Fabri, Honoré, Tractatus physicus de motu locali, 1646

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 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N270EE">
            <p id="N296BC" type="main">
              <s id="N296DC">
                <pb pagenum="422" xlink:href="026/01/456.jpg"/>
              def.5. igitur centrum percuſſionis eſt idem cum centro grauitatis, quod
                <lb/>
              erat dem. </s>
            </p>
            <p id="N296E8" type="main">
              <s id="N296EA">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              1.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N296F7" type="main">
              <s id="N296F9">Hinc quatuor centra concurrunt in idem punctum, ſcilicet magni­
                <lb/>
              tudinis, grauitatis, impreſſionis, & percuſſionis. </s>
            </p>
            <p id="N296FE" type="main">
              <s id="N29700">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              2.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N2970D" type="main">
              <s id="N2970F">Idem prorſus dicendum eſt de Rectangulo, Parallelogrammate, Cir­
                <lb/>
              culo, Ellipſi, Cylindro, Priſmate, Parallelipedo, Sphæra, &c. </s>
              <s id="N29714">in quibus
                <lb/>
              poſito motu recto, hæc quatuor centra in eodem plano, immò & linea
                <lb/>
              reperiuntur. </s>
            </p>
            <p id="N2971B" type="main">
              <s id="N2971D">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              2.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N2972A" type="main">
              <s id="N2972C">
                <emph type="italics"/>
              Si planum triangulare cadat motu recto deorſum, v.g. horizonti paralle­
                <lb/>
              lum, centrum percuſſionis eſt idem cum centro grauitatis eiuſdem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N29737" type="main">
              <s id="N29739">Sit enim triangulare planum FBH, cuius centrum grauitatis ſit I: </s>
              <s id="N2973D">
                <lb/>
              dico eſſe centrum percuſſionis; </s>
              <s id="N29742">quia, cùm ſit æqualis motus, & impetus
                <lb/>
              omnium partium plani, ſi ſuſtineatur in I, ſtat in æquilibrio, per def.1.
                <lb/>
              igitur totus impetus impeditur; igitur eſt maxima percuſſio, per
                <lb/>
              Poſ. 2. </s>
            </p>
            <p id="N2974F" type="main">
              <s id="N29751">
                <emph type="center"/>
                <emph type="italics"/>
              Scholium.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N2975D" type="main">
              <s id="N2975F">Obſeruabis punctum I poſſe haberi duobus modis; </s>
              <s id="N29763">Primò, ſi ducatur
                <lb/>
              FC diuidens æqualiter HB; </s>
              <s id="N29769">diuidit etiam æqualiter GA, & omnes alias
                <lb/>
              parallelas HB; </s>
              <s id="N2976F">igitur in FC eſt centrum grauitatis: </s>
              <s id="N29773">ſimiliter ducatur
                <lb/>
              HD diuidens æqualiter FB, centrum grauitatis erit etiam in HD; </s>
              <s id="N29779">igi­
                <lb/>
              tur in communi puncto I. Secundò, ita diuidatur FH in G, vt FG ſit
                <lb/>
              dupla GH, ducaturque GA: </s>
              <s id="N29781">ſimiliter ducatur KE diuidens HB eodem
                <lb/>
              modo, punctum communis ſectionis I eſt centrum grauitatis; </s>
              <s id="N29787">quippe
                <lb/>
              duo triangula DIC, FIH ſunt proportionalia; </s>
              <s id="N2978D">igitur vt DC ad FH,
                <lb/>
              ita DI ad IH, ſed DC eſt ſubdupla FH; </s>
              <s id="N29793">igitur DI ſubdupla IH: </s>
              <s id="N29797">ſimi­
                <lb/>
              liter IC ſubdupla IF; </s>
              <s id="N2979D">igitur GH ſubdupla GF; igitur inuentum eſt
                <lb/>
              centrum grauitatis, quod erat faciendum. </s>
            </p>
            <p id="N297A3" type="main">
              <s id="N297A5">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              3.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N297B2" type="main">
              <s id="N297B4">
                <emph type="italics"/>
              Si planum triangulare cadat parallelum lineæ verticali,
                <emph.end type="italics"/>
              v. g. in ſitu FH
                <lb/>
              B, ita vt FH ſit parallela horizonti, centrum percuſſionis eſt in G; </s>
              <s id="N297C3">cùm
                <lb/>
              enim GA ducatur per centrum grauitatis I, ſitque parallela HB, eſt
                <lb/>
              linea directionis, per def.4. igitur ſi ſuſtineatur in G, ſtabit in æquili­
                <lb/>
              brio, per p.5. igitur totus impetus impeditur, vt patet; igitur eſt maxi­
                <lb/>
              ma percuſſio per p. </s>
              <s id="N297CF">2. igitur centrum percuſſionis eſt G, quod erat de­
                <lb/>
              monſt. </s>
            </p>
            <p id="N297D4" type="main">
              <s id="N297D6">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              1.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N297E3" type="main">
              <s id="N297E5">Hinc corpus ſolidum ex multis huiuſmodi triangulis æqualibus quaſi
                <lb/>
              conflatum, idem prorſus percuſſionis centrum habet; ſiue cadat lineæ
                <lb/>
              verticali parallelum, ſiue ipſi verticali. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum