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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 554, page id 867984570:0582
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=582
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 99 lines, status machine
# Lines: 99 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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554
F C
tus Polyeoni; circule circumscripii habentis a
tera 96.
Ca
nunner cErreaDo NVycor conpas ExerS
Cum ieitur ry ad ya, demonstrata sit, ma. 255 Eet S  Y reos d ya, dede) p
jorem habere rationem, quam 4673 = ad 253:
Sicque ipsius cy dupla ay, ipsiusque n y dupla
AN: Tlabet itaque ay ad nH majorem ratio-
nem, quam 4673 = ad 253. Contra erso, n p
ad a minorem rationem habet, quam F53 ad
46733. Cumque HE ap Polysoni latuS Ia
tera habentis 06; Ambitus igitur Polrgoni elt
24688, (nam 06 in 253 mulciplicatus, hunc
numerum Facit.) Ambitus icieur Potysoni, ad
ay diametrum, minorem rationem habet, quam
14088 ad 4673 2. Ambitus isicur Polysoni, 265 à ea 3 Nvycer e05 rld a  , E
Diamerri Circularis Triplum superat, unitati
bu5667=, quae minus sunt quam diametri pars
septima, nempe, unius unitaris parte septima.
Nam, Sexruplum 6672, hoc elt 4672 E, uni-
rare minus Cst quam Diameter. Cum isitur.
Polrenum hoc sit (ambitu) minus quam Pri-
plum cum parte septima; licque ambitus Cir-
culi, minor quam Polygoni: Multo macis iei
tur. Circuli Perimetrus, minor est quam Dia
metri tripla cum parte septima.
Deinde, reliquam Theorematis partem Con-
Aruens, Sit, inquie, Circulus, cujus Diameter
ay; ansulusque Bay, tertia pars recti. 7. Id
aurem tier, si, d puncto r, Tumto areu yB X-
quali arcui Flexasoni, junsamus a B. Oui enim = a, car, dero r3 Y, 2 Tn re haycovs e
arcui Flexagoni insiltit angulus; si ad Cen
crum, est, recti duxe cerrixe; si ad Peripheriam,
terria parS.
Cum ilaque rectus sic aBy angulus, recti 285 Eret SV op) esir i o a βY,  re1rot ) 1 Cud
que pars certia Bay; elt itaque ayB, due ter-
Eix. Si itaque, a puncto B, continuata recta
2B. sumeaque cidem aequali, rectam ab a jun-
samus: criangulum tier aquilaterum. PF, prO.
pter balin a cacheto aB bilectam, dupla erit
ay ipsius VB. Posita ieitur 27, 2560; erit
38, 780. Frirque iplius ay quacratum, 2433600;
_ quadrarum 2B, 608400: Ablatoque quadra-
10 yB, ab ay quadrato, reliduum relinquetur
quacratum aB, +825200: Cujus lacus quadra.
cieum, elt, +35F proxime. Hujus enim qu2. 29571 55 con cind ea rere aycorrrn a rV a eat
dracum, elt julto majus, unitate F. Freo ha-
bet, inquie a B ad By, minorem rationem, quam
2352 ad 780. Mutciplicationes aucem subjis
CiunEuT.
25
Pora noror exxou ince dX0Y L =e05 pV 7 n
15t D ado EY dconn n a Y, D; ny n au 
in a y apa Xed5 X p pEt C oV Negov EXC, 1
8X0Y LL r e05 PrY. AVaNW epa i X p
3805 8 7, E arova Regor exa, ne pv  6
dX  ai exet i Ap, nonvycere est No
ea 8 nd eaS ExrroS 25 n c Ejuersos aea 1
tcors, 51  d X X n (0 ed 35 emi Y pr
MONV NaOAC oudOS TSTOV NoLET.) H WEqur)
rova Rog Exa, nce n dX n n Xeds dX0YL
H nEeErEOS aea 3 nNvycorS, ~ Mlauer_ 73
HVKAB ESt TEIX Navia, n en inEpEXW. ZEEV
rairae de enartora est 8 ibdous d HauereS
pses peoraedos abdouco peper (ras gae e Ecta neorae
X EG L, ane C5t d X oB L, Eha Dova e51 Y
AIGEEBS, N. _.) ENEI XV ~ HNOYcovOV ÉNaTOV
C5IV,  re Néorer  en ibdouco vnrvexor n de
NECLILETSOS S NVHNS ENCOSCOV E51 D F8 HoNVyCoVS
3I3LOMCO apa i ZS NVKNS WE, DEpCta, ~ 2)QuETSB
Est ree Naoia C Er inepexd Enaoror n eboouu puepd
EE75 dE NaONS CON ~ NOIOV peeES 78
DecoenarS, PnoI ESCI NWKNOS ne XIQUETCCV
ri ay n 2 reeror opdns, n d Ba Y.) F8T
Deeeta ionr dronaberres rs y B,  cuscopdr Tlud
aB. H 3ae em ~ 78 eharcors E, Depeias Beoraja
Ycoviae eos edio rcd verreco,  dipoieor 
dys roos dE rn e DEpeta, TCtroV.
Ba Y 8 diuorpor à eq erir i o a y B. Lur
esenMovreS rs yB dri X B, C iono  abt
ditonaorres, do S a S cuEcopd iooono e
Eces F rErYcovor. Kai, 218 X rus e. B nöderor M.
xorouto tlu Baow,  dconu esiv n a. Y D yB. EaV
Si anm NaScopdo ri a Y, _ DG ÉGa A Y.
Y X. Ka) x  diro ay ea  Y X ~) diro
YB, i A V. Raj ear à Dencoudo x diro 7B,  dro
S dero a y NoiV naranCD de x dio a B,
(aer Debet zue x on avris X ane 6SS, M. a.)
A1o Pnoir, exaoora Noyor ext, i aB vees BY.
ise, a FVa WoCs V N. Oi ) noMa conaorao t
LLvOHCNTCI.
X B. dxain. y B. us rd A dcaipra quod deleo; est enim pars posterior cheorematis cerrii. Z B. +
in Dro rin  sC CxPC. B Suppleo adepeia. cB. râ nerreu, absque, Subseripeo. et B. dipoipo
in rirv. fB. reirv. 8 B. diuoiev. B R airn.
3. Bet. X.
in aderqu
B. derd 3 a Y.