Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/475.jpg" pagenum="447"/>
                  intervalla quaterna diviſas
                    <emph type="italics"/>
                  e,
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  e,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>& ſic deinceps; id eſt, ita
                    <lb/>
                    <arrow.to.target n="note476"/>
                  ut ſit
                    <emph type="italics"/>
                  b=(AH-BI/HI), 2b=(BI-CK/IK), 3b=(CK-DL/KL),
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>dein
                    <lb/>
                    <emph type="italics"/>
                  c=(b-2b/HK), 2c=(2b-3b/IL), 3c=(3b-4b/KM),
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Poſtea
                    <emph type="italics"/>
                  d=(c-2c/HL),
                    <lb/>
                  2d=(2c-3c/IM),
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Inventis differentiis, dic
                    <emph type="italics"/>
                  AH=a, -HS=p,
                    <lb/>
                  p
                    <emph.end type="italics"/>
                  in -
                    <emph type="italics"/>
                  IS=q, q
                    <emph.end type="italics"/>
                  in +
                    <emph type="italics"/>
                  SK=r, r
                    <emph.end type="italics"/>
                  in +
                    <emph type="italics"/>
                  SL=s, s
                    <emph.end type="italics"/>
                  in +
                    <emph type="italics"/>
                  SM=t
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  pergendo ſcilicet ad uſque perpendiculum penultimum
                    <emph type="italics"/>
                  ME,
                    <emph.end type="italics"/>
                  & erit
                    <lb/>
                  ordinatim applicata
                    <emph type="italics"/>
                  RS=a+bp+cq+dr+es+ft,
                    <emph.end type="italics"/>
                  &c. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note476"/>
                  LIBER
                    <lb/>
                  TERTIUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Hinc areæ curvarum omnium inveniri poſſunt quampro­
                    <lb/>
                  xime. </s>
                  <s>Nam ſi curvæ cujuſvis quadrandæ inveniantur puncta ali­
                    <lb/>
                  quot, & Parabola per eadem duci intelligatur: erit area Parabolæ
                    <lb/>
                  hujus eadem quam proxime cum area curvæ illius quadrandæ. </s>
                  <s>
                    <lb/>
                  Poteſt autem Parabola, per Methodos notiſſimas, ſemper quadrari
                    <lb/>
                  Geometrice. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA VI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Ex obſervatis aliquot locis Cometæ invenive locum ejus ad
                    <lb/>
                  tempus quodvis intermedium datum.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Deſignent
                    <emph type="italics"/>
                  HI, IK, KL, LM
                    <emph.end type="italics"/>
                  tempora inter obſervationes,
                    <lb/>
                    <emph type="italics"/>
                  (in Fig. </s>
                  <s>præced.) HA, IB, KC, LD, ME
                    <emph.end type="italics"/>
                  obſervatas quinque
                    <lb/>
                  longitudines Cometæ,
                    <emph type="italics"/>
                  HS
                    <emph.end type="italics"/>
                  tempus datum inter obſervationem pri­
                    <lb/>
                  mam & longitudinem quæſitam. </s>
                  <s>Et ſi per puncta
                    <emph type="italics"/>
                  A, B, C, D, E
                    <emph.end type="italics"/>
                    <lb/>
                  duci intelligatur curva regularis
                    <emph type="italics"/>
                  ABCDE
                    <emph.end type="italics"/>
                  ; & per Lemma ſupe­
                    <lb/>
                  rius inveniatur ejus ordinatim applicata
                    <emph type="italics"/>
                  RS,
                    <emph.end type="italics"/>
                  erit
                    <emph type="italics"/>
                  RS
                    <emph.end type="italics"/>
                  longitudo
                    <lb/>
                  quæſita. </s>
                </p>
                <p type="main">
                  <s>Eadem methodo ex obſervatis quinque latitudinibus invenitur
                    <lb/>
                  latitudo ad tempus datum. </s>
                </p>
                <p type="main">
                  <s>Si longitudinum obſervatarum parvæ ſint differentiæ, puta gra­
                    <lb/>
                  duum tantum 4 vel 5; ſuffecerint obſervationes tres vel quatuor
                    <lb/>
                  ad inveniendam longitudinem & latitudinem novam. </s>
                  <s>Sin majores
                    <lb/>
                  ſint differentiæ, puta graduum 10 vel 20, debebunt obſervationes
                    <lb/>
                  quinque adhiberi. </s>
                </p>
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