Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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TA,
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E</
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COROLLARIUM II.
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Et hinc patet compoſitio vis directæ
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AD
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ex viribus quibuſvis
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obliquis
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AB
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&
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BD,
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& viciſſim reſolutio vis cujuſvis directæ
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AD
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in obliquas quaſcunque
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AB
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&
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BD.</
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Quæ quidem compoſitio
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& reſolutio abunde confirmatur ex Mechanica.
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<
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>Ut ſi de rotæ alicujus centro
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O
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exeuntes radii inæquales
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OM,
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ON
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filis
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MA, NP
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ſuſtineant pondera
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A
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&
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P,
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& quærantur vi
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res ponderum ad movendam rotam: Per centrum
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O
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agatur recta
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KOL
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filis perpendiculariter occurrens in
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K
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&
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L,
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centroque
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O
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&
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intervallorum
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OK, OL
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majore
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OL
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deſcribatur circulus occurrens filo
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MA
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in
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D:
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& actæ rectæ
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OD
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pa
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rallela ſit
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AC,
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& perpendicularis
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DC.
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Quoniam nihil refert, utrum
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filorum puncta
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K, L, D
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affixa ſint
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an non affixa ad planum rotæ; pon
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dera idem valebunt, ac ſi ſuſpende
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rentur a punctis
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K
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&
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L
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vel
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D
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&
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L.
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Ponderis autem
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A
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exponatur vis to
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ta per lineam
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AD,
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& hæc reſolvetur
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in vires
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AC, CD,
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quarum
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AC
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trahendo radium
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OD
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directe a cen
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tro nihil valet ad movendam rotam; vis autem altera
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DC,
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trahen
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do radium
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DO
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perpendiculariter, idem valet ac ſi perpendiculari
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ter traheret radium
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OL
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ipſi
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OD
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æqualem; hoc eſt, idem atque
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pondus
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P,
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ſi modo pondus illud ſit ad pondus
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A
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ut vis
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DC
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ad
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vim
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DA,
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id eſt (ob ſimilia triangula
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ADC, DOK,
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) ut
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OK
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ad
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OD
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ſeu
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OL.
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Pondera igitur
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A
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&
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P,
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quæ ſunt reciproce ut
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radii in directum poſiti
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OK
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&
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OL,
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idem pollebunt, & ſic conſi
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ſtent in æquilibrio: quæ eſt proprietas notiſſima Libræ, Vectis, &
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Axis in Peritrochio. </
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<
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>Sin pondus alterutrum ſit majus quam in hac
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ratione, erit vis ejus ad movendam rotam tanto major. </
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<
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p
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ponderi
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P
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æquale partim ſuſpendatur filo
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Np,
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partim incumbat plano obliquo
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pG:
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agantur
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pH, NH,
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prior ho
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rizonti, poſterior plano
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pG
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perpendicularis; & ſi vis ponderis
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p
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deorſum tendens, exponatur per lineam
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pH,
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reſolvi poteſt hæc in
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vires
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pN, HN.
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Si filo
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pN
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perpendiculare eſſet planum aliquod
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pQ,
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ſecans planum alterum
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pG
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in linea ad horizontem paral
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lela; & pondas
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p
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his planis
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pQ, pG
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ſolummodo incumberet; ur-</
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