# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1040780814:0463 # Permalink to this reading: https://leibnizlegible.com/page/1040780814:0463?run=74 # Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124) # Folio 445, page id 1040780814:0463 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1040780814&page=463 # Source image: https://digitale-sammlungen.gwlb.de/content/1040780814/jpgs/default/00000463.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 78 lines, status machine # Lines: 78 recognised, mean confidence 0.84 # 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. netM al CumElUMI Iterte Mte DPt Lib. V. imrecta nique ersecti puncte Par pro Co Ierit uum il ratiOM M1 il H0 Ducta C daluu eria IM erit leoque cund ne 10 ItiOn Il M Lib. V. _E GTEOMEFRLCA L LFMKHLA. 4.4u5 One Si ad SA; _E aSatUT per S recta SDC, cujus pars D0 a cruribus ansuli a se interjecta aequetur rectae +N, quod cM Veterum Pro. blema univertale de Iuclinationibus, conticiturque per corum Me- thodum, vel per S. VII. Lect. OptIC. V. auFS. II. L ect. C eOm. VT. Bar- rovii: Punctum c sic determinatum cA illud iptum quod commode primâ vice usurpatur pro restigio Cometa in plano Lcliptica. Po- natur c este restisium Cometa in plano Feliptiea, d arcum Para- Bolicum per a, B _ C transeuntem esse rostigium arcus Trajectorix inter Obserrationem primam et tertiam delcripti: Ouoniam isi- tur in hypothesi quod gravitas acceleratrix rersus Solem eadem sit vel aequalis in distantia Telluris à Sole acque in distantia Cometa 2b codem, (hoc est, in trpothesi graritatis quam Calilaeus Forit, quaque d vero non multum abest,) cD _ tN sunt xquales; quippe spatia cadendo rersus Solem eodem tempore percurta d Cometâ e a Tellure, erit (per PFOP. XXII.) AB chorda Parabola ad v2 ~ YY chordam circuli, cujus centrum cum foco Parabola congruit, in Subduplicata ratione rectae st ad so rectam. Sed Facta cst AB ad Y 2 ~F = in subduplicata ratione 57 ad 5s, _ etiam AB secat rC. etam +e in ansulo debito, de porro cD aequalis cAt ip(I tH: Recta isitur aB habet proxime omnes conditiones requisitas ut tat chor- da arcis qui est vestisium Frajectoria Cometiea interjecta inter Tonsitudinem primam Ta _ tertiam =B; punctumque proinde c habet omnes conditiones ut fat proxime vestigium Cometae in OB. serratione secunda. Recte isitur assumitur punctum c restigium Cometa (postea quidem corrisendum) in dicta Obserratione sccunda. Determinato puncto c prima rice astumendo, qua deinde altu- muntur puncta (nempe 2C 8 3C) non sunt absque contideratione al- sumenda; nec lusticit Prop. Praec. data cautio, quod nempe pun- ctum 2c sumendum sit propius puncto cum linea Z minor est quam AB, _ e contra: Sed cum eo tandem deveniendum sit, ut AB rite dueta aqualis st congrux Lonsitudini Z; in sc capiatur punetum 2C, Cd lesc ut dictantia 2C sit ad distantiam oc in ra- eione compolita ex ratione 2 ad aB _ ratione subduplicata sc ad 52c. Causa, cur prior ratio componens adhibetur, manifecta est ex praedictis: nam cum in- venienda (t a B qua sit congrua 2 aqualis, A illa hâc (t major aut minor, minuenda erit aut onsenda donec aequales fiant; forent autem aequates pel tolam ori. orem rationem componentem, s Z. eNet constans e inrariabilis: cum vero pro direrta ae direrta perpetuo proveniat longitudo 2, ideo secunda componentium necestaria cst. Consat autem (Cx PrOP. XXHT.) quod in Parabolis, arcuum aCB, 2 A 2C2B, in quibus x I K H 3 GlanEUE