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Si Cometa motu omni privatus de altitudine SN seu Sμ+⅓Iμ de∣mitteretur, ut caderet in Solem, & ea semper vi uniformiter continuata urgeretur in Solem qua urgetur sub initio; idem quo tempore in orbe suo describat arcum AC, descensu suo describeret spatium longitudini Iμ aequale.
Nam Cometa quo tempore describat arcum Parabolicum AC, eodem tempore ea cum velocitate quam habet in altitudine SP (per
Lemma novissimum) describet chordam AC, adeoque eodem tem∣pore in circulo cujus semidiameter esset SP revolvendo, describeret arcum cujus longitudo esset ad arcus Parabolici chordam AC in di∣midiata ratione unius ad duo. Et propterea eo cum pondere quod habet in Solem in altitudine SP, cadendo de altitudine illa in Solem, describeret eodem tempore (per Scholium Prop. IV. Lib. I.) spati∣um aequale quadrato semissis chordae illius applicato ad quadruplum altitudinis SP, id est spatium AIq./4 SP. Unde cum pondus Cometae in Solem in altitudine SN sit ad ipsius pondus in Solem in altitu∣dine SP, ut SP ad Sμ: Cometa pondere quod habet in altitudine SN eodem tempore, in Solem cadendo, describet spatium AIq./4 Sμ, id est spatium longitudini Iμ vel Mμ aequale. Q.E.D.