# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1040780814:0298 # Permalink to this reading: https://leibnizlegible.com/page/1040780814:0298?run=74 # Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124) # Folio 280, page id 1040780814:0298 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1040780814&page=298 # Source image: https://digitale-sammlungen.gwlb.de/content/1040780814/jpgs/default/00000298.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine # Lines: 55 recognised, mean confidence 0.90 # 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. 280 AST RONOMLA PAZSTCE L iD. LII Radii, quibus Planeta Terram illustrat, illi sunt qui a Sole pri mitus manantes a Planeta reftectuntur in Terram. Supponimus iditur Planctam quemris radios omnes Solares in se incidentes un diquaque refectere; hoc est (ad majorem facilitatem) supponimus Planetam (lucidi primarii instar) radios a sui hemisphaerio Soli obverlo undiguaque emittere, tot sc. quot à Sole in illum incidunt. Palam est Illustrationem Ferra à Sole este ad Ilustrationem ejul dem per Planetam pleno Orbe Fulgentem ut radii omnes Solares in Terram incidentes ad omnes radios a Planeta manantes in candem incidentes: Sed ratio radiorum Solarium in Terram incidentium ad radios Planetarios in eandem incidentes componitur ex ratione ra diorum Solarium in Ferram incidentium ad radios Solares in Plane tam incidentes, (hoc est, omnes radios a Planeta hemisphaerio manan- tes,) e ratione omnium radiorum à Planetae hemilphaerio manan tium ad omnes ex illis qui in Terram incidunt. Fit componentium harum rationum prior, sive ratio radiorum Solarium in Terram in- cidentium ad radios Solares in Planetam incidentes, aegualis est (per PrOD. PFaC.) duplicata rationi Parallaris horizontalis Solis e Ferra spectati ad Parallaxin horizontalem Solis ex isto Planeta sxectati; Dolterior rero, nempe ratio radiorum omnium à Planeex hemisphae rio Terram illustrante manantium ad omnes ex illis qui in Terram incidunt camque illustrant, aequalis cA (per Schol. PrXC.) rationt quam habet quadratum circulo inseriptum ad quadratum chordae Parallaxis horixontalis dicti Planeta ex Terra Spectati. FF isitUI ratio Mustrationis Terra à Sole ad ejusdem Mlustrationem à Planeta pleno Orbe fulsente componitur ex duplicata ratione chordarum Parallarium horizontalium Solis ex Perra e Planeta isto spectati, ec ratione quadrati circulo inferipri ad quadratum chorda Parallaxis horiconcalis dicti Planera e Terra visi. C. F. D. PROPOSTTTO LX Tellae Fixae Distantiam definire. Flisatur Fixa ejusdem quamproxime splendoris cum Plane. tarum aliquo, quando pleno Orbe fulset; quo calu Terra ab ictis duabus Stellis aequaliter illustratur. Sed ex connitis (per PrOD. XEV.) Solis, Terra e Planeex Distantiis mutuis ad Tempus obserrationis praedicta, _ (Per PFOP. XL. VT.) horum trium COr- Porum Magnitudinibus, innOtEsCUnE (DeF PFOP. XLVIIT. L. IB. H.) Parallares horixontales Solis e Planeta e Terra vilorum et an sulus quo dictus Planeta ex Sole videtur, cujus semistis est Paral laxis horizontalis Solis ex ilto Planeta vili. AC proinde (per PFOP. PTaC.) innoreseit ratio illustrationis Terra per Solem ad ejusdem il. lustrationem per dictum Planctam; hoc elt, ratio inter illustratio nes lerra per Solem e per Fixam: Sed (per Prop. LVIT.) illustra tio Lerra per Solem est ad illustrationem ejuidem per Fixam (Soli aqualem et aequilucidam) in duplicata ratione Distantia Fixae TPOTTa d N x M re DEd