Fabri, Honoré, Tractatus physicus de motu locali, 1646

Page concordance

< >
Scan Original
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N1137F">
            <pb pagenum="46" xlink:href="026/01/078.jpg"/>
            <p id="N13FB0" type="main">
              <s id="N13FB2">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              76.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N13FBE" type="main">
              <s id="N13FC0">
                <emph type="italics"/>
              Extenſio impetus respondet extentioni ſui ſubiecti, ſcilicet mobilis
                <emph.end type="italics"/>
              ; </s>
              <s id="N13FC9">cum
                <lb/>
              enim extra ſubjectum eſſe non poſſit, cum ſit qualitas; </s>
              <s id="N13FCF">certè ibi eſt, vbi
                <lb/>
              ſubjectum eſt; nam penetratur accidens cum ipſo
                <expan abbr="ſujecto">ſubjecto</expan>
              . </s>
            </p>
            <p id="N13FD9" type="main">
              <s id="N13FDB">
                <emph type="center"/>
                <emph type="italics"/>
              Scolium.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N13FE7" type="main">
              <s id="N13FE9">Obſeruabis qualitatem omnem ita ſuo ſubjecto coëxtendi, vt æqua­
                <lb/>
              lem omnino quodlibet eius punctum, ſeu pars extentionem habeat ex­
                <lb/>
              tentioni puncti, ſeu partis ſui ſubjecti; </s>
              <s id="N13FF1">nec enim aliud eſt, vnde poſſit
                <lb/>
              determinari extentio qualitatum, præter ipſam extenſionem ſubjecti; </s>
              <s id="N13FF7">
                <lb/>
              quod maximè in impetu videre eſt, cuius partes in mobili denſo minori
                <lb/>
              extentioni ſubjacent, quàm in mobili raro; </s>
              <s id="N13FFE">cum ex maiore ictu ſeu per­
                <lb/>
              cuſſione in mobili denſo plures impetus agentis partes eſſe conſtet; quia
                <lb/>
              ſcilicet ſunt plures partes ſubiecti. </s>
            </p>
            <p id="N14006" type="main">
              <s id="N14008">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              77.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N14014" type="main">
              <s id="N14016">
                <emph type="italics"/>
              Datur impetus altero impetu perfectior ſecundum entitatem
                <emph.end type="italics"/>
              ; dixi ſecun­
                <lb/>
              dum entitatem; </s>
              <s id="N14021">quia iam dictum eſt ſuprà dari perfectiorem ſecundum
                <lb/>
              intenſionem; </s>
              <s id="N14027">huius Theorematis veritas mihi maximè demonſtranda
                <lb/>
              eſt, ex quo tàm multa infrà deducemus; </s>
              <s id="N1402D">ſic autem probamus; </s>
              <s id="N14031">Quotieſ­
                <lb/>
              cunque mouetur corpus, producuntur ſaltem tot partes impetus quot
                <lb/>
              ſunt partes mobilis per Th. 33. Quotieſcunque producuntur in mobili
                <lb/>
              tot partes impetus quot ſunt in mobili partes ſubjecti, mouetur mobile,
                <lb/>
              modó non impediatur; </s>
              <s id="N1403D">quia poſita cauſa neceſſaria, & non impedita per
                <lb/>
              Ax. 11. ponitur effectus, quod de omni cauſa, ſed de formali potiſſimum
                <lb/>
              dici debet; </s>
              <s id="N14045">præterea datur aliquod pondus, quod data potentia ſine me­
                <lb/>
              chanico organo mouere non poteſt, licèt cum organo facilè moueat; </s>
              <s id="N1404B">hæc
                <lb/>
              hypotheſis certa eſt; </s>
              <s id="N14051">igitur cum mouet, producit tot partes impetus quot
                <lb/>
              ſunt neceſſariæ, vt omnibus partibus mobilis diſtribuantur per idem Th.
                <lb/>
              33. cum verò non mouet, non producit tot partes impetus vt conſtat ex
                <lb/>
              dictis; </s>
              <s id="N1405C">igitur producit plures cum organo in mobili, quàm ſine organo;
                <lb/>
              igitur imperfectiores, quod demonſtro: </s>
              <s id="N14062">ſit enim vectis BF, cuius cen­
                <lb/>
              trum ſeu fulcrum ſit in A, potentia in B, pondus G, quod attollitur in F; </s>
              <s id="N14068">
                <lb/>
              plures partes impetus produci poſſunt in F, vel in E, quàm in B, ſcilicet
                <lb/>
              in ipſo pondere; </s>
              <s id="N1406F">quia pondus quod non poteſt attolli in B, attollitur in
                <lb/>
              E, vel in F, vt patet ex dictis; </s>
              <s id="N14075">præterea punctum F mouetur tardius, quàm
                <lb/>
              B; </s>
              <s id="N1407B">quia motus ſunt vt arcus, arcus vt ſemidiametri, hæ demum vt AF,
                <lb/>
              ad AB; </s>
              <s id="N14081">igitur motus puncti F, eſt tardior, vel imperfectior; </s>
              <s id="N14085">igitur im­
                <lb/>
              petus puncti F, eſt imperfectior impetu puncti B, per Ax. 13 num.4. atqui
                <lb/>
              non eſt imperfectior ratione numeri partium, igitur ratione entitatis,
                <lb/>
              quæ imperfectior eſt; igitur datur impetus altero impetu imperfectior. </s>
            </p>
            <p id="N1408F" type="main">
              <s id="N14091">
                <emph type="center"/>
                <emph type="italics"/>
              Scholium.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1409D" type="main">
              <s id="N1409F">Obſeruabis primò multa hîc ſupponi ſeu deſiderari, quæ pertinent
                <lb/>
              ad propagationem impetus, de quibus infrà; Secundò hoc Theorema </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum