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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 598, page id 867984570:0634
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59E
L4LLOD A LL A A ND R INV S
PROP. XVI.
Sunto iterum quoteunque nuheri B, quorum FEcoE Se nNV 600, Sy orS ae duoi, a cot
quilibet minor sit millenario, a centenario
autem mensuretur: e3 oporteat solidum ex
ipses factum exhibere, numeros ipsos non
multiplicando.
Orundem aucem numeri duptus, menture.
LTUT, DrimO, Q RuETO QUatErHaTIO, (DuTa
Der F; nimieum 2.) Lc ponatur sub quoli
Det numerorum B, centenarius unus. Numeri.
que per quos quilibet numerorum B a cente.
nario mensuratur Funto C. l’undi itaque erunt
numeri C, numerorum B. CF. C isitur qui ex
cencenariis tic solidus, una myrias dupla, seu
Mrriadum myrias. ) Dui autem ex Fundis tit
Tolidus, elto F; puca unitates 120. Ostensum
e  ADCot EcCoS egco b C. 787E51 110-
est isitur, lineari demonstratione; quod qui vades pX. ACiuW) Sr =3 2 geapucov, o Xg
tie ex numeris B Tolidus, est myriadum du-
plarum 120: Duoniam qui ex numeris B Ac
Tolidus, aequalis est solido ex centenariis in
Tolidum ex Fundis ducto: est autem una my-
rias dupla (seu myriadum myrias) In 220
umilates.
B 200, 300, 400, 500.
20,0000,0000.
100, 100, 100, 100. 1,0000, 0000.
27 31 4, 5. F. 120.
Sed non menturetur a quaternario, duplus
numerus numerorum B. Onaternarius isitr
illum metiens puta per V) relinquet necel
Pario binarium. Hhoc enim ance demonstratum
elt. Adeoque _ duplus numeri centenariorum, a
quacernario dirilus, (puta per H, relinquet 2.)
Numerus itague centenariorum per binarium
dirilus, relinquee e centenarium. Lrgo qul ex
centenariis tic solidus, erit, myriadum 100 ipti
F cognominum, hoc est duplarum. C Oui-
que ex tundis tic Tolidus, clt L, hoc elt 120.
Mlaniteltum itaque elt, quod, qui ex numeris
B Fic Colidus, lune myriades 100 ipsi F cogno-
mines, hoc Cs duplxe) ducta in KR, 120 uni
tates: Fiune aurem una myrias et bis mille,
myriadum duptarum.
B 100, 200,300, 100, 500.
22000,0000,0000.
(00, 100, 10O, 100, 100, 100,0000,0000.
13 27 33 43 5. F 120.
TCV EP coN ra B EEPEOS pveradcor dcoNCOV PX.
Enddi (C 0 3) 9 ZCoV ED ion r  B EEpE05, 1005
nobudicor ESpEoV, 78re5t dconn pveas petes d
ras ex poradah.
40 2 B. Cor EHAGOS En_aCOI id ZINIaSoS,
ueretaDo Se 2200 exa 2orra 05. y d 
 eE aur FCOI etCiB un 20 N A
AaDQVT∞ 20VS aC1 185.
AL o dicondores S CH DSs aurior peci
Ld coegrepor, iod rereados (uaro F 2.
oove B.) Kas Loneidc enasor X D B
EHATOVTaS n a _ xado pErPCi enagoS Z D B.
Lad Exarovrados, Escorav CF. ToDuveS oea eioir
oi e cor ra C F. F ED cov ra v B. (O roivuo 3) 
7 EaToVTADCON EEpEoS est dconn uvecaS puta: ) 
Est T dioi TCoV Chbtod EccD Y CM ZCOV
PN AIV. NIV.
a Nv. 2v.
ui
AM ci drconcioros S oiDBS X eD cov Tu B, pin
MEpedcood er egdo5 pcresidvos aea (na
 7 Z) neiVa duada e arayens 2870 qd
edEd c). AGE i o dconaoros  CNHDSS TCV
Exarorradcr per psdvos dreeados (nara 
2, neird duada) 20  Cg WnDOS Y EHaTOVT
Ocor pecrpsvor ouados nend puiar enaro-
rada. O rotruus dic. T EKaTOVTÄd COY GEPEOS ésc u-
eraedcor e B oucoropucor (7C0)  Z, 28 7251 dhconcov
(93 dia  CoD GEPEOS EGH E, Z8FE3L P H pIC-
rades. ) 5c dy Nov, on (0) dia Fer CP cov ra
b lveades aior e oucorouot 24 L, 78165101
conat,) Quouvat d Y dE, raS ex psradas It
ver.) L. 3) pvpreos pisa digincas drconcor propradcor.
+B AV. 21V.
P AIV. NIV.
DH
a Liceras majusculas hujusmodi substituo (cum hic, cum in sequenribus,) pro minulculIs, que  a
a liceris pumerariis: pro quibus promisene habentur in MS. minuscule. B Resticuo e aliquoties; pro quo
perperam scriberetur duo. c Pros (quod perperam Ceripeum existimo pro r) restituo P. d Pro L, reltituoF:
quia lic habetur in sequenribus. C. Pro perearas Substicuo presi , ec suppleo, 5 r Z, det + duaeda quia sC res
boctulat.
Prorrados, hic resticuo duados. C R estItO = - paV PrO -- . B Pro N (quod hic irreptisse suspicon
ex Z dejecto) resticuo Z, quia sic occurrit in sequentibus. Nec solebant vereres, neslectis Alphaberi literis
erioribus, ubi supreteren, polleriores actibere. Pro dioi relticuo e.
Pro