Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
361
361 		362
362
363
363 		364
364
365
365 		366
366
367
367 		368
368
369
369 		370
370
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/367.jpg" pagenum="339"/>
                  panſionem mediocrem quam pars illa habet in loco ſuo primo
                    <lb/>
                    <arrow.to.target n="note347"/>
                    <emph type="italics"/>
                  EG,
                    <emph.end type="italics"/>
                  ut V-
                    <emph type="italics"/>
                  IM
                    <emph.end type="italics"/>
                  ad V in itu, utque V+
                    <emph type="italics"/>
                  im
                    <emph.end type="italics"/>
                  ad V in reditu. </s>
                  <s>Unde
                    <lb/>
                  vis elaſtica puncti
                    <emph type="italics"/>
                  F
                    <emph.end type="italics"/>
                  in loco
                    <foreign lang="grc">εγ</foreign>
                  , eſt ad vim ejus elaſticam medio­
                    <lb/>
                  crem in loco
                    <emph type="italics"/>
                  EG,
                    <emph.end type="italics"/>
                  ut (I/V-
                    <emph type="italics"/>
                  IM
                    <emph.end type="italics"/>
                  ) ad I/V in itu, in reditu vero ut
                    <lb/>
                  (I/V+
                    <emph type="italics"/>
                  im
                    <emph.end type="italics"/>
                  ) ad I/V. </s>
                  <s>Et eodem argumento vires elaſticæ punctorum
                    <lb/>
                  Phyſieorum
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  in itu, ſunt ut (I/V-
                    <emph type="italics"/>
                  HL
                    <emph.end type="italics"/>
                  ) & (I/V-
                    <emph type="italics"/>
                  KN
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  ad I/V; & virium differentia ad Medii vim elaſticam mediocrem,
                    <lb/>
                  ut (
                    <emph type="italics"/>
                  HL-KN
                    <emph.end type="italics"/>
                  /VV-VX
                    <emph type="italics"/>
                  HL
                    <emph.end type="italics"/>
                  -VX
                    <emph type="italics"/>
                  KN+HLXKN
                    <emph.end type="italics"/>
                  ) ad I/V. </s>
                  <s>Hoc eſt, ut
                    <lb/>
                  (
                    <emph type="italics"/>
                  HL-KN
                    <emph.end type="italics"/>
                  /VV) ad I/V, ſive ut
                    <emph type="italics"/>
                  HL-KN
                    <emph.end type="italics"/>
                  ad V, ſi modo (ob angu­
                    <lb/>
                  ſtos limites vibrationum) ſupponamus
                    <emph type="italics"/>
                  HL
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  KN
                    <emph.end type="italics"/>
                  indefinite
                    <lb/>
                  minores eſſe quantitate V. </s>
                  <s>Quare cum quantitas V detur, diffe­
                    <lb/>
                  rentia virium eſt ut
                    <emph type="italics"/>
                  HL-KN,
                    <emph.end type="italics"/>
                  hoc eſt (ob proportionales
                    <lb/>
                    <emph type="italics"/>
                  HL-KN
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  HK,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  OM
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OI
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  OP,
                    <emph.end type="italics"/>
                  dataſque
                    <emph type="italics"/>
                  HK
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <emph type="italics"/>
                  OP
                    <emph.end type="italics"/>
                  ) ut
                    <emph type="italics"/>
                  OM
                    <emph.end type="italics"/>
                  ; id eſt, ſi
                    <emph type="italics"/>
                  Ff
                    <emph.end type="italics"/>
                  biſecetur in
                    <foreign lang="grc">Ω</foreign>
                  , ut
                    <foreign lang="grc">Ωφ. </foreign>
                  </s>
                  <s>Et eodem
                    <lb/>
                  argumento differentia virium elaſticarum punctorum Phyſieorum
                    <lb/>
                    <foreign lang="grc">ε</foreign>
                  &
                    <foreign lang="grc">γ</foreign>
                  , in reditu lineolæ Phyſicæ
                    <foreign lang="grc">εγ</foreign>
                  eſt ut
                    <foreign lang="grc">Ωφ. </foreign>
                  </s>
                  <s>Sed differentia
                    <lb/>
                  illa (id eſt, exceſſus vis elaſticæ puncti
                    <foreign lang="grc">ε</foreign>
                  ſupra vim elaſticam pun­
                    <lb/>
                  cti
                    <foreign lang="grc">γ</foreign>
                  ,) eſt vis qua interjecta Medii lineola Phyſica
                    <foreign lang="grc">εγ</foreign>
                  acceleratur;
                    <lb/>
                  & propterea vis acceleratrix lineolæ Phyſicæ
                    <foreign lang="grc">εγ</foreign>
                  , eſt ut ipſius di­
                    <lb/>
                  ſtantia a medio vibrationis loco
                    <foreign lang="grc">Ω. </foreign>
                  </s>
                  <s>Proinde tempus (per Prop. </s>
                  <s>
                    <lb/>
                  XXXVIII. Lib. </s>
                  <s>1.) recte exponitur per arcum
                    <emph type="italics"/>
                  PI
                    <emph.end type="italics"/>
                  ; & Medii pars
                    <lb/>
                  linearis
                    <foreign lang="grc">εγ</foreign>
                  lege præſcripta movetur, id eſt, lege oſcillantis Pen­
                    <lb/>
                  duli: eſtque par ratio partium omnium linearium ex quibus Me­
                    <lb/>
                  dium totum componitur.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note347"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Hinc patet quod numerus pulſuum propagatorum idem
                    <lb/>
                  ſit cum numero vibrationum corporis tremuli, neque multiplica­
                    <lb/>
                  tur in eorum progreſſu. </s>
                  <s>Nam lineola Phyſica
                    <foreign lang="grc">εγ</foreign>
                  , quamprimum
                    <lb/>
                  ad locum ſuum primum redierit, quieſcet; neQ.E.D.inceps move­
                    <lb/>
                  bitur, niſi vel ab impetu corporis tremuli, vel ab impetu pulſuum
                    <lb/>
                  qui a corpore tremulo propagantur, motu novo cieatur. </s>
                  <s>Quie­
                    <lb/>
                  ſcet igitur quamprimum pulſus a corpore tremulo propagari
                    <lb/>
                  deſinunt. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum