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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 578, page id 867984570:0606
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 1L +D+ A A CAOD, DA MTDS.
Pappus in Fodem Loco.
Describemus autem unum lemma ex iis,
quae traduntur in quareum theorema ejusdem
libriu inquisicione dixnum.
ETF circulus ABC (Fig. 20.) cujus diame.
1 ter producta ACD; centrum F.: ee a pun
Ato L ipsi ACD ad rectos angulos ducacur
BKF: ab ipso aurem D ducatur DFI, circulum
ABC contingens: ee dimidix ipsiuS FH aequa
lis ponatur ac utrasque parres Cn videlicet RC
CL: JanGAnEUrqUe 3KD DL FD. DICO an
Sulum KDL angulo F DFI majorem eAc. Prae
mitruntur autem Bac.
Sic circulus ABC CFIC, FT.) cujus diame
cer producta ACD: et a puncto D ducatr
quaepiam recta linea DEF. Dico circumteren
tiam AF circumterencia CF majorem esse.
Sumatur enim cireuli centrum G: 13 CF
CF junsantur. Erit angulus ad P ansulo ad
 aequalis (5. CL.) Sit quoniam trianeulum
est GFD, e anculus exterior ACF major est
interiori, e opposiro, eo qui ad P: Boc est eo
qui ad P; anculus autem ad  major est an-
culo DCF, propierea quod est extra trianeu
Tum: erit anculus ACF anculo FCF major
Et sunt ad centrum. Circumferentia ieitur AF
major est circumferentia CL. Quod demon-
Arare oporrebat.
Sic (F15. 12.) circulus AB, cujus cencrum
D: _ extra circulum punctum C: duCanEur
que a CLDK, e circulum continsens CF. DC
inde per D cenerum ad rectos ansulos ipsi RL
dIaetrO aGREUE DA; SCCCtUIrque AF circum-
terencia Bitariam in puncto F. FF CBA COF
jungantur. Dieo angulum ACF. angulO FCF
majorem esfe.
Funeantur enim (Fi5, 23.) FB FC. Et
quoniam P. B major est quam FC, e BC mi-
nor quam C. G; habebit F B ad BC. majorem
proportionem, quam ( ad GC, (3. C5.) Lta-
que srat ut L.D ad BC, ita TI ad GC, e
TTC junsatur. Duoniam icitur anculi ABs
FCF inter se aequales sunt, quod  circum-
ferentia AP. circumferentiae FF (21. C 3;
 reliqui aneuli KBC FGC. aequales (73. CF:
e circa aequales angulos latera sunt proportio
nalia: erit trianeutum FBC trianeulo CC
aequianculum (6. c6.) Freo aneuli AC.t
FCLT inter se aequales sunt. Aneulus icitur
ACF, aneulo FC F est major.
Sit denique eadem figura, qua prius (FG. 10.)
HAAM FK P S FaXNE ZUVAXCOVIOI.
Er Si n anuua rearloudo ex 2IS oceo
percor ets 20 s deona 5 B6a 18, 8 (n
noccos a E1on.
Erco mnReS a a β Y, dioereos ) avrs en
Candeioa n a Y d. nevrsor) x E. i inxdc
dero 8 E En a Y d Xpos opdas y βC~ eso de
8 d rS a B Y NoNNS EPanoudion n dd nat
neidco rns Cd iputoda ED cudrcea 8 y, n XY
YN n ExE CCx cou ait Xd, d N, Ed. Neyco
d2t pet  cor E5WV n uno Xd X xnS ino  rcov Ed. 3.
ceorea DE) de rade.
ESCo NnNOS S a β3 Y. C diapereos enBNy deiva
n a yd i dro 3 d nxco rs codeia n dE
aerco on n  ce eperos perlcor e5t F 15 YC
et DEpetas.
Finy ODca id X vevrpoV S KVZNS x n’onueiov 
Ere Cir Davur ai n8, n5. Kat Ycovtes apa n X po5
∞ B Ycorta En XpOS Y E con E51 H Et Zei-
Vcovor E5t ∞ n d, CC enros ycoria n vnd p
et (COV ESI FHS CVTS I OEEVaVTOV FyS XpOS TC
T8TESI 2H5  po5 ∞ E. eM a n XpOS TW E peil cot
est 2y5 uno dnE, dia X Cn ro5 Eva 3 Ze γcov
3n d a n ae pet  cor 251 FHS OEnd.
ie etor eoS TC HerrPCO. Me cov eseq r E D
ecra n a  rus Y e, dnre (ed et dcizai.
E5C0) nonNOS o a β, S vevrpor ~ d, ie CnroS 8
nonNS onpucior ~ Y.  dinxbc n Y X d v C EP
anocdon S nixNS i Y C; X, dia _ d vEVEPS  poC
opdas rn u N Z) apuerpco i d’a C rer poncd co n o C
Et DEpera dya τC E. Kat ExElCuxDcU a
Y Ba, 715. Aeyco or pet C cov E5 ib n 0  76
Ycorics 245 20CY
ErcE evXBcooar a EB, G1. Eret peil cor esiv
n CB 7n5 CH, EraNcr) a βY 215 yn n es
poS BY pei Cevae negov exd iree in Cn XpoS Y n
Fegoverco 3V cos n Eβ 7005 BY, i nB +005 n y
CC Em  evxbco n b y. E Et 3V at 200 BE EnC
Ycorias oc a Nais eioir, ETEt no)  E DEpCtn
a E Et DEpeta FH CC, iG ai Norey oces etoW N
XNais ai d EBY CnY, Na Ee iou5 Yco-
vias ai pa arenogoi eion coycorio eax
EBY reiYcovoV TC = MY resXcorcs as espae
ctoir ai 0 a YE=EY d ycoVa]. NeE cor een
Vro a VE ri5 Vdc78
Esco Norror i aurn narageapn ru Aphrepo
ee eadem maneant. Dico angulum IDL. an. vat ra avra dedouva. Nerco or pet  coV Es iv n
sulo FDH majorem cAe.
rd dX ycoria ris vno 6dd.
Terpenadco
a Dele, Si DIaCCE, ~. GUaIVIS CHIH HC LOGUI IOICL LAatCHUIS, BON CateH LaPDUS. Reltiuo aurem ade
DEpeice
KF in CO
al erD DFO nOr. eE uo PrO ad. CC psud pro iopd
vis ille idem sic aroulus) ut eraereniae, estque aptior nocacio. Acque interpono (ex C0d. 5.) houram
b NuI
2, perspicuitatio Graria
randini vextione, HD prO AB, _E CLDK prO CBB