Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Et hinc facile colligitur, quod corporum ſimiles ſimi­
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                  lium Figurarum partes temporibus proportionalibus deſcribentium
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                  Errores, qui viribus quibuſvis æqualibus ad corpora ſimiliter ap­
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                  plicatis generantur, & menſurantur per diſtantias corporum a Fi­
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                  gurarum ſimilium locis illis ad quæ corpora eadem temporibus iiſ­
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                  dem proportionalibus abſque viribus iſtis pervenirent, ſunt ut qua­
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                  drata temporum in quibus generantur quam proxime. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Errores autem qui viribus proportionalibus ad ſimiles
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                  Figurarum ſimilium partes ſimiliter applicatis generantur, ſunt ut
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                  vires & quadrata temporum conjunctim. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Idem intelligendum eſt de ſpatiis quibuſvis quæ corpo­
                    <lb/>
                  ra urgentibus diverſis viribus deſcribunt. </s>
                  <s>Hæc ſunt, ipſo motus iNI­
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                  tio, ut vires & quadrata temporum conjunctim. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Ideoque vires ſunt ut ſpatia, ipſo motus initio, deſcripta
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                  directe & quadrata temporum inverſe. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  5. Et quadrata temporum ſunt ut deſcripta ſpatia directe
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                  & vires inverſe. </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
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                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Si quantitates indeterminatæ diverſorum generum conferantur
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                  inter ſe, & earum aliqua dicatur eſſe ut eſt alia quævis directe vel
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                  inverſe: ſenſus eſt, quod prior augetur vel diminuitur in eadem
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                  ratione cum poſteriore, vel cum ejus reciproca. </s>
                  <s>Et ſi earum aliqua
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                  dicatur eſſe ut ſunt aliæ duæ vel plures directe vel inverſe: ſenſus
                    <lb/>
                  eſt, quod prima augetur vel diminuitur in ratione quæ componitur
                    <lb/>
                  ex rationibus in quibus aliæ vel aliarum reciprocæ augentur vel di­
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                  minuuntur. </s>
                  <s>Ut ſi A dicatur eſſe ut B directe & C directe & D in­
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                  verſe: ſenſus eſt, quod A augetur vel diminuitur in eadem ratione
                    <lb/>
                  cum BXCX1/D, hoc eſt, quod A & (BC/D) ſunt ad invicem in ratio­
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                  ne data. </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XI.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Subtenſa evaneſcens anguli contactus, in curvis omnibus curvatu­
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                  ram finitam ad punctum contactus habentibus, est ultimo in ra­
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                  tione duplicata ſubtenſæ arcus contermini.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Caſ.
                    <emph.end type="italics"/>
                  1. Sit arcus ille
                    <emph type="italics"/>
                  AB,
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                  tangens ejus
                    <emph type="italics"/>
                  AD,
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                  ſubtenſa anguli con­
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                  tactus ad tangentem perpendicularis
                    <emph type="italics"/>
                  BD,
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                  ſubtenſa arcus
                    <emph type="italics"/>
                  AB.
                    <emph.end type="italics"/>
                  Huic
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                  ſubtenſæ
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  & tangenti
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  perpendiculares erigantur
                    <emph type="italics"/>
                  AG, BG,
                    <emph.end type="italics"/>
                  </s>
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