# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/867984570:0601 # Permalink to this reading: https://leibnizlegible.com/page/867984570:0601?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 573, page id 867984570:0601 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=601 # Source image: https://digitale-sammlungen.gwlb.de/content/867984570/jpgs/default/00000601.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 101 lines, status machine # Lines: 101 recognised, mean confidence 0.82 # 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. ARIST A R GTIDS S AMIVS. pcranmo su YECS ophas in a Kar Parepor, en n S Parera aurs Dany oparpcor enddn n YC nara avu peraexiror EDaE 2 AB K ApaCB Lhcooar de ai oDaipa) MEXW, Cov VEVTEA E5 ra ∞ (3, c 100t pci L COV nS XEVTCOV ∞ MEYa ort 345 6Daipas o auros NoV O WEINOCaveL ui nopPl ExcoV NEOS Tn EN aOOVt OData. ENE Ecoxdcon aB, n ex Beb Nodco Da F aB S edor roihod du EToaS ex E ∞DaIpaIS XVX 3SS TONIEC CV Y dEC B pelcor ào y dEr nD XVKAS CoGE ngi n en r8 verres r8 yd NvNS pect C CoV Est D CK +S verre s FBC nD nond Auvaeror du est Ra st opuctor, Cd5 ∞ X, iv cds n CA 18 aCD FEX FB Y dE NONNS EOS M TB NEVTES TBC nB LBKNB, 8TCO5n d X A63 h B d. EGC BV EtAM aNOV ∞ N ompecior, CC 1Xda n C Pamoudon 78C nB nXNS CC end cox SF X D)4 rB a rn BE W DgmnNOS nxdco a y na) ExEEuXDc n Y C. C eret Es cos n an reos i XB, n a d pos ro BV ion den id adEn a Y, n de BV rn B3. aea ios n a pos oed n B, n a Y X pos ro BS est c d AyNO5 i a Y FHB Codea aeq Esir i YC o ésr de d n D Y CB opdn aeq n io T) n Y a PanC) aeqnXY FS ydE nonNS efticiet, (ex 2F def. C FF.) cujus bales CtAM circuli circa dioerros CF FH, recti existen tes ad iplam AB; propterea quod in OMHE ConrertiOne CF FHI ad iptam AB rectae per manenE. F.C perspicuum est superficiem ipsius concingere sphaeras, quoniam CP in omni con- rextione Lemicirculos RCD OFL. contingit. Sint rursuS (Fig. 2.) Sphaerae inaequales, qna rum centra A B: ec sic major, cujus cencrum A. Dico dictas sphaeras eundem conum com prehendere, qui rerricem habeat ad minorem Ephaeram. Pungatur AB, b et per iptam pro ducatur planum, quod faciet sectiones in Sphae- ris circulos. (L Sphaeric. Theodos.) Faciat cir- culos CDF. FOFI. Circulus isItuT CDE. ma- ior est circulo FOFI: ergo _ quX Cx CenITO circuli CDE major erit ca qua ex centro cir- culi FCFI. Pieri isicur pocelt, ut lumatur aliquod punctum, velue R, ita ut quam pro- portionem habet quxe ex centro circuli CDF. ad eam quae ex centro circuli FOFI, eandem habeat AR ad RB d. SMIATUE, e SIE R. ducaturque RF cansens circulum FOH: FB junsatur. Deinde per A ipli BF parallela ducacur AC; et jungatur CF. Ouoniam issi. cux elt, UE AK ad RB, ita AD ad BNI; ac. uc elt AD quidem aequalis ipli AC; BN verO ipE BF: CTIE UE AK ad RB, ita AC ad BF: eltque AC paraHela ipsi BF. Recta igitur li- nea est CFI E. Sed angulus RFB rectus est (28C 3.) ArgO _ rectuS KCA; (2OCF.) ac propterea RC circulum CDE contingit 6. (L7 C3.). DUCANEIT CL FM ad ipsam AB per Dendiculares. Si igitur manente RX, semicir. cudi XCD GFN, d criangula RCL RFM Convertantur, quousque rurtus restituantur in cundem locum d quo moveri caeperunt; semi- circuli quidem XCD OFN in sphaeris Feren. EUIE; TrIENGUIIa VeTO RCL REM conos etti- cient, (18 def. CTT.) quorum bales lune cir culi circa diametros CF FFI, recti existentes ad HL axem, _ corum centra L M. ConuS vero sphaerarum continget superticies, quoniam e RFC in omni convertione Lemicirculos ZCD OFN concingit. s Baos Éoorry oi Wei SS taSYE XVHNOI op)o orres nCOS ) aB, _a x ev nus HXcavaer di as Y N L p Bi + a B na D Cr1 S. ea dn advsonS F ibC, ra EEY d n CV HABINUXNtd (C ra H Y A X C H FeircoVa, WEurex derrae e5 2 avro nnW dstouaSi ode npEarO DEpEdai edo EYd, HG pVNNa CVEZ DoE) Xait oDaiptor X dE X Y N reircovor i X X C u aoro rcoros, t Bd015 cioW et W et Z)∞ MErCX5 345YB D NVXNOI, op)ot OVTES XPOS Z H M a EOVa Vevreq daorCoV a N CO NcovOS F0 Paspv EDaLE naras rud Bparcar, entdn dDanE) dN CV ijurux dicor vara o e axirnor 3C.tO. b Suppleo si placet, C enmrodiadas ue prius. Arabs habet, EE prorrabatur utrinqtio. o C (vE priuS) DrO roui. d Com. Illud autem punctum hoc modo inveniemus. Ducal Sorsan (F18. 3.) ea qu centro majoris CDF, sit que AD: e ex ipsa AD abscindatur A aequalis ei quae ex centro minor ul Fiatque ut DO ad O A, ita AB ad aliam, quae sit BK. Frit enim, componendo, ut D A ad AD. (hoc est, u quae ex centro circuli majoris, ad eam quae ex centro minoris,) ita LR ad RB. e RectitvO eianposdior PrO ancopdion. fCOm. HoC est, si a puncto C ad K ducatur recta linean transibit ea per F. Quod nos demonstra- vimus in commentariis in 20 proP. libri Archimedis de iis quae in aqua vehuneur, lemmate primo. S. Ad hunc cionis, prout ea verbis hie concipitur, est camen ad sequencem ucile: (ubi praelumuneur L.M citra centra AB. Duod itaque subjeci de Latine redoidi. B Resticuo nE PrO non BE MOX PrO nEn. ireruquC PrO ulv. LC En ver Tione, AB DrO AN; et mOx conus continces pro coni contingent. ex loc EcCC a Sux.