Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/327.jpg" pagenum="299"/>
                    <lb/>
                  mittantur perpendiculares
                    <emph type="italics"/>
                  BE, DL,
                    <emph.end type="italics"/>
                  & vis qua particula Medii,
                    <lb/>
                    <arrow.to.target n="note275"/>
                  ſecundum rectam
                    <emph type="italics"/>
                  FB
                    <emph.end type="italics"/>
                  obliQ.E.I.cidendo, Globum ferit in
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                  erit
                    <lb/>
                  ad vim qua particula eadem Cylindrum
                    <emph type="italics"/>
                  ONGQ
                    <emph.end type="italics"/>
                  axe
                    <emph type="italics"/>
                  ACI
                    <emph.end type="italics"/>
                  circa
                    <lb/>
                  Globum deſcriptum perpendiculariter feriret in
                    <emph type="italics"/>
                  b,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  LD
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  LB
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  BE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BC.
                    <emph.end type="italics"/>
                  Rurſus efficacia hujus vis ad movendum
                    <lb/>
                  Globum ſecundum incidentiæ ſuæ plagam
                    <emph type="italics"/>
                  FB
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                  eſt ad ejuſ­
                    <lb/>
                  dem efficaciam ad movendum Globum ſecundum plagam determi­
                    <lb/>
                  nationis ſuæ, id eſt, ſecundum plagam rectæ
                    <emph type="italics"/>
                  BC
                    <emph.end type="italics"/>
                  qua Globum di­
                    <lb/>
                  recte urget, ut
                    <emph type="italics"/>
                  BE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BC.
                    <emph.end type="italics"/>
                  Et conjunctis rationibus, efficacia
                    <lb/>
                  particulæ, in Globum ſecundum rectam
                    <emph type="italics"/>
                  FB
                    <emph.end type="italics"/>
                  obliQ.E.I.cidentis, ad
                    <lb/>
                  movendum eundem ſecundum plagam incidentiæ ſuæ, eſt ad effi­
                    <lb/>
                  caciam particulæ ejuſdem ſecundum eandem rectam in Cylindrum
                    <lb/>
                  perpendiculariter incidentis, ad ipſum movendum in plagam ean­
                    <lb/>
                  dem, ut
                    <emph type="italics"/>
                  BE
                    <emph.end type="italics"/>
                  quadratum ad
                    <emph type="italics"/>
                  BC
                    <emph.end type="italics"/>
                  quadratum. </s>
                  <s>Quare ſi ad Cylin­
                    <lb/>
                  dri baſem circularem
                    <emph type="italics"/>
                  NAO
                    <emph.end type="italics"/>
                  erigatur perpendiculum
                    <emph type="italics"/>
                  bHE,
                    <emph.end type="italics"/>
                  & ſit
                    <lb/>
                    <emph type="italics"/>
                  bE
                    <emph.end type="italics"/>
                  æqualis radio
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  bH
                    <emph.end type="italics"/>
                  æqualis (
                    <emph type="italics"/>
                  BE quad/CB
                    <emph.end type="italics"/>
                  ): erit
                    <emph type="italics"/>
                  bH
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  bE
                    <emph.end type="italics"/>
                    <lb/>
                  ut effectus particulæ in Globum ad effectum particulæ in Cylin­
                    <lb/>
                  drum. </s>
                  <s>Et propterea ſolidum quod à rectis omnibus
                    <emph type="italics"/>
                  bH
                    <emph.end type="italics"/>
                  occu­
                    <lb/>
                  patur erit ad ſolidum quod à rectis omnibus
                    <emph type="italics"/>
                  bE
                    <emph.end type="italics"/>
                  occupatur, ut
                    <lb/>
                  effectus particularum omnium in Globum ad effectum particu­
                    <lb/>
                  larum omnium in Cylindrum. </s>
                  <s>Sed ſolidum prius eſt Parabolois
                    <lb/>
                  vertice
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  axe
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                  & latere recto
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                  deſcriptum, & ſolidum
                    <lb/>
                  poſterius eſt Cylindrus Paraboloidi circumſcriptus: & notum eſt
                    <lb/>
                  quod Parabolois ſit ſemiſſis Cylindri circumſcripti. </s>
                  <s>Ergo vis
                    <lb/>
                  tota Medii in Globum eſt duplo minor quam ejuſdem vis tota
                    <lb/>
                  in Cylindrum. </s>
                  <s>Et propterea ſi particulæ Medii quieſcerent, &
                    <lb/>
                  Cylindrus ac Globus æquali cum velocitate moverentur, foret re­
                    <lb/>
                  ſiſtentia Globi duplo minor quam reſiſtentia Cylindri.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                    <lb/>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                    <lb/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note275"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>Eadem methodo Figuræ aliæ inter ſe quo­
                    <lb/>
                    <figure id="id.039.01.327.1.jpg" xlink:href="039/01/327/1.jpg" number="182"/>
                    <lb/>
                  ad reſiſtentiam comparari poſſunt, eæQ.E.I.­
                    <lb/>
                  veniri quæ ad motus ſuos in Mediis reſiſten­
                    <lb/>
                  tibus continuandos aptiores ſunt. </s>
                  <s>Ut ſi baſe
                    <lb/>
                  circulari
                    <emph type="italics"/>
                  CEBH,
                    <emph.end type="italics"/>
                  quæ centro
                    <emph type="italics"/>
                  O,
                    <emph.end type="italics"/>
                  radio
                    <emph type="italics"/>
                  OC
                    <emph.end type="italics"/>
                    <lb/>
                  deſcribitur, & altitudine
                    <emph type="italics"/>
                  OD,
                    <emph.end type="italics"/>
                  conſtruen­
                    <lb/>
                  dum ſit fruſtum Coni
                    <emph type="italics"/>
                  CBGF,
                    <emph.end type="italics"/>
                  quod omni­
                    <lb/>
                  um eadem baſi & altitudine conſtructorum & ſecundum plagam </s>
                </p>
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