Fabri, Honoré, Tractatus physicus de motu locali, 1646

Page concordance

< >
Scan Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N15AC3">
            <p id="N16D2F" type="main">
              <s id="N16D42">
                <pb pagenum="94" xlink:href="026/01/126.jpg"/>
              pla illius, quæ ſit poſt vnum inſtans motus, & quæ fit poſt tria tripla, poſt
                <lb/>
              4. quadrupla, atque ita deinceps; cùm enim æqualibus temporibus æqua­
                <lb/>
              lia acquirantur velocitatis momenta, id eſt æquales impetus, impetus
                <lb/>
              erunt vt tempora, percuſſiones vt impetus, igitur percuſſiones vt tem­
                <lb/>
              pora. </s>
            </p>
            <p id="N16D55" type="main">
              <s id="N16D57">Dixi in primo inſtanti contactus; nam reuerâ ſecundò inſtanti con­
                <lb/>
              tactus, niſi fiat reflexio, augetur vis ictus, quia cauſa neceſſaria eſt ap­
                <lb/>
              plicata. </s>
            </p>
            <p id="N16D5F" type="main">
              <s id="N16D61">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              55.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16D6D" type="main">
              <s id="N16D6F">
                <emph type="italics"/>
              Hinc poſſunt comparari duæ percuſſiones duorum grauium inæqualium
                <lb/>
              dum cadunt deorſum
                <emph.end type="italics"/>
              ; </s>
              <s id="N16D7A">ſi enim cadunt æqualibus temporibus, percuſſio­
                <lb/>
              nes erunt vt corpora ſeu grauitates, vt patet v.g. corpus 2. librarum poſt
                <lb/>
              2. inſtantia motus infligit duplam percuſſionem illius, quam infligit cor­
                <lb/>
              pus vnius libræ poſt 2. inſtantia motus; </s>
              <s id="N16D86">ſi verò tempora motus ſunt inæ­
                <lb/>
              qualia, & grauitates æquales, percuſſiones erunt vt tempora; </s>
              <s id="N16D8C">ſi demum
                <lb/>
              grauitates inæquales, & tempora motus inæqualia, percuſſiones erunt
                <lb/>
              in ratione compoſita ex ratione grauitatum & temporum, quæ omnia
                <lb/>
              patent ex dictis in Th. ſuperioribus, v. g. ſit corpus duarum librarum,
                <lb/>
              & alterum trium librarum; </s>
              <s id="N16D9C">primum moueatur per 5. inſtantia, & ſecun­
                <lb/>
              dum 2.per 5. ratio grauitatum eſt 3/2; </s>
              <s id="N16DA2">ratio temporum eſt 7/5; </s>
              <s id="N16DA6">compoſita
                <lb/>
              ex vtraque erit (21/10); & hæc eſt ratio percuſſionum. </s>
            </p>
            <p id="N16DAC" type="main">
              <s id="N16DAE">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              56.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16DBA" type="main">
              <s id="N16DBC">
                <emph type="italics"/>
              Hinc poteſt ſciri ratio percuſſionis. </s>
              <s id="N16DC1">& grauitationis eiuſdem mobilis in pri­
                <lb/>
              mo inſtanti vtriuſque, ſi cognoſcatur numerus inſtantium motus
                <emph.end type="italics"/>
              ; </s>
              <s id="N16DCA">cum enim
                <lb/>
              ſingulis inſtantibus æqualis impetus accedat, vt ſæpè dictum eſt; </s>
              <s id="N16DD0">certè
                <lb/>
              erit percuſſio ad grauitationem, vt numerus inſtantium motus ad vnita­
                <lb/>
              tem, v.g. grauitatio ſit vt 4.ſitq́ue motus eiuſdem corporis per 8. inſtan­
                <lb/>
              tia; percuſſio erit ad grauitationem, vt 32. ad 4.vel vt 8.ad 1.quæ om­
                <lb/>
              nia conſtant ex dictis. </s>
            </p>
            <p id="N16DDE" type="main">
              <s id="N16DE0">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              57.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16DEC" type="main">
              <s id="N16DEE">
                <emph type="italics"/>
              Hinc data percuſſione, ſi cognoſceretur probè numerus inſtantium motus,
                <lb/>
              dari poſſet grauitatio ipſi æqualis
                <emph.end type="italics"/>
              ; </s>
              <s id="N16DF9">v.g. ſit percuſſio dati corporis cadentis
                <lb/>
              per 8.inſtantia, eius percuſſio eſt octupla grauitationis eiuſdem per Th.
                <lb/>
              56. igitur ſi detur grauitatio octupla huius, erit æqualis datæ percuſ­
                <lb/>
              ſioni; dabitur autem grauitatio octupla, ſi detur corpus eiuſdem mate­
                <lb/>
              riæ octuplò grauius, vt conſtat. </s>
            </p>
            <p id="N16E08" type="main">
              <s id="N16E0A">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              38.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16E16" type="main">
              <s id="N16E18">
                <emph type="italics"/>
              Hinc primo inſtanti grauitationis nullum ferè ſentitur pondus,
                <emph.end type="italics"/>
              quia mini­
                <lb/>
              ma vis eſt, quæ conſequentibus inſtantibus augetur, hinc licèt corpus
                <lb/>
              breui tempore quis ſuſtineat, paulò poſt tamen ponderi cedit, ratio eſt
                <lb/>
              clara ex dictis. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum