# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/867984570:0302 # Permalink to this reading: https://leibnizlegible.com/page/867984570:0302?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 274, page id 867984570:0302 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=302 # Source image: https://digitale-sammlungen.gwlb.de/content/867984570/jpgs/default/00000302.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 111 lines, status machine # Lines: 111 recognised, mean confidence 0.81 # 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. L14 Zochconaoror 3)asqua ex du0 7 uegi ut M. WCICOV OcVESE EK 28 qqroNtS nat CK 28 DHTetTS. EsCO raep o uo a 28 B quion B 58 Y BrerroS Aeyco ot 2 drronaor 6) L Y putXioS CGNDrS B oe EX Cx quroo aurs. duo a 100t cior 28102 2015 B TIa NHV, EHEI 3 28 Y ii Mrtros o âea Béxar y, C ret FV ait8 58E15 à Cg oi B, Ejoir ioet OSCP or 5015 Y O â eg à 1005 ésir dvoi 2o15 N a0 (O aC_ Esir o a 28Y. Oudets noMa coNaorS, oy) e Seor Noycor, et pen povos o dem nâor 6. Et yd duvaror. a O noM a Naor O Nogos o a y ovynetd e duo Sruoeicor Norcor, 2BrC a β 23 By. C 55c0 POR PHIY R I per Parcicularibus rationious coniponitur: tel qui altera scilicet, et lelgat. Cela. L CM A iptius B Te(quI alter; et B ipluS C lelquitertius. Dico, quod A clt ipEIIIS C. dupluS. CAMI CHII HE A iP Tius B Selguralter; continet ergo A ipsum B, ejusque parcem dimidiam Duo igitur A, aequales TunE tribus B. Trem, cum B sE ip SIUS C SelquI TCTEIUS; CON tinet B ipsum C ejusque parrem terriam. LrsC tres B, aequales TUINE quaTUOF C. LTBO A X qualis elt. duobus C. Duplus isitur clt A IP trus C. 7. Nulla ratio mulcipla, componitur ex ra- tionibus super. particularibus, excepta lola ra- sione dupla. Si enim lit poltibile; FIto AC alia rario mulcipla, composica ex duabus rario- nibus Cuper. Particularibus AB et BC; licque D 6. Diastema duplum, ex duabus maximis Fu- iptiUS F. se(quI aIEer; _ F ipsIuS F lelquI. Let- tius. Duplus isicur est D iplius F. Cumque sic ex Cuper porcicularibus, rario maxima, lel- qui altera; secunda vero, lesqui tertia: Una rationum DE EF, uni iplarum AB BC, auE eadem ipta elt, aue altera major altera, aut anibae ambobus majores. Vicunque tuerit, ma- jorem habet D ad E rationem, quam A ad C. Ouod impossibile est. Nam, racionum mul. ciplarum, dupla est minima. Nulla isitur rario mulcipla, componitur ex duabus rarionibus, su per particularibus, nili Cola dupla. S. FX diastemate duplo _ se(qui alLerO, FE diactema criplum. Fcto enim A ipsiuS B du- Dlus; de B ipsius C sesqui alter. Dico; quod A est iplius C eriplus. Cum enim A lic ipBus B duplus; est igieuT A aequalis duobus B. Item, eum lic B ip(iuS C. selqui alter; continet ergo B iptum C, ejusque dimi- dium: duo isicur B aequales Tunt cribus C. Sed duo B aequales sunt ipsI A. ErsO e A ipsius C est eriplus. O. Si, a diastemate sesqui altero, auteratur diastema sesqui cercium, relinquitur (residuum) sesqui octarum. FRo enim A iplius B selqui alter; de C iplius B selqui tertius. Dico, quoc A est ipsius C sesqui octarus. Cum enim lic A ipsuis B selqui alter; ergo A continet B, ejusque semil Tem. Erso octo A aequales IUNE duodecim B. Trem, cum C sII ip. Bus B Celqui tertius; ergo C COn tinet B, ejusque partem certiam. Novem igi- cur C, aequales lune duodecim B. Duodecim erxo B, aequales sunc octo A. Octo isitur A, PrO ro c naoror, reDONO o SiNao . n PYO NI nao, reDONO dxA. O PTO n rCPONO EnI. P PrO rore daoror P0nO ro iiuov. r Suxpleo osixdnor SME. 0 U drBE uiON1OS o)E8G Srsios ed XNor o eq Esir o d F8 . 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O c dey rS B ireiros NEyc, 87 6 a 28 y Esr enordo6) OxTC apa oi a 100 eisr dcodexa roi EEt 3C o a rZ B Es iv ipereN O apa a Exd r B, u x quroo airs co estet 6Y 58 B vit d 8C17050 ap Y Ex+2 B, C1 16t airs Crrea apa et 7, 100t eio dco dena 2015 B. du 100t dexa de oi B, ioot eisir ourco rois d orco épa i c