Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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tas O, & erit hæc ſuperficies (per de
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monſtrata
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Archimedis
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) ut
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PFXDFXO.
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Ponamus præterea vires attractivas par
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ticularum Sphæræ eſſe reciproce ut
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diſtantiarum dignitas illa cujus Index
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eſt
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n
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; & vis qua ſuperficies
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FE
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trahit
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corpus
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P
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erit ut (
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DFXO/PF
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n-1
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). Huic pro
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portionale ſit perpendiculum
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FN
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duc
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tum in O; & area curvilinea
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BDLIB,
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quam ordinatim applicata
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FN
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in lon
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gitudinem
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DB
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per motum continuum
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ducta deſcribit, erit ut vis tota qua
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Segmentum totum
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RBSD
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trahit corpus
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P.
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E. I.
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LIBER
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PRIMUS.</
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PROPOSITIO LXXXIV. PROBLEMA XLIII.
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Invenire vim qua corpuſculum, extra centrum Sphæræ in axe Seg
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menti cujuſvis locatum, attrahitur ab eodem Segmento.
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<
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>A Segmento
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EBK
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trahatur corpus
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(Vide Fig. </
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>Prop. </
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>LXXIX,
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LXXX, LXXXI) in ejus axe
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ADB
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locatum. </
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interval
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lo
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PE
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deſcribatur ſuperficies Sphærica
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EFK,
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qua diſtinguatur
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Segmentum in partes duas
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EBKF
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&
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EFKD.
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Quæratur vis par
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tis prioris per Prop. </
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LXXXIII; & ſumma virium erit vis Segmenti totius
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EBKD.
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E. I.
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Scholium.
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<
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>Explicatis attractionibus corporum Sphærieorum, jam pergere
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liceret ad Leges attractionum aliorum quorundam ex particulis at
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tractivis ſimiliter conſtantium corporum; ſed iſta particulatim
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tractare minus ad inſtitutum ſpectat. </
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>Suffecerit Propoſitiones
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quaſdam generaliores de viribus hujuſmodi corporum, deque mo
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tibus inde oriundis, ob earum in rebus Philoſophicis aliqualem
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uſum, ſubjungere. </
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