# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/867984570:0635 # Permalink to this reading: https://leibnizlegible.com/page/867984570:0635?run=74 # 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 599, page id 867984570:0635 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=635 # Source image: https://digitale-sammlungen.gwlb.de/content/867984570/jpgs/default/00000635.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 86 lines, status machine # Lines: 86 recognised, mean confidence 0.80 # Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. # Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text. # Wording rule: say "the machine reads it as …", never "Leibniz wrote". # After the first blank line: the recognised lines in reading order, one per line. P APPVS AVLLLLDK11O3. e Fgcoq dbd eum 23 6. 80 a eto. cio c oS, leOS dE D EHa 20124d65, 0101 MoraSes P. O sEB En éacY p Ena. rorrddos, ue SEdvo5 s r 1od SEnados, oio povades u iy 8bor e5co d aurcor EEpedv eITEEII, Un HOMIAH Naor OCVTa aVT8S. ZM ) Parepor, 319 ae ducor oi yd 5, edes cbbo b86ch. pllt0b0 et C o 1b0de oa EVTES notoV a (O Iy 1 noMaco aoracDErrS rSOr Zinta.) vini nis 3 o ce uos noei uveredas duo, noisos 5 iao L B qwoudvor. LKOPOSIIIO XVII 59C Sunto aud t L D. Et ponatur A mi- nor quimto incuenario. sed centenario di- visibile, ut ntates 500. B vero cente- nario minor, sed divisibilis denario, ut unitates 40. Et oporteat numerum ex illis factum exhibere, ipsos non multipli cando. anitectum autem illud est numerali de L monstracione. Nam, cum ipsorum funde FInE 5 ∞ 4 unitates 5, ee unitates 4, invicem ductae, factune unitates 20: Fitem 100 _ IC Sumprus numerus 20, Facie myriadas duas: qua multiplicati TaCLMI, MMIIIC. J Missies autem numerum praectant ex A B Factum. LII. Fri se (m) decopaTOS. F5Co nN ndo5 r a- etBuucor) 2d e cor ra A, Cov ENaEDS E e’ aON ExarorTadoS, uer Suvos se rd Sene- db5. 2 a 0 dos aerdqcor e0 con r B, Co) EnaGOS Ex ea ZXIEdoS, MErE S pvOS Se rD CHaTOVTadoS. iy Séor e ex Y ED Cor Ta A B EEpCoV a NEI Un 2 3BNa HN aOrLOarTa aVT8S. 10. 2, 0000. 2000. 20 PROPOSTEIO ZVIII quaedam nuncet iano L quorui qui libet sit centenario minor, sed quem me- tiatur denarius: atque alia multitude numerorum B, quorum quilibet sit mil- lenario minor, sed per centenarium di- visibilis: C oporteat solidum ex ipsis A B factum extribere, ipsos non multipli Oloboctbo Ba. A 500. B 40. 100. e I C78) Theoremate. Esto multitudo 78 n)oVS TCOV ED CoV TaB, pETSCDCO, pOTE uco Bicur Fundi numecorum L nummele ∞, unitales 1, 2, 3, 4: e numerorum B, numeri FI, unitates 2, 3, 4, 5: Tumatur Tolidus ex Fundis F, 2, 3, 4; 29 3, 4, 5: qui AE F, unitates 2880. Mulcicudinem numero- Tum A, una cum duplo mulcicudinis nume- rorum B, meciatur, primo, quaternarius per E. Octendit Apollonius, solidum ex omnibus per, uno rereados. nara F Z, peree de aurSS. iy dervon d AH CiVOS, Y CK MVECV EV co 2rcoour jae robuts et et 10 1 C_ cov ra H, parcobes l y B h Yd ror de E con Fa B, oi Ep cor Ta O, porades F Yna) d n E i anDBerros S en rcv noD vcor EEpes rcor (a) B Y d, B y d 5, YSF. cst 28E, porades ovros Cdkso FcoV ED coV TO A, CNabo d dcoaoia a Pro aenucs sublicuo soscor d tircis PrO vrar. B Rellituo . d pro 1E. ∞ PrO a reltituo d. a RCitu vavrae, Pro-oavraj. b Restituo practs, PrO porados, quod perperam irrepisse ridetur propter lequens orros. cRectituo t cem quud sitraios saeve contundi solent, nihil muto. e Liquet hinc (& ex sequentibus) Apollonium quen- dam (Persaeum creco) cractatum CcripsSC (qui periic) de numeris quancumvis magnis incer se mulcipli- candis; unde haec desumpta sune collectanea. Ouis fuerit ille liber, aue quomodo appellatus, non constar. (eo quod secundi hujus collectaneorum libri inicium desic;) nisi forre (quod non est vero ablimile) ille fueric, quem Futocius (sub sinem commencariorum in Archimedis Dimensionem circuli) cnvris VOCAE ab Apollonio Pereao conscripeum, (sed qui periit;) cujus argumentum huic absumile non suisse, inde Constat. FPrO