxa, n red nevrenadenatco ad
(b Fcor podeet, Ena To dEn ZWO TOSapEonaidE-
et pebrco Ta dE ( po n Z a 8 p d, petC o
CC id VEPEYCI, n TEd ErEaNaIdExarae adtr
l peporiea or den r ouconauenat L0
Enaosor aeq 3 reirs ri p  C B
aneiNMa 28 d TOa CCOV, WC95 T d
F torco. 2C ∞ idi TS NEpCpaTOS pcZC)B
’éxaTtor ijutroris ouvazcadai 50 dE dia
Capcor oNoV, En aoor du0 C juto 65 10
a aurem est AD aequale utriris iptorum
cFA CB. DaatvO ieitur FA AD CB
BF sunt inter se aequalia. Sed 
e facit (inguiunt) Consonantiam Dia. Den
acse; (Alumentes iterum, cx obserratione
ce quod FF. Poni, Faciunt Dia pente Con-
cc Conanciam.) Adeoque, cum sit AB Ba-
Ce resaron,  FF. Dia pente; carumque
c FixcesaS sit TOnUS, (quOL LUPBONIE Ari-
 Hoxenus iplique dicunt;) hinc sequi-
ccur (earum excessum) F2 8 BF 
et mul sumpra, unius esse toni; e utrum
et vis eorum, (adeoque utrundis ipsorum
AD CB,) dimidu tont. est lo AC.
Sic isitur illi quodammodo oltendum quoll
non ita esse.
a Nam hoc semel ostenso, quo d Lonus sit in
a ratione sesqui octava  Dia tessaron in
ec sesqui tertia; manifestum inde fit (per
a demonstrara ab Fuelide de PcolemXO,)
quod Facessus ille, quo Dia ressaron (u
perat Diconum, Limma auctum, mi-
nus est quam Fhemitonium. Sumpto iei
cur numero minimo, qui possit osten-
aere, non tancum in qua racione sIC
T imma, sed et exceltum quo diastema
pe Tonicum, excedie Limma: F.st autem
I ille nMmerUS, 1536. FTujus numeri ses
 qui octavus est X728: FTujasque
aitidem sesqui octavus est 2044:
ec qui scilicet ad 2526 rationem Ba-
a bet Ditoni. Fest autem ipsius 1536,
Sesqui tertius 2048. Fst e5d C i
eema in ratione numeri 2048 hd
1044. Sin autem nunat 1944
sumamus sesqui octavi, ubebi.
CCMaS 2187. sStque major ratio
ac numeri 2187 ad 2040 (qua A-
pocome dicitur,) quam 2048 ad
(2044. Nam numetuS 2187 ex-
a cedit numerum 2648, plusquam
a Bujus parce decla quintam sed mi-
cc mus quam parte decima quar. d
c 2048 excedit 29443 Plusuu Basas
ac parte decima octava. Lt laque quoc
ccuna cum Diono. i fusip E
a Dia ressaron est tertii toni portio mi-
a por. Adeoque Limmatis maenitudinem
ac hinc collicitur, Flemitonio minorem es
se; torumque Dia tessaron, minus esse
quobus tonis cum semise. Lstqu sile
C (L immatis) rationi, 2040 ad 1944, ea.
dem, quae est 230 ult 245.
Avroi pd sr 8rco ncos Edcicar x oegnudvor
En ajodod KaTNONSDoaVTES CsE X rlu) 3) a nV
ouuDcovicr TCiV naj ipeso85 L CDDerry rovceV
us dE ∞)9 acoV, 5 Forcor. O dE Nogos aGom
pO cdrnon d ajdjorcos ev F i ZWo BeaXVra S
∞)a PoC∞tS, CNEYXI F8rO pon 3FCS EXOV.
C NaZ Id 3 rors dx Derros enoydo8,  8 dha
140a ecor DareIS dnnor auroder Wve)
aC (Nada  EvXNCIdnS EdcGE  o HLTONC-
cc paros  20  inpoxlin ineexe x dia d
ac r8 ctrors, nansulvor se reiupa, Exar)oy
Ce ciras nurroris AaScor gd d1BpOV EN aXIGOV.
a r duvarduer deiha (3 X neipopcae peovor cv
et noico Neycoe aMa CC T irepoxlu n ircee
b 2d, ∞ FOVICION diasa, 28 Resd 1oS
1C Ovros de o deuos est poredes) a PX5
ab 2870V id enoydoor Cxndenu rov
β po n. 20C95
crat propolicum; sensui oblequentes. Accole
ee Dia pente consonanciam lupponu ete 
norum erium cum dimidio;  la pate lex
conorum. Sed ratio (qua tide dignior elt, quam
7536 (8
1O2
2728 (8
216
2944 (8
243
2187
2536
512
rcor at est ri rcr  EOS r a D pd WWYC, 0 aVriS O FCV SVS reds ra 6 u Y
SUINEque
2048
ee dironum. Adeoque constat AB, Diatessa-
eron, ex duobus ronis e semisse.
e a Vun r8r8 dc en enordoor, 2
Senlus in tam minums disterentiIs) arguie hoc
ee parre decima nona, minus autem quam