Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  DE MOTU
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                  CORPORUM</s>
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                    <emph type="italics"/>
                  Corol.
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                  6. Et motus Globi cum ejus reſiſtentia ſic exponi poteſt.
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                  Sit
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                  AB
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                  tempus quo Globus per reſiſtentiam ſuam uniformiter con­
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                  tinuatam totum ſuum motum amit­
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                  tere poteſt. </s>
                  <s>Ad
                    <emph type="italics"/>
                  AB
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                  erigantur per­
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                  pendicula
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                  AD, BC.
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                  Sitque
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                  BC
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                  motus ille totus, & per punctum
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                  C
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                  Aſymptotis
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                  AD, AB
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                  deſcribatur
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                  Hyperbola
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                  CF.
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                  Producatur
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                  AB
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                  ad
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                  punctum quodvis
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                  E.
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                  Erigatur per­
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                  pendiculum
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                  EF
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                  Hyperbolæ occur­
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                  rens in
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                  F.
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                  Compleatur parallelo­
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                  grammum
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                  CBEG,
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                  & agatur
                    <emph type="italics"/>
                  AF
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                  ipſi
                    <emph type="italics"/>
                  BC
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                  occurrens in
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                  H.
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                  Et ſi Globus tempore quovis
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                  BE,
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                  motu
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                  ſuo primo
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                  BC
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                  uniformiter continuato, in Medio non reſiſtente de­
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                  ſcribat ſpatium
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                  CBEG
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                  per aream parallelogrammi expoſitum, idem
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                  in Medio reſiſtente deſcribet ſpatium
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                  CBEF
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                  per aream Hyper­
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                  bolæ expoſitum, & motus ejus in fine temporis illius exponetur
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                  per Hyperbolæ ordinatam
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                  EF,
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                  amiſſa motus ejus parte
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                  FG.
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                  Et
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                  reſiſtentia ejus in fine temporis ejuſdem exponetur per longitudi­
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                  nem
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                  BH,
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                  amiſſa reſiſtentiæ parte
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                  CH.
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                  Patent hæc omnia per
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                  Corol. 1. Prop. v. Lib. II.
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                    <emph type="italics"/>
                  Corol.
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                  7. Hinc ſi Globus tempore T per reſiſtentiam R unifor­
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                  miter continuatam amittat motum ſuum totum M: idem Globus tem­
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                  pore
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                  t
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                  in Medio reſiſtente, per reſiſtentiam R in duplicata velocitatis
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                  ratione decreſcentem, amittet motus ſui M partem (
                    <emph type="italics"/>
                  t
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                  M/T+
                    <emph type="italics"/>
                  t
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                  ), manente
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                  parte (TM/T+
                    <emph type="italics"/>
                  t
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                  ), & deſcribet ſpatium quod ſit ad ſpatium motu uni­
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                  formi M eodem tempore
                    <emph type="italics"/>
                  t
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                  deſcriptum, ut Logarithmus numeri
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                  (T+
                    <emph type="italics"/>
                  t
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                  /T) multiplicatus per numerum 2,302585092994 eſt ad nume­
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                  rum
                    <emph type="italics"/>
                  t
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                  /T. Nam area Hyperbolica
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                  BCFE
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                  eſt ad rectangulum
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                    <emph type="italics"/>
                  BCGE
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                  in hac proportione.
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                  Scholium.
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                    <emph.end type="center"/>
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                  <s>In hac Propoſitione expoſui reſiſtentiam & retardationem Pro­
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                  jectilium Sphærieorum in Mediis non continuis, & oſtendi quod
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                  hæc reſiſtentia ſit ad vim qua totus Globi motus vel tolli poſſit vel </s>
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