Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/278.jpg" pagenum="250"/>
                    <arrow.to.target n="note226"/>
                  pori atque adeo ſectori huic proportionalis eſt; in Medio reſiſten­
                    <lb/>
                  te eſt ut triangulum; & in Medio utroque, ubi quam minima eſt, ac­
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                  cedit ad rationem æqualitatis, pro more ſectoris & trianguli. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note226"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XIV. THEOREMA XI.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Iiſdem poſitis, dico quod ſpatium aſcenſu vel deſcenſu deſcriptum,
                    <lb/>
                  eſt ut differentia areæ per quam tempus exponitur, & areæ cu­
                    <lb/>
                  juſdam alterius quæ augetur vel diminuitur in progreſſione A­
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                  rithmetica; ſi vires ex reſiſtentia & gravitate compoſitæ ſu­
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                  mantur in progreſſione Geometrica.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Capiatur
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  (in Fig. </s>
                  <s>tribus ultimis,) gravitati, &
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  reſi­
                    <lb/>
                  ſtentiæ proportionalis. </s>
                  <s>Capiantur autem ad eaſdem partes pun­
                    <lb/>
                  cti
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ſi corpus deſcendit, aliter ad contrarias. </s>
                  <s>Erigatur
                    <emph type="italics"/>
                  Ab
                    <emph.end type="italics"/>
                  quæ
                    <lb/>
                  ſit ad
                    <emph type="italics"/>
                  DB
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DBq
                    <emph.end type="italics"/>
                  ad 4
                    <emph type="italics"/>
                  BAC:
                    <emph.end type="italics"/>
                  & area
                    <emph type="italics"/>
                  AbNK
                    <emph.end type="italics"/>
                  augebitur vel
                    <lb/>
                  diminuetur in progreſſione Arithmetica, dum vires
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  in pro­
                    <lb/>
                  greſſione Geometrica ſumuntur. </s>
                  <s>Dico igitur quod diſtantia cor­
                    <lb/>
                  poris ab ejus altitudine maxima ſit ut exceſſus areæ
                    <emph type="italics"/>
                  AbNK
                    <emph.end type="italics"/>
                  ſupra
                    <lb/>
                  aream
                    <emph type="italics"/>
                  DET.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam cum
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  ſit ut reſiſtentia, id eſt, ut
                    <emph type="italics"/>
                  APq+2BAP
                    <emph.end type="italics"/>
                  :
                    <lb/>
                  aſſumatur data quævis quantitas Z, & ponatur
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  æqualis
                    <lb/>
                  (
                    <emph type="italics"/>
                  APq+2BAP
                    <emph.end type="italics"/>
                  /Z); & (per hujus Lemma 11.) erit ipſius
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  mo­
                    <lb/>
                  mentum
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  æquale (2
                    <emph type="italics"/>
                  APQ+2BAXPQ
                    <emph.end type="italics"/>
                  /Z) ſeu (2
                    <emph type="italics"/>
                  BPQ
                    <emph.end type="italics"/>
                  /Z), &
                    <lb/>
                  areæ
                    <emph type="italics"/>
                  AbNK
                    <emph.end type="italics"/>
                  momentum
                    <emph type="italics"/>
                  KLON
                    <emph.end type="italics"/>
                  æquale (2
                    <emph type="italics"/>
                  BPQXLO
                    <emph.end type="italics"/>
                  /Z) ſeu
                    <lb/>
                  (
                    <emph type="italics"/>
                  BPQXBD cub.
                    <emph.end type="italics"/>
                  /2ZX
                    <emph type="italics"/>
                  CRXAB
                    <emph.end type="italics"/>
                  ). </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Caſ.
                    <emph.end type="italics"/>
                  1. Jam ſi corpus aſcendit, ſitque gravitas ut
                    <emph type="italics"/>
                  ABq+BDq
                    <emph.end type="italics"/>
                    <lb/>
                  exiſtente
                    <emph type="italics"/>
                  BET
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                  Circulo, (in Fig. </s>
                  <s>Caſ. </s>
                  <s>1. Prop. </s>
                  <s>XIII.) linea
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                    <lb/>
                  quæ gravitati proportionalis eſt, erit (
                    <emph type="italics"/>
                  ABq+BDq
                    <emph.end type="italics"/>
                  /Z), &
                    <emph type="italics"/>
                  DPq
                    <emph.end type="italics"/>
                  ſeu
                    <lb/>
                    <emph type="italics"/>
                  APq+2BAP+ABq+BDq
                    <emph.end type="italics"/>
                  erit
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  XZ+
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  XZ ſeu
                    <lb/>
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  XZ; ideoque area
                    <emph type="italics"/>
                  DTV
                    <emph.end type="italics"/>
                  erit ad aream
                    <emph type="italics"/>
                  DPQ
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DTq
                    <emph.end type="italics"/>
                  vel
                    <lb/>
                    <emph type="italics"/>
                  DBq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  XZ. </s>
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