Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
441
441 		442
442
443
443 		444
444
445
445 		446
446
447
447 		448
448
449
449 		450
450
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/441.jpg" pagenum="413"/>
                  tus medius Nodorum circulo toti reſpondens. </s>
                  <s>Et motus Nodo­
                    <lb/>
                    <arrow.to.target n="note442"/>
                  rum, quo tempore Sol pergit ab
                    <emph type="italics"/>
                  N
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  eſt ad 19
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  49′. </s>
                  <s>3″. </s>
                  <s>55′. </s>
                  <s>
                    <lb/>
                  ut area
                    <emph type="italics"/>
                  NAZ
                    <emph.end type="italics"/>
                  ad circulum totum. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note442"/>
                  LIBER.
                    <lb/>
                  TERTIUS.</s>
                </p>
                <p type="main">
                  <s>Hæc ita ſe habent, ex Hypotheſi quod Nodus horis ſingulis in
                    <lb/>
                  locum priorem retrahitur, lic ut Sol anno toto completo ad No­
                    <lb/>
                  dum eundem redeat a quo ſub initio digreſſus fuerat. </s>
                  <s>Verum per
                    <lb/>
                  motum Nodi fit ut Sol citius ad Nodum revertatur, & compu­
                    <lb/>
                  tanda jam eſt abbreviatio temporis. </s>
                  <s>Cum Sol anno toto conficiat
                    <lb/>
                  360 gradus, & Nodus motu maximo eodem tempore conficeret
                    <lb/>
                  39
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  38′. </s>
                  <s>7″. </s>
                  <s>50′, ſeu 39,6355 gradus; & motus mediocris. </s>
                  <s>Nodi
                    <lb/>
                  in loco quovis
                    <emph type="italics"/>
                  N
                    <emph.end type="italics"/>
                  ſit ad ipſius motum mediocrem in Quadraturis
                    <lb/>
                  ſuis, ut
                    <emph type="italics"/>
                  AZq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ATq
                    <emph.end type="italics"/>
                  : erit motus Solis ad motum Nodi in
                    <emph type="italics"/>
                  N,
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                  360
                    <emph type="italics"/>
                  ATq
                    <emph.end type="italics"/>
                  ad 39,6355
                    <emph type="italics"/>
                  AZq
                    <emph.end type="italics"/>
                  ; id eſt, ut 9,0827646
                    <emph type="italics"/>
                  ATq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                    <expan abbr="AZq.">AZque</expan>
                    <emph.end type="italics"/>
                    <lb/>
                  Unde ſi circuli totius circumferentia
                    <emph type="italics"/>
                  NAn
                    <emph.end type="italics"/>
                  dividatur in particu­
                    <lb/>
                  las æquales
                    <emph type="italics"/>
                  Aa,
                    <emph.end type="italics"/>
                  tempus quo Sol percurrat particulam
                    <emph type="italics"/>
                  Aa,
                    <emph.end type="italics"/>
                  ſi cir­
                    <lb/>
                  culus quieſceret, erit ad tempus quo percurrit eandem parti­
                    <lb/>
                  culam, ſi circulus una cum Nodis circa centrum
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  revolvatur,
                    <lb/>
                  reciproce ut 9,0827646
                    <emph type="italics"/>
                    <expan abbr="ATq.">ATque</expan>
                    <emph.end type="italics"/>
                  ad 9,0827646
                    <emph type="italics"/>
                    <expan abbr="ATq+AZq.">ATq+AZque</expan>
                    <emph.end type="italics"/>
                  Nam
                    <lb/>
                  tempus eſt reciproce ut velocitas qua particula percurritur, &
                    <lb/>
                  hæc velocitas eſt ſumma velocitatum Solis & Nodi. </s>
                  <s>Igitur ſi tem­
                    <lb/>
                  pus, quo Sol abſque motu Nodi percurreret arcum
                    <emph type="italics"/>
                  NA,
                    <emph.end type="italics"/>
                  expo­
                    <lb/>
                  natur per Sectorem
                    <emph type="italics"/>
                  NTA,
                    <emph.end type="italics"/>
                  & particula temporis quo percurreret. </s>
                  <s>
                    <lb/>
                  arcum quam minimum
                    <emph type="italics"/>
                  Aa,
                    <emph.end type="italics"/>
                  exponatur per Sectoris particulam
                    <lb/>
                    <emph type="italics"/>
                  ATa
                    <emph.end type="italics"/>
                  ; & (perpendiculo
                    <emph type="italics"/>
                  aY
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  Nn
                    <emph.end type="italics"/>
                  demiſſo) ſi in
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  capiatur
                    <lb/>
                    <emph type="italics"/>
                  dZ,
                    <emph.end type="italics"/>
                  ejus longitudinis ut ſit rectangulum
                    <emph type="italics"/>
                  dZ
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  ZY
                    <emph.end type="italics"/>
                  ad Sectoris
                    <lb/>
                  particulam
                    <emph type="italics"/>
                  ATa
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AZq
                    <emph.end type="italics"/>
                  ad 9,0827646
                    <emph type="italics"/>
                  ATq+AZq,
                    <emph.end type="italics"/>
                  id eſt, ut
                    <lb/>
                  ſit
                    <emph type="italics"/>
                  dZ
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  ATq
                    <emph.end type="italics"/>
                  ad 9,0827646
                    <emph type="italics"/>
                  ATq+AZq
                    <emph.end type="italics"/>
                  ; rectangu­
                    <lb/>
                  lum
                    <emph type="italics"/>
                  dZ
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  ZY
                    <emph.end type="italics"/>
                  deſignabit decrementum temporis ex motu Nodi
                    <lb/>
                  oriundum, tempore toto quo arcus
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  percurritur. </s>
                  <s>Et ſi pun­
                    <lb/>
                  ctum
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  tangit Curvam
                    <emph type="italics"/>
                  NdGn,
                    <emph.end type="italics"/>
                  area curvilinea
                    <emph type="italics"/>
                  NdZ
                    <emph.end type="italics"/>
                  erit decre­
                    <lb/>
                  mentum totum, quo tempore arcus totus
                    <emph type="italics"/>
                  NA
                    <emph.end type="italics"/>
                  percurritur; &
                    <lb/>
                  propterea exceſſus Sectoris
                    <emph type="italics"/>
                  NAT
                    <emph.end type="italics"/>
                  ſupra aream
                    <emph type="italics"/>
                  NdZ
                    <emph.end type="italics"/>
                  erit tempus
                    <lb/>
                  illud totum. </s>
                  <s>Et quoniam motus Nodi tempore minore minor eſt
                    <lb/>
                  in ratione temporis, debebit etiam area
                    <emph type="italics"/>
                  AaYZ
                    <emph.end type="italics"/>
                  diminui in eadem
                    <lb/>
                  ratione. </s>
                  <s>Id quod fiet ſi capiatur in
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  longitudo
                    <emph type="italics"/>
                  eZ,
                    <emph.end type="italics"/>
                  quæ ſit
                    <lb/>
                  ad longitudinem
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AZq
                    <emph.end type="italics"/>
                  ad 9,0827646
                    <emph type="italics"/>
                    <expan abbr="ATq+AZq.">ATq+AZque</expan>
                    <emph.end type="italics"/>
                  Sic
                    <lb/>
                  enim rectangulum
                    <emph type="italics"/>
                  eZ
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  ZY
                    <emph.end type="italics"/>
                  erit ad aream
                    <emph type="italics"/>
                  AZYa
                    <emph.end type="italics"/>
                  ut decremen­
                    <lb/>
                  tum temporis quo arcus
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  percurritur, ad tempus totum quo
                    <lb/>
                  percurreretur ſi Nodus quieſceret: Et propterea rectangulum illud
                    <lb/>
                  reſpondebit decremento motus Nodi. </s>
                  <s>Et ſi punctum
                    <emph type="italics"/>
                  e
                    <emph.end type="italics"/>
                  tangat </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum