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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 284, page id 867984570:0312
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# Lines: 90 recognised, mean confidence 0.81
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POR P HLLLI
c plus e Ouadruplus, tum Sesqui-alter 
ae Duplus: Sesqui tertiam faciet rationem,
e cum duadruplus ad Triplum, tum Du-
e plus ad Sesqui alterum comparatus. Ad
e eoque, quanto consonantius est Dia pa-
son quam Dia pente; tanto erit conso
eenantius Dis. dia pason quam Dia pason
 dia pente.
Ad horum evidentiam, Altumitur cheorema
quoddam hujusmodi: Si lic, ejusdem numeris
tum numerus guadruplus e criplus, cum ejul-
dem item duplus e lelqui alter: FXcelliis qua
drupli ad eriplum, rationem taciens selquiter-
tiam; idem erit arque exceltus dupli ad sel
qui alterum: EIL enim ee hic in racione sel
qui tertia. Puca numeri 2, ello quadruplus 8.
de criplus 6: item, ejusdem 2, duplus 4, de
selqui alcer 3: Si isitur, d ratione 8 ad 2, qua
elt quadcupla; auteramus rationem 6 ad 2
quxe est cripla; reltat ratio, 8 ad 6. (5) 3 (3
Irem, li d ratione 4 ad 2, quae cA dupla; au
feramus rationem 3 ad 2, quae elt lelqui altera;
restat racio 4 2a 3, (2) E (3) eadem ipla: UIra-
que enim elt selqui cerria. Adeoque, quam ha-
bec rarionem, dupla ad selqui alteram; hoc est
4 ad 3; eandem rationem habet, quadrupla ac
eriplam. ErgO, quanco (seu, qua ratione,
excedie quadrupla triplam, canto (seu, eadem
ratione) dupla excedit lesqui alteram. Nam
relqui altera (duplicata) facic criplam; ee dupla,
quadruplam; eandemque rationem habet qua-
drupla ad duplam, et tripla ad selqui alte-
ram. Hlis aurem lic se habentibus: Cum Dil.
dia pason in ratione quadeupla conspicicur:
acque Dia Pason e dia. penre in cripla; Tolum
que Dia pason in dupla, ee Dia pence Polum
pos i) rui rircor oleverar, napbare) de-
enpae n TOISTV FaV eros cebuS, o pd ns de-
buos n rerea naor , d) rer NaoO i Es
3 avrs, o di dexnaor , o ) quron. 6). _
rOECOXH TB TTBaMNasis WC9S Y EpIn Naoror
SITPETOV NOISOU KogoV n aurn EccI Tn L EPOX
s cirnasis vegs t quiontor est qd’ aurn ev ci-
Telrco Noyco. Oiov, 28 B deDuS, E5 Co TerPan Na
orO edv on, TPIX Na0r O ) 05. nai mN , 28
B di neoros pdi o d, iutod 105) o Y. Ear àa
deto F3n cC95 ra B X5yB, orroS rerCaH NaiS
a DEncop F F5 APOS ra B NogOV, OVTA TPIXNa
OrV RetE) NegeS Tn 7005 2_ 5. C XW, éar
dero 28 d pos ra B N0yS, orros dr nasis, àDe
Ncopdo F rcv Y ipoS ra B Nogov, usoNOV erra
AEtHE) Regos o T rEOSapCOV X POS ra Tela, o avros
Eist Id aDc BurerTot. S2SC dV ÉX et o dXNaoS
Nogor reoS Y isoNLN, TBTESL sa d  poS r Teicn
r8TOV Exet F NogoV o TETCaT Na0 O 7p05 Y re
HNaOTOV  Id LEDEPEXCLO TEZPAHNaOO TS TCI-
NaSIS, TZTCO L’CEPEXet o dmNaor O τ8 iio-
X∞ Kai Id  Sxnaoradeis o psoNiOS Z TP-
neoror nosei o 3 d nao O, Y TETpan Na oV
nai Y avror ) Rogor Exto TETCaN Nao O Xp05 Z
in sesqui alcera: Sic isitur se habebic DiL. dia. Am Naorov, i o Tp1 Naor 6 C poS Y iuioNo
pason, ad Dia pason et dia pence, ut Tolum TBTcV) STCS ExerTCIV, eet x dis D9 nascr ev
Diapason, ad Tolum Dia Pente: Adeoque,
quanco Tolum Dia pason consonancius clt (0-
10 Dia pence; tanto e Dil dia. palon conso
nancius est quam Dia Pason et dia- Dente. Fi
nis Sexri Capiris. Princixium Sepcimi Ca
Ditis.
DETCa NariCO Noyco decoperroi Y dE V)a nascor
i dae nevre, ev rpin Naoic 20 d56 Ha naocor pe-
ver, ev c Nacico τ0 dE )_ HEVTE uovor, ev nur
Nico drcoS apa Ehe x ds dia HasCor r eoS ∞ 
aocor i D)e HEVTE, 1o5 ∞ ueror duue naocor  pos
∞ povor D)_ AErT A2GE, sco ∞ povor c XasCoY
oup Dcroreper est rS p. vor H a TEvre ros srco C ∞ dis D4 esscor oou Dcoverepov est 28 da aocor
in cao Nevre. Tes O r8 exrs vepa Nais. ApXn r8 ib d opex nepa Najs.
ETCLNaoS  d e dMaons. Nai m
ce XW ntoS TE C oInNdo EHiTeETOV
( no1SOL Nogor o reT CRN NaoroS reos Y re
 Naoror, i o dI NaorS poS F iuioNtor
 25C C oupDcové eper es d di XaCV, E
 dia Nerre 200 8rco oouDcoverepor Zwea, 
c∞ dis dia raocorits dia nascor idia
NEVTE.
204
K F 4.
Dei taocor peror - dis ( g. raorot 12550
CME. o. d _F. decst dm nacoraodeis - - movi. d 3. e Suppleo mess. f PTO ini reDONO imt, B ME. deest
E PXC