Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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pagenum
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144
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DE MOTU
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CORPORUM</
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<
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>Nam ſi vis, qua corpus trahitur de
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T
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verſus
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C,
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exponatur per
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rectam
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TZ
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captam ipſi proportionalem, reſolvetur hæc in vires
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TY, YZ
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; quarum
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YZ
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trahendo corpus ſecundum longitudinem
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Fili
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PT,
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motum ejus nil mutat, vis autem altera
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TY
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motum ejus
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in curva
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STRQ
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directe accelerat vel directe retardat. </
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>Proinde
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cum hæc ſit ut via deſcribenda
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TR,
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accelerationes corporis vel re
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tardationes in Oſcillationum duarum (majoris & minoris) parti
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bus proportionalibus deſcribendis, erunt ſemper ut partes illæ, &
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propterea facient ut partes illæ ſimul deſcribantur. </
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<
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quæ partes totis ſemper proportionales ſimul deſcribunt, ſimul de
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ſcribent totas.
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E. D.
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Corol.
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1. Hinc ſi corpus
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Filo rectilineo
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AT
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a centro
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A
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pen
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dens, deſcribat arcum circularem
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STRQ,
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& interea urgeatur ſe
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cundum lineas parallelas deorſum a vi aliqua, quæ ſit ad vim uNI
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formem Gravitatis, ut arcus
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TR
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ad ejus ſinum
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TN:
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æqualia e
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runt Oſcillationum ſingularum tempora. </
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>Etenim ob parallelas
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TZ, AR,
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ſimilia erunt triangula
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ATN, ZTY
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; & propterea
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TZ
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erit ad
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AT
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ut
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TY
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ad
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TN
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; hoc eſt, (ſi Gravitatis vis unifor
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mis exponatur per longitudinem datam
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AT
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) vis
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TZ,
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qua Oſcil
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lationes evadent Iſochronæ, erit ad vim Gravitatis
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AT,
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ut arcus
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TR
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ipſi
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TY
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æqualis ad arcus illius ſinum
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TN.
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Corol.
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2. Igitur in Horologiis, ſi vires a Machina in Pendulum
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ad motum conſervandum impreſſæ ita cum vi Gravitatis componi
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poſſint, ut vis tota deorſum ſemper ſit ut linea quæ oritur appli
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cando rectangulum ſub arcu
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TR
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& radio
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AR
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ad ſinum
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TN,
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Oſcillationes omnes erunt Iſochronæ. </
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PROPOSITIO LIV. PROBLEMA XXXVI.
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Conceſſis Figurarum curvilinearum quadraturis, invenire Tempora
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quibus corpora Vi qualibet centripeta in lineis quibuſcunque cur
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vis, in plano per centrum Virium tranſeunte deſcriptis, deſcen
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dent & aſcendent.
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<
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>Deſcendat corpus de loco quovis
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S
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per lineam quamvis curvam
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STtR,
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in plano per virium centrum
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C
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tranſeunte datam. </
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<
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>Junga
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tur
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CS
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& dividatur eadem in partes innumeras æquales, ſitque
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Dd
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