Newton, Isaac, Philosophia naturalis principia mathematica, 1713
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/155.jpg" pagenum="127"/>
                  nitum diminutam, rationes ultimæ erunt RGG ad T
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  ut-FF
                    <lb/>
                    <arrow.to.target n="note103"/>
                  ad-3TT ſeu GG ad TT ut FF ad 3TT & viciſſim GG ad
                    <lb/>
                  FF ut TT ad 3 TT id eſt, ut 1 ad 3; adeoque G ad F,
                    <lb/>
                  hoc eſt angulus
                    <emph type="italics"/>
                  VCp
                    <emph.end type="italics"/>
                  ad angulum
                    <emph type="italics"/>
                  VCP,
                    <emph.end type="italics"/>
                  ut 1 ad √3. Er­
                    <lb/>
                  go cum corpus in Ellipſi immobili, ab Apſide ſumma ad Ap­
                    <lb/>
                  ſidem imam deſcendendo conficiat angulum
                    <emph type="italics"/>
                  VCP
                    <emph.end type="italics"/>
                  (ut ita di­
                    <lb/>
                  cam) gradum 180; corpus aliud in Ellipſi mobili, atque adeo in
                    <lb/>
                  Orbe immobili de quo agimus, ab Apſide ſumma ad Apſidem
                    <lb/>
                  imam deſcendendo conficiet angulum
                    <emph type="italics"/>
                  VCp
                    <emph.end type="italics"/>
                  gradum (180/√3): id
                    <lb/>
                  adeo ob ſimilitudinem Orbis hujus, quem corpus agente uniformi
                    <lb/>
                  vi centripeta deſcribit, & Orbis illius quem corpus in Ellipſi re­
                    <lb/>
                  volvente gyros peragens deſcribit in plano quieſcente. </s>
                  <s>Per ſu­
                    <lb/>
                  periorem terminorum collationem ſimiles redduntur hi Orbes, non
                    <lb/>
                  univerſaliter, ſed tunc cum ad formam circularem quam maxime
                    <lb/>
                  appropinquant. </s>
                  <s>Corpus igitur uniformi cum vi centripeta in
                    <lb/>
                  Orbe propemodum circulari revolvens, inter Apſidem ſummam
                    <lb/>
                  & Apſidem imam conficiet ſemper angulum (180/√3) graduum, ſeu
                    <lb/>
                  103
                    <emph type="italics"/>
                  gr.
                    <emph.end type="italics"/>
                  55
                    <emph type="italics"/>
                  m.
                    <emph.end type="italics"/>
                  23
                    <emph type="italics"/>
                  ſec.
                    <emph.end type="italics"/>
                  ad centrum; perveniens ab Apſide ſumma ad
                    <lb/>
                  Apſidem imam ubi ſemel confecit hunc angulum, & inde ad Apſi­
                    <lb/>
                  dem ſummam rediens ubi iterum confecit eundem angulum; &
                    <lb/>
                  ſic deinceps in infinitum. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note103"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Exempl.
                    <emph.end type="italics"/>
                  2. Ponamus vim centripetam eſſe ut altitudinis A dig­
                    <lb/>
                  nitas quælibet A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -3
                    <emph.end type="sup"/>
                  ſeu (A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  /A
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  ): ubi
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -3 &
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  ſignificant digNI­
                    <lb/>
                  tatum indices quoſcunQ.E.I.tegros vel fractos, rationales vel irratio­
                    <lb/>
                  nales, affirmativos vel negativos. </s>
                  <s>Numerator ille A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ſeu —T-X
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                    <lb/>
                  in ſeriem indeterminatam per Methodum noſtram Serierum conver­
                    <lb/>
                  gentium reducta, evadit T
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  -
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  XT
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  +(
                    <emph type="italics"/>
                  nn-n
                    <emph.end type="italics"/>
                  /2)XXT
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -2
                    <emph.end type="sup"/>
                  &c. </s>
                  <s>
                    <lb/>
                  Et collatis hujus terminis cum terminis Numeratoris alterius
                    <lb/>
                  RGG-RFF+TFF-FFX, fit RGG-RFF+TFF ad T
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                    <lb/>
                  ut-FF ad-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  T
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  +(
                    <emph type="italics"/>
                  nn-n
                    <emph.end type="italics"/>
                  /2)XT
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -2
                    <emph.end type="sup"/>
                  &c. </s>
                  <s>Et ſumendo ratio­
                    <lb/>
                  nes ultimas ubi Orbes ad formam circularem accedunt, fit RGG
                    <lb/>
                  ad T
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ut-FF ad-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  T
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  , ſeu GG ad T
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  ut FF ad
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  T
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  ,
                    <lb/>
                  & viciſſim GG ad FF ut T
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  ad
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  T
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  id eſt ut 1 ad
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  adeoque G ad F, id eſt angulus
                    <emph type="italics"/>
                  VCp
                    <emph.end type="italics"/>
                  ad angulum
                    <emph type="italics"/>
                  VCP,
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum