# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/867984570:0300
# Permalink to this reading: https://leibnizlegible.com/page/867984570:0300?run=74
# 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 272, page id 867984570:0300
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=300
# Source image: https://digitale-sammlungen.gwlb.de/content/867984570/jpgs/default/00000300.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 116 lines, status machine
# Lines: 116 recognised, mean confidence 0.79
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

72
P OR PH Y R I
Tem, raLIOnES POTIOreS lunE; c ua 
acque tum pociores poctorsous compatate, c
applicacio, quam qua est uper- parciencium, le-
cundum cerminos applications. Lralu M.
plicium e Tuperparricularium applIcatiO, Par
iem habet in se simplicem (seu aliquotam:
ver Particularium vero, excellum majoris ter-
mini, unam partent aliquotam Conte.
In luper parciencium vero collatione, nulla pars
simplex; sed plurium parcium appendiculi com
plexio. Reltat autem, ut ostendamus, quam
obrem Consonantiae Dia pason accommodare o-
POrceaL, (ex muscpCtOIS) rationem aupTaI;
Epligue Dia-TelTarOM, (ex Luper- parerCutaLLBIIS,)
selqui cerciam; Iplique Dia pente, sesqur alte.
ram; quod a Pcolemao diferre dietuim elt. 105
autem, quae a principio de MIICu Capicis haben-
tur, illultrabimus: adMIBIEIS LRCOTeMALIS Ll
nearibus ad demonstrationes eorum perrinenti.
buS; quae habentur in Kveliais Sectione Cano-
Dis: Fo quod Prolemaus curforie dixerie Py.
chagoriorum tradita. Ouorum proposiiones.
hae Tunt. Dialtema Dia- pente, eli, in ratione
Taper parciculari; e Dia cellaron. Trem, Dia
Dason dialtema, elt in ratione mulcipla. Dia
Hema DIa- Pence, est selqui alterum: et Dia-
cellaron, selqui tercium. Draltema duplum, com
Donitur ex duobus maximis Cuper- parricularibe
Nulla ratio mulcipla, componitur ex duabus ra
tionibus superparcicularibus; nili Cola dupla.
Fonus elt in ratione lesqui octava., POnus
non dividitur in duo aequalia; adeoque Poni-
dimidium non est. Dialtemaris Cuper Parricula
ris nullus incidie medius proporcionalis nume.
FUIS. Dis-Pason e dia- pente, elt diastema cri
plum. Dil dia palon, quadruplum. Llarum ve.
ro demonstrationes, lic le habent.
I. Si cialtema Merpum bes compotuum
diastema tacic; erie ec iplum mulciplum. Flto
dialtema BC; lirque B terminus
iptius C mulciplus. Fiacque VE C
aet B, sic B ad D. Dico, e D iplius
C mulciplum elle. Nam cum B sIC
iptius Ci mulciplus, metitur igieur C
iplum B. EraE auteM ut C ad B, Sic B ad D:
adeoque e C mecicur D. Mulciplus isicur est
D iptius C.
16 pidr  pol 8 pletC or
OP3S, ptCD HEHIMLiCOV ENS DE T CMIIIEpCOV, O7t GOI
V 35 ∞ N OTHS à A O pOeIOV ZON CtOVcON DE1OZHS
oE16ON. Aoinov dE, 29. H 2n edi 2ta ascov
EDaPUSSEOV, Y ~oM a WNCooV, Y dhconésoror nég
7n dEd ocsplot, b Etbor, AGHod En
de dia perre, Y isoNtO cien O DCS 2 Da TCI
HroNCpaj Ta dE EGaPXHS aXeL S XNBS S HE-
Danaje, ou pluroou ueis Cn dEvOEgaI
Ha Decop po. (a, Wo C95 2a5 drodeizes aurcr ouvrit-
vorra neudvo de ev ru 3 vavr FuxNcids na-
raroin La ∞ nar emopoplee cipynevas Y HTONE-
Nator Ta Z TVDaropeicor Wr ai coeaos eioir aide.
F0 2da nerre casqua ev empoeco Noyc es 
∞ dio TeOSapcor ∞ dia nes cor diasna = Ey noN-
Naronaoro NyCoesi 20 da nevee dies nua iuuis-
Ner esi 3G X dha recapcor, dre roV 20 dcona
oror casna oyve ex duo pegcor em-
escor Oudets no a, vyn) e ep
eicor deo Noycor et pin povos o dconaos. O rvos
ev erordoco Nosco esW O ravos 8 D)estpeircy et5 duo
Ioc cosE iperroVoN CoN EG. LmuoeS casiaToS
3d etS peoos avners cumnet decis. F0 dia
d
naes cor n da HEVTE, 21 aorov es τ0 de dis da
aSCV, Ter Cg cod doror Ai de drodéthas aurciv
CxBoW codc.
Far dhasqua noma conaoror dis ouvre der  no
 da = nua, na) avro noMa CoNCOrOV ECcI. E5Cd 2t
diasqua x B V naj EGco MaToNa
0ros o B8 Y. Kat 2oodc, 105 8
Y oee5 Y B, o B e95 Y d. eypet
dn C 7 d cdco5 Y Y noMC cNaoO
Eivaei Exet gd o B 8 y noM acona
oies Est, MErBet ae 0Y Y β iu de ios Y NEoS
+ B, dBn805 Y d. conC pei C o Y no Y d
oMa N Nas 1 (O aeq Est n9 o d 8 y
Tuperparciculares, alixe Cuperparcientes; Con. Duoerot, oi 3)  Bapepcis Anons) lu 
dErica 3 sE 17ot pes 3 1007c t
cruum est dispicere, Ouaenam, post aequalica
dCteTIOTES ACTCTIOTIBUS. InaequaliU VerO raLIO
num, mulcipices ee luper Particulares, Punc su-
WEs ot Xele85 Eid XCOS a DG  bOV d
Tcer SV art ot scob, et  ot conato  b
per partiencibus poriores: EE TnxquitOnOrum S Ot, XpeSS Z dECOV FCV aVSoDOICOI
Sonorum, concitm a consoni, pociores lunt in-
consonis. RCCOMOdanda igituE TUnE raLIONES
Superparciculares  mulriplices, Contonis; et,
Superparciences, Inconsonis. Sunt autem porio.
res mulciplices ee superparriculares, quam su-
upet DBs rois npetEoor CV 7 X e1p85 7015 X etBo-
noet bIOh ei EppEMeIS nai et oupDCoVOI, F a0d Cd
VcoV EPaGpOSEOV eq CV SpoeiSS nay nm
CoMaoS 13Y85, 5015 OVD CavOIS 66V  CEeS
5015 a Vp DCovOS. Eior dE npet T) 85 oi noM a coNaore
naj Empse OLT empeu Exet Sr à consse, n’ev
a030: 5, id 3g60N, D T Emprecor, nar coV 985
 960AS. H yd Y NM a CoNaoicor Y N, Emqoe icoV
o)LCCONADTCOV, ENANSOV OpCOV EZOVECN, 28 pet o-
10 9bon Eet dcnor et aden sur ur
Far
Der. Parciences: co quod, in eis, simplicior ett
rium minorem, aliquotam partem majoris: (u
Nempe; uscpe cerminorum continen-
E FFO enporacis, repONO empEpCtS. W MF. In, Sed D. iv. _ MLC. cut A husonA. YD. dCC  empea ae
60d1. 1
sovet (Cd D. noin n.