# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1040780814:0018 # Permalink to this reading: https://leibnizlegible.com/page/1040780814:0018?run=74 # Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124) # Folio - , page id 1040780814:0018 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1040780814&page=18 # Source image: https://digitale-sammlungen.gwlb.de/content/1040780814/jpgs/default/00000018.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 23 lines, status machine # Lines: 23 recognised, mean confidence 0.97 # 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. P R A F A F T0. eadem tensio in chordam subsesquialteram aeit in ratione dupla se s quiquarta: nam duintam sive harmoniam Diapente efficit, chorda, quae dato pondere datum tonum edit, pondere duplo sesqui- quarto tendi debet ut duintam efficiat. Pt universaliter, pondera, quibus toni omnes in chordis aequalibus audiuntur, sunt reciproce ut quadrata loneitudinum chordarum aequaliter tensarum, quibus in strumentum musicum tonos eosdem emittit. Proportionem his ex- perimentis inventam Pychasoras applicuit ad Caelos, inde didicit FTarmoniam Sphaerarum. Ideoque conserendo pondera illa cum pon- deribus Planetarum, es intervalla tonorum cum intervallis sphae- rarum, atque adeo loncitudines chordarum cum distantiis P laneta- rum ab orbium centro, intellevit per Tharmoniam Caelorum quod Gravitates Planetarum in Solem (ad cujus utique Frram omnes saltant) essent reciproce ut quadrata distantiarum eorum à Sole. Fractenus ostensum est quaenam fuerit de Gravitate veterum Dhilosophorum sententia; iisque persuasum esse constat, quo d Cra- vitas non modo Terrae se d e corporibus Caelestibus competat, quod corpora omnia in se mutuo sravia sunt, quodque Planetae vi Cra- vitatis in Orbitis suis retineantur, quo d denique Gravitates Plane- tarum ad Solem sint reciproce ut duadrata distantiarum ab ipso. duaenam hisce reterum inventis incrementa adjecerit Recentiorum solertia, sequentes parinae fuse ostendunt.