Philosophiæ naturalis principia mathematica autore Js. Newton ...

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Title: Philosophiæ naturalis principia mathematica autore Js. Newton ...
Author: Newton, Isaac, Sir, 1642-1727.
Publication: Londini :: Jussu Societatis Regiae ac Typis Josephi Streater ...,; 1687.
Rights/Permissions: To the extent possible under law, the Text Creation Partnership has waived all copyright and related or neighboring rights to this keyboarded and encoded edition of the work described above, according to the terms of the CC0 1.0 Public Domain Dedication (http://creativecommons.org/publicdomain/zero/1.0/). This waiver does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
Subject terms: Mechanics -- Early works to 1800.; Celestial mechanics -- Early works to 1800.
Link to this Item: http://name.umdl.umich.edu/A52251.0001.001
Cite this Item: "Philosophiæ naturalis principia mathematica autore Js. Newton ..." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A52251.0001.001. University of Michigan Library Digital Collections. Accessed June 4, 2024.

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Lemma XIV.

Perpendiculum quod ab umbilico Parabolae ad tangentem ejus demit∣titur, medium est proportionale inter distantias umbilici a puncto contactus & a vertice principali figurae.

Sit enim APQ Parabola, S umbilicus ejus, A vertex princi∣palis, P punct∣um

[illustration]

contact∣us, PO ordi∣natim applica∣ta ad diame∣trum princi∣palem, PM tangens dia∣metro princi∣pali occur∣rens in M, & SN linea perpendicularis ab umbilico in tangentem. Jungatur AN, & ob aequales MS & SP, MN & NP, MA & AO, parallelae erunt rectae AN & OP, & inde triangulum SAN rectangulum erit ad A & simile triangulis aequalibus SMN, SPN, Ergo PS est ad SN ut SN ad SA.Q.ED.

Corol. 1. PSq. est ad SNq. ut PS ad SA.

Corol. 2. Et ob datam SA, est SNq. ut PS.

Corol. 3. Et concursus tangentis cujusvis PM cum recta SN quae ab umbilico in ipsam perpendicularis est, incidit in rectam AN, quae Parabolam tangit in vertice principali.