# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1040780814:0359 # Permalink to this reading: https://leibnizlegible.com/page/1040780814:0359?run=74 # Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124) # Folio 341, page id 1040780814:0359 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1040780814&page=359 # Source image: https://digitale-sammlungen.gwlb.de/content/1040780814/jpgs/default/00000359.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine # Lines: 52 recognised, mean confidence 0.94 # 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. 110. 0 L ib. IV. _E (TEOMETRTCA E LEMENFA. 34. L ex Luna centro B videtur Cb angulo PD N aequali summae Semidia- metrorum Lunae ex Solis de Terra centris apparentium, minutae Se- midiametro apparenti Solis e centro Luna rili. Ft quoniam, propter immensam Diltantiam Solis a Terra respectu Distantia inter Lunam e Terram, Solis Diamerer ex Luna in eodem proxime angulo ride tur quo ex Terra, d Lunx Diameter ex Sole vila pro nulla quali est habenda, quippe sub. quadrupla fere Parallaris Solishorizontalis; Semidiameter Ombra Luna in Dilcum Telluris excepta ridetur excentro Lunx sub ansulo aequali fere differentia angulorum, sub quibus solis e Luna Semidiametri ex Terrae centro apparent. Verum, si Solis Semidiameter e Ferra visa major sit Semidiame ero Lunx spectata ex eadem, apparens Semidiameter Umbrae (cum Tit aequalis minori post demptam majorem) nesatira cradit; hoc est, post terminatam finitamque Ombram in Coni apice, circellus Factus ex sectione Coni, Vmbroso Cono ad verticem positi, ex J una videtur sub angulo aequali difterentia angulorum, in quibus Sol e Luna ex Terra centro apparent. Circellus autem hic circelli Ombrosi locum tenet: est enim totius circuli penumbroh maxime obscurus, e (Umbra plenae instar) aqualiter obscurus; cujus nempe puncta sinsula illustrantur ab excestu Solaris Disei supra Lunarem ex Tellure apparente: Nam praecedentia omnia vera sunt de ON recta ultra c ducta. PROPOSTTIO ZXXIV. T sphaera opaca sphaerae lucidae exponatur, praeter umibram to- talem sive plenam fiet penumbrâ (hoc est, spatium medii cir- cumfusi a cujus sinculis punctis aliqui per opacam sphaeram arcentur ractii) ad partes à sphaera lucida aversas, inclusa superficie cont recti, cujus axis idem est cum are umbrae plenae, e anculus ver- ticalis trianeuli per axem aequalis est summae anculorum, qui Bus Bhaera lucida ex centro opacae phaera ovaca ex cen- ero lucidae videntur. Et si conus hic penumbrosus secetur utcun- que plano ad planum basis paraltelo, penumbrosi circuli su ceniti cinctuso circulo plene umbroso ad ejus centrum, si quis sit, diame ter ex centro opacae sphaerae spectata videtur sub anculo aequali ae grecato trium anculorum; eorum nempe sub quibus opaca sphaera ex centris sphaerae lucida es circuli penumbrosi videtur, ejusque in quo shaera lucida ex opacae centro spectatur. Reliquis manentibus ut in prXC. duCantuE recta DE, FC circuloS ad partes alternas contingentes, se mutuo in rectae aB puncto c de cuctantes. Patet praeter umbram totalem projici etiam circa hanc penumbram in partes à lucida sphaera avertas, quia spatium omne intra superticiem conicam, senitam a recta D P. ultra spharam opa- cam producta circa axem AB rotata, tale est ut ab ejus Aingulis puin- etis quidam sphaera lucida radii arceantur per interpolitionem opaca; ec ideo non tantum illustratur atque reliquum huic spa- lio conico circuntulum, a quo nulli aecentur. Et spatii hujis Partes