Prop. XXII. Prob. XIV.
Trajectoriam per data quin{que} puncta describere.
Dentur puncta quin{que} A, B, C, D, P. Ab eorum aliquo A ad alia duo quaevis B, C, quae poli nominentur, age rectas AB, AC his{que} parallelas TPS,
[illustration]
Philosophiæ naturalis principia mathematica autore Js. Newton ...
About this Item
- Title
- Philosophiæ naturalis principia mathematica autore Js. Newton ...
- Author
- Newton, Isaac, Sir, 1642-1727.
- Publication
- Londini :: Jussu Societatis Regiae ac Typis Josephi Streater ...,
- 1687.
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- Subject terms
- Mechanics -- Early works to 1800.
- Celestial mechanics -- Early works to 1800.
- Link to this Item
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http://name.umdl.umich.edu/A52251.0001.001
- Cite this Item
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"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 10, 2024.
Pages
PRQ per punctum quartum P. Dein∣de a polis duobus B, C age per punc∣tum quintum D in∣finitas duas BDT, CRD, novissime duc∣tis TPS, PRQ (priorem priori & posteriorem posteri∣ori) occurentes in T & R. Deni{que} de rectis PT, PR, acta recta tr ipsi TR parallela, abscinde quas∣vis
Page 80
Pt, Pr ipsis PT, PR proportionales, & si per earum termi∣nos t, r & polos B, C actae Bt, Cr concurrant in d, locabitur punctum illud d in
[illustration]
Idem aliter.
E punctis datis jun∣ge
[illustration]
Page 81
crurum BA, CA, vel BD, CD intersectio, quae jam sit d, Tra∣jectoriam quaesitam PADdB delineabit. Nam punctum d per Lem. XXI continget sectionem Conicam per puncta B, C trans∣euntem & ubi punctum m accedit ad puncta L, M, N, punctum d (per constructionem) accedet ad puncta A, D, P. Describetur ita{que} sectio Conica transiens per puncta quin{que} A, B, C, D, P. Q.E.F.
Corol. 1. Hinc rectae expedite duci possunt quae trajectoriam in punctis quibusvis datis B, C tangent. In casu utrovis accedat punctum d ad punctum C & recta Cd evadet tangens quaesita.
Corol. 2. Unde etiam Trajectoriarum centra, diametri & la∣tera recta inveniri possunt, ut in Corollario secundo Lemmatis XIX
Schol.
Constructio in casu priore evadet paulo simplicior jungendo BP, & in ea si opus est producta, capiendo Bp ad BP ut est PR ad PT, & per p agendo rectam insinitam pD ipsi SPT pa∣rallelam, in{que} ea capiendo semper pD aequalem Pr, & agendo rectas BD, Cr concurrentes in d. Nam cum sint Pr ad Pt, PR ad PT, pB ad PB, pD ad Pt in eadem ratione, erunt pD & Pr semper aequales. Hac methodo puncta Trajectoriae inveni∣untur expeditissime, nisi mavis Curvam, ut in casu secundo, de∣scribere Mechanice.