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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 308, page id 867984570:0336
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=336
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 103 lines, status machine
# Lines: 103 recognised, mean confidence 0.80
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300
POR P HI R II
Sempex autem substituatur, in illis, pro den peiova aci a DgNapbaVE)3. Cd aundr, avri
licare, tentio, (uc quae roborat, e indurat,
eoque limilior tic tenlio ei quae elt in minori.
bus distanciis:) maniteltum est, quod (exeteris
supposiris pariter se habentibus, unicaque exi
Rence ditterentia; puca, nunc propter chorda-
rum centionem, quae pro denlitare substieuatur;
nunc, proxree cireuitum; nunc, propter diltan-
tiam:) VE est censio major ad minorem; lic
qui elt d majori centione Conitus, ad eum qui
Cs a minor: VE autem major circuitus ad mi
norem cirenitum; sic qui a minori circuieu H
Tonitus, ad eum qui d majori: VE aurem ell
major distantia (seu loncitudo) ad minorem; lic
qui a minori diltancia tie Ponicus, ad eum qui 2
majori. Ilis aurem ita Tupposcis; Dico, quod, dil-
similium chordarum, quando factae lunc, in
lonsicudinibus aequalibus, aquitona; id quod
proxcer majorem cirenicum lonicui deest, ab c0
compentatur, quod proxier majorem centionent
redundat. Aeque omnino tit, cadem majoris
circultus ad minorent lacio, quae cA majoris
centionis au moremt. Id act Del neas
Aertiontra, hoc modo; sunco, in longicudint
ori) c 9. rw euxli ore de a g rl 214
 ourcobeh, nadis rovet nd CC oxnqpurei  dha
23r0 p MoY E ev Z en à J0or D)aScocor Xopd 15
qoia ruors dyNor, o2t cor LLONCICY
aurcor, 719.D0C45) sons poiees ore pdi, 0 de r
raow rat t  a nonrcobto nDon
Guorr SIS p n CoNSICOV ZVE) TaOS  (95T EMa
rora, 87C05 o nara rlo nciora raor o o
ech xara rle ena ttova Ses den poe con  et
Xn roees rlio eartova ac, STCoSo naro Y
enartora Wecoxlu ooDo5, reos i nara rlio uei
Ecrai s den uri (cor D) aorS reoS Tlv enar
rova, 8rc05 o xara rluo enarora Xaisaom 1005.
2005 Y nora rluo pecic ovo. T8r cor dE 3F C05 1.
neudicor Nerco, en F arouoicor xopdcor, erar et
IocIS (InXEOI ioOrOVOL noIn. Jcior arrava coyeS 
da rlio p ora oEroxlo erd eor 28 bo8,
cda adit orri  rive ct
T15, 0 p roB dEIDXHS X POS TlO EK AOSOVA NO-
qur linc quoad lonicum invariati,) A et B;
TIEGue ipLIMS A CIrCUIEIS, quam CITCUICUS B ma-
soc: manitestum est, quod a censio major est.
Sumacurque lonus alius, in aequali lonsirudine,
C; qui cireuitum habeat eundem cum B; Ten-
lionem vero eandem cum A. Guandoquidem
203, buoroS TC Y CONCiOVOS TaECOS Xpos Y énaDo
va TBr id auros anedchE da reapucor 3Zco5
EScooUV er iocIS pnxcor iveroroi d1o D007 b1, TBT È5WV
sut  cox1O 1 D78B WEIOXHS C dyNor
a  MaxroI NaTa Y Lo PoV, ei à n β. nai p
bus aequalibus, aequiconi duo Toni, (hoc elt,
igitur C a B Cola centione diftert; exit (secun-
I B,  Los C al o.  Taors neos riv TZ B 8rc05 dr8 7 1op05 eoS
on i, i raors Kai ec aMoz oylS, er iou
reo pennd. 0y. rlu idi WErOXIV, ionV EXCoV TCo B
riv dE radi, ionv rco a L torY 16P pon
rn raod ca Dep Escp dia Ta r LOCNa, 105 n 78
AciEcor ruor5.
major renlI0.
dum jam polita) uc in C centio ad censionem
NciEcor adecoxi.
major circuitus.
Ee
netcor aerori.
minor cireuitus.
cum C ab A Colo cireuitu ditterat; erie, ut Y rs B LoPor. HaN, CMt 0Y 10 a In e
circuitus A ad circuicum C, lic C. Tonicus ad
Tonitum A. Sed ut C Ponitus ad lonitum A
sic idem C. Tonitus ad Tonicum B, (aequales
enim ucique TunE A et B ConituS.) OE igi
cur tensio C ad centionem B, SC A CireUItS
ad circuicum C. FAque ut C tensio ad cen-
tionem B, sic A tentio ad centionem B, (aqua-
les enim sunE A _ C centiones:) OIque cir.
cuicus A ad cirenitum C, sic cireuicus A a0
circuitum B, (aequales enim sunE B _ C CIr-
cuicus.) ErgO, ut censio A ad centionem B
sic A circuitus ad cireuitum B. HIOC autem
io zae ai rcor β nai Y necoxai Ka1 cos aeq
n rB a raors xpos riv rS B raon VrcS i rB à meex rpds ri 2S B meoxir Yiro s’ar
aurois
ios centio
X PaDEpet, EGC, co5 n T8 _ WeIOXn X poS
ri 18Y cEcX YrC050 r8Y 40D05 e05 Y
25 a Vopor AN 1os 028 Y +oO reos  2t
a 82105078y 210   p03 + 18 β. 100t ga
oi 20Dot 7 a 2 n B SS a eg n 18Y abi
eo5 rio r8 B 3TC05n 18 d WdeiOXN H (05 1
Y Rj E5iV, co5 (d n 28 Y TdoIS XpoS riV 18
B, 8rCo X n 2Z a TaoIS (03 tyr 28 B. ocs zae
ai rcra X, Y raos 2S den r8 a ne x X pos
rv 28Y 32105 n 18d   05 ri 28 B
lis i 3. n PTO C X, repono C, delcto 
IME. decst clausula is J n pelitar = nB rud puritora. sed ex in Pcolemao decst. m P1O un, sepOnOi, nis MA.
ecor
e
85