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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 324, page id 867984570:0352
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3241
LOR PIX R 11
Frie igitur 9 numerus pracedens; quique Esc ZV o idi rY SW O d. o uer avr, cir
Dost illum sequitur (ejus (elqui nonuS) 10; qui
que cetrachordum concludir (iptius o lesqui
TerEIUS) T2. TteruM; cum oporcCAL, huie pEOXI
mum, iplius r0 este selqui octavum; OpOrret
isicur illum, qui est pro 10 ponendus, trabere
Darcem decimam, ee parcem octaram; minimum-
que elte eorum qui has habene parres: Sumpea
enim iplorum r0 ec 8 maxima communi mentu
ra 2; dirilogue, per 2, COTLM AIECPHETO; Per nuI
merum prodeuncem mulciplico reliquum: Puta
20 per 2 divitus, tic 5; acque hric in 8 ductus
tic 40. FriC igITuE, pro 10, Donendus 40; de
Pro D, ponendus 36; (eo quod 40 sic numeri
20 quadruxlus:) iptiusque 40 selqui octarum,
oporiet esse 45; numerumque cecrachordi tina-
lem (nuMCEI 12 quadeuplum) 48. F’ritque h0c
Tetrachordum, 36, 40, 45, 48. RurtUS; cum
tercia ratiOMIS lelqui cerrix divilio, sic, in Tel.
quiterram ee selqui sepcimam diltributa; a1
lixnac selqui leprimam acuriori dialtemari (quod
elt praecedens;) e selquisexcam dividie limili-
per in duas rationes; criplicans numeros Funda.
n05 6 et 7; tiunique 18 _ 2Y; ipsilque inter-
medii LInE 19 8 20. AF 20 non pocelt, cum
utroque excremo, rationem tacere luper. parti-
cutarem. Sed 20, elt ip(ius 18 selqui-nonus
et 22, clt (iplius 20) selqui viselimus. Frir
igitur aliud cecrachordum, quod componitur ex
racione praecedente (ad acurum) selqui septima;
mediaque, selqui nona; gravillimaque, lesqui-
viselima. Invenieneur autem, qui hoc LeTra-
chordum faciant numeri primi, hoc modo. F. X.
Donimus icerum rationem lelqui cerriam, nume.
eis tundanis 3 e g. Cumque OpOrrCat nume
rum, qui elt polt 3 ponendus, selqui seprimum
eHC ipliuS 3: OpOrtet igituT, qui PrO 3 POnen
dus clt, habere parcem seprimam, et parten
cerciam. Suncque 7 ec3, numeri incer se pri
mI. Ideoque qui nuIerIS 3 _ 7 COnCInCTUF
numerus, minimus est eorum qui partes ha
vene cerriam ee seprimam. LrIC ISITUT, PTO 3.
Ponendus 21; _, polt cum proximus, 29. Cum.
que oporcea, iplius 24, haberi sesqui nonum.
oportet isitur numerum, qui ell prO 24 po.
Em d, o r na o cEiexcor ~ er exceder, 15
EGWV EnrSITOS 78 d, +B. HaNW Exet det F CEy5.
circt  enoYdoor d’et deg,  avrt 8 1 ra
odvor, Exer i nai n. EN CXISOV orra Y ÉXoVTCOV
Ta avra pepr AaCcor gd 8 1 i rod n X uE
qo roivoV 2 uereor Y duo uce l do E
porSV avrior ∞ D9. Y dvo, 2, ToV NOUOV No I _ CNC
orel co Bri ror zrrodvor oior o idi + 4 TV
duo ziveras c 2579 d Y Novon Y n, notet
2oV p ESC 3V, arri udi rod 1, o p avrt de
28 d,  0n5 219 ∞ 5oV p YS 1 Ter e∞ toN 
oror cirai rov de 28 p enoydoor n Y pE 
) ren drajor rod rer (∞ X opd8, (C  rov rer C∞ CN 
orev 78 1(, +oV pe n. ESC) EV X5, po, pE, pLH.
HaNN enei n reim DaipEors a Se
NorS lo, eis r DZIENToV nay rov eiedouor
D)a1EDeon roSCI ov di Emedouon es
FE dEvreoco o esv iYSivor, Xasuari FoV )
Srrexror 3)gtec eis duo N3ySS ouoicOS: TeLTNa
oraoas coV ob dva,  roV E 5 n 2ov G
C
ZWErCI LH, X _ Cor MEOOI o T 1d _ X. Ka10
ido 1d, Con Iga coedS auDorpSS 78S ane85
Regor emise or 0) X, 20d ido in Jvc) ext
d. o ) CX ay ai ENLCMOSOS EGCI ZV  Y
erceer rere xopdor, ep suyne) en re irysus
Noy8, 878 nSOS rW eE vrepco, d D doux C
NEOS,  ExHVVaTS not BaPVTATR, 28 ENL u.
EVpE)oeTaI  o l T CaXopd deuo nEcorot
3FC5 ExrdCNd nN or SeoV ex noDu
rE Y i 2C d. Ka enddu dei iov M or
Y racodvor deuor EDEBdouor cirai  2d y
dei aeg, rov avri r8 Y od vor, 6dquor
Excr C retror nai cioir o 3 C o Y, xpco
201 20e95 . M N85. 0 deg d rd y nat
20d Z. ENaxisIS ESt ZCV EXOVTCON ZCLToV nai
ebdouor Eccy SV, avr pdi rod Y, n a 0 de
HEE aVToV EGHS, Xd. Kat ExEt Det ExerVaTOV Et
vas 2od xd, dei âeg, rov avri rod X d rae
nendus, habere parcem nonam, sed ee pariem edvor, d’Exci, à Ma ny X d. Net a e crpeir
vigelimam quartam. Oporcet isitur numerum deor P 05, EnaXIGoS cor, iha d, nai ud
InVeNITC, (EHIgUE MINIU,) qui habeat par-
tem nonam, parcemque vigelimam quarca. Su-
mo maximam communem mensuram iplorum s
e 24, gul elt 3. St Ittur ucriutris iplorum
Tumplero partem certiam, ee in reliquum mulei
elicarero, numerum habebo qui ucralque ha
RapBarco x periSO novor persor rod d, nat
2od X d. est dE d y. FaV ov ooTepS auriO
NabCor ∞ TeTOV, Mi ron RoinoV Ma CNao
oco. eEco rov exerro aupco ra peen 20di X d
∞ recrovE n. ravra em 2oV S, roiet 70v 0β
Dec parces. Numeri aurem 24, pars cerria est TccCSV, avri r8 nd, rov oB o ) rhr8 eEy5,
8; qui in 9 ductus, lacic 72. Pro numero isiur 28, Pono 72. Acque huic proxyous (eju(que
2 PrO pip O ran repono pireor Y. a ME vrasi sed D. ErC. BMF. + F. D. o per rCpCIO 0 N5. CN 
P. decs. D. rectius r.  MF. aurir cimAcoror. D. Y Sm AaorOr rCDONO Y ra hadtot. C1 tot re euror C + ib
douco reDonO ror re s C Y C, hoc est, ror re il ny Y exru. f PrO aingsis CroS, TCDONO nan HOC CC nGoLd. E MF
ravra. D. rad, repono 5. B NF. reaxedor. D. - - don reBONO rereased B. I PYO dCTOV, RCPOHO CesroI. L HII.
rd retra C nd rntera. D. rectius nd Y C rd d. L PrO F retror repOnO F Y. n PrO an 8 reirv, rCpot
dicx, seet D. rectius, o 7 -- 3 7 -- 8C. B BtO on, Ed aXEM rEPONO de Eda zuroi
Pic
Ne
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