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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 601, page id 867984570:0637
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PA PPDS AL F X A N D R IN VS. 605
TEV SEPEOS pevpsa So aS opcoVOIS ZW Z
0005 25tv 0  Ma a 8 E de d us.
6 83 6367574
∞7HM, NV. BAV. NV.
83 83 8, 8. 6
_ NV. NV. NV.
OB, Y. B, B, c.
E Ban.
Ouando autem Fres relicti sunt: aequalis
est Tolidus ex ipsis Factus, tor myriadibus nii-
meto s’ebenominibus, quot elt Millecuplus
A 70,20,30, 20, 20. B 200,300,200,200,500.
F0, TO, 1O, XO, 10.
2880000,0000,0000,0000.
700, 100, 100, 100, 100.
2000,0000,0000,0000.
612,3, 22. H 27 3, 2 2 5.
F 2880.
4d 5. = 10 = 25 (32. F + 3
PROPOSTTIO XIX.
In Theoremate 29. Sit numerus A minor
centenario sed denario divisibilis; atque
alii quotlibet numeri denario minores.
IBCDF.) Et oporteat solidum ex ipsis
ABCD F factum exhibere.
Sco iditur, per quem A denario dividitur.
La numerus F: hoc est numeri A FinduS. HF
lumatur Colidus ex ipsis FBCDF, qui SIE C.
Dico, quod qui ex ABCDH AE COlidus, elt
G decies. Fstque in numeris manisestum. P0.
Eco enim A verbi gratia 20, _ B3, C. 4, D5.
F 6. Oui ex ipsis tic Colidus, elt 7 200. Sed cunr
F SE 2, qui est Fundus numeri 20; qui ex eo
ipsiIque B C. D F. Fic Solidus, decies sumpTIS, est
7200; aequalis Tolido ex ABCDF. Lincaris
demonstrario apud Apollonium habetur.
quoudv , isai porades 65, iots rid e FcV ABTAE Sepeo. X0 de geapunot o  n n cvis
dedcirny.
numeri F.
D
6.
7200.
720
PRO.
OTau de Xeis arNe DDor o5 esn d e au
1y 1, 27 v, V
H an B, Y. B, B.
E m S H DEcopna 205. =2 F5C  a et duoS d A,
Ear d Exae rordo5, uc FS1dvo5 st 
SEnado5.  à No1 500IInNOTS aeuoIe
Reectodes SeneSos (BF AF.  iy Sbor eE
= Ex Z ABPA F GEPEOV et XEIV.
Zrcogd nab or perecirus o A Lod  dena
1d05 oZ, 7875 6 roDulo 8 A n cinnda
O CK Z ZBFAB 54E05, i E5 co H. YCo, o (0
ata t ABFAE GEpEOS, denanIS coir oi H. KC
Est Davepor  2)9 rcov d Bplt 8 id A LONEI
adis DEpeEN ovedES X, 96 B uorades Y
n 3 F povades d, n 8 a porades 1 C8 L. po-
vades 5 d e aur SEPEOS WVE) Mor
AMa n) _ Z ovros peovades B, 65 et obplle
 BH F8TB naI ZCV BL LL GEPEOS (dENaNIS
a RepOnO isa pro ist. B ReponO ihcisions pro inaesior. e Pacet ex vocibus a rat geauron de seuprunos et
gERHCOIKCS, PFOP. 16, T9, 20. 22, 23. 24. 26. ex 2)∞ X axbpucr, PrOD. 10. 19. 2V. 21. 23. Apollomum (adHXC PrO
Banida) demonstrationes adhibuisse Lineares nescio an numerarias eriam:) Pappn veto lI His Collecta.
neis) omillis, probationibus Linearibus, (pro quibus lectorem ad spollonium remitric,) concentum else eotu
eridenciam in numeris ostendere. d Malim practor quam praects. Sed cum sic seriprum reperio, cum hic
cum alibi, (qua(i 3rxvmaS,) nihil MUEO. Fit Cimiliter pasSII. OBi autM pv, _C vo, (PrO uverades E pades
contracte scribitur, (quod plerumque Fc,) arbierio uror meo, cerminationem adscribendo. Lt quidem, ubs
voces tae scribuntur inreera, non abnuerim quin L ector (si id ipsi videbitur) pro arbirrio luo terminationes
Sic imuter, ut aptius conrenire videatur. Credo enim Librarios qui haec antea deseriplerine, (nec crant
harum rerum satis periti,) Forcuito, ut concixerit, nunc recte, nunc perperam, terminationes appoluisse. C Pro
Eo repono (. fScribitur duo B. S PTO En reDONO.
aMale