Fabri, Honoré, Tractatus physicus de motu locali, 1646

List of thumbnails

< >
11
11 		12
12
13
13 		14
14
15
15 		16
16
17
17 		18
18
19
19 		20
20
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N1A407">
            <p id="N1A5D4" type="main">
              <s id="N1A5D6">
                <pb pagenum="155" xlink:href="026/01/187.jpg"/>
              bile in A, ſitque impetus per AB, & alter æqualis per AD, motus mixtus
                <lb/>
              fiet per AE, aſſumpta ſcilicet DE æquali, & parallela AB, quod probatur
                <lb/>
              per Th.137.l.1. </s>
            </p>
            <p id="N1A5E9" type="main">
              <s id="N1A5EB">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              2.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1A5F8" type="main">
              <s id="N1A5FA">
                <emph type="italics"/>
              Linea AE eſt diagonalis quadrati, quotieſcumque vterque impetus eſt æ­
                <lb/>
              qualis, & lineæ determinationum decuſſantur ad angulos rectos
                <emph.end type="italics"/>
              ; probatur per
                <lb/>
              idem Th.137. </s>
            </p>
            <p id="N1A608" type="main">
              <s id="N1A60A">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              3.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1A617" type="main">
              <s id="N1A619">
                <emph type="italics"/>
              Hinc deſtruitur aliquid impetus
                <emph.end type="italics"/>
              ; </s>
              <s id="N1A622">alioquin motus eſſet duplus cuiuſli­
                <lb/>
              bet ſeorſim ſumpti, quod falſum eſt; </s>
              <s id="N1A628">nam motus ſunt vt lineæ ſed diago­
                <lb/>
              nalis quadrati non eſt dupla lateris; hoc etiam probatur per Th. 141.
                <lb/>
              & 142.l.1. </s>
            </p>
            <p id="N1A630" type="main">
              <s id="N1A632">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              4.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1A63F" type="main">
              <s id="N1A641">
                <emph type="italics"/>
              Motus mixtus ex duobus æquabilibus inæqualibus est etiam rectus
                <emph.end type="italics"/>
              ; ſit
                <lb/>
              enim mobile in A eadem figura ſitque impetus per AC, & alter ſubdu­
                <lb/>
              plus prioris per AD, motus fiet per AF ducta DF æquali, & parallela AC,
                <lb/>
              quod probatur per Th.137.l.1. </s>
            </p>
            <p id="N1A651" type="main">
              <s id="N1A653">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              5.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1A660" type="main">
              <s id="N1A662">
                <emph type="italics"/>
              Linea AF eſt diagonalis rectanguli, quotieſcunque lineæ determinationum
                <lb/>
              decuſſantur ad angulos rectos
                <emph.end type="italics"/>
              ; probatur per idem Th.137. </s>
            </p>
            <p id="N1A66E" type="main">
              <s id="N1A670">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              6.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1A67D" type="main">
              <s id="N1A67F">
                <emph type="italics"/>
              Hinc deſtruitur aliquid impetus per Th.
                <emph.end type="italics"/>
              141. & 142.
                <emph type="italics"/>
              l.
                <emph.end type="italics"/>
              1. idque pro rata
                <lb/>
              ne aliquid ſit fruſtrà per Ax.2. & ſæpè iam probatum eſt. </s>
            </p>
            <p id="N1A68F" type="main">
              <s id="N1A691">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              7.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1A69D" type="main">
              <s id="N1A69F">
                <emph type="italics"/>
              Hinc determinari poteſt portio vtriuſque impetus destructi,
                <emph.end type="italics"/>
              v.g. ſi ſint æ­
                <lb/>
              quales, portio detracta vtrique æqualibus temporibus eſt differentia
                <lb/>
              diagonalis & compoſitæ ex DA, AB, quod clarum eſt; ſi vero impetus
                <lb/>
              ſint inæquales, portio deſtructa erit ſemper differentia diagonalis, v.g.
                <lb/>
              AF & compoſitæ ex AC.AD. </s>
            </p>
            <p id="N1A6B3" type="main">
              <s id="N1A6B5">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              8.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1A6C1" type="main">
              <s id="N1A6C3">
                <emph type="italics"/>
              Aliquando impetus qui remanet in motu mixto est rationalis
                <emph.end type="italics"/>
              ; </s>
              <s id="N1A6CC">id eſt habet
                <lb/>
              proportionem ad vtrumque, quæ appellari poteſt, aliquando ad neutrum,
                <lb/>
                <expan abbr="aliquãdo">aliquando</expan>
              ad alterutrum; </s>
              <s id="N1A6D7">ad vtrumque v.g. ſi alter impetuum ſit 8.alter 6.
                <lb/>
              haud dubiè linea motus mixti erit 10. ad neutrum vt in diagonali qua­
                <lb/>
              drati, & in multis aliis; </s>
              <s id="N1A6E1">ad alterum denique v. g. ſi alter ſit ſubduplus la­
                <lb/>
              teris æquilateri; alter verò eiuſdem perpendicularis; nam diagonalis, ſeu
                <lb/>
              linea motus mixti erit latus ipſum æquilateri. </s>
            </p>
            <p id="N1A6ED" type="main">
              <s id="N1A6EF">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              9.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1A6FB" type="main">
              <s id="N1A6FD">
                <emph type="italics"/>
              Si lineæ determinationum decuſſentur ad angulum obtuſum, ſintque æqua­
                <lb/>
              les impetus, linea motus mixti erit diagonalis Rhombi
                <emph.end type="italics"/>
              ; </s>
              <s id="N1A708">vt patet per Th.140.
                <lb/>
              l.1. poteſt autem hæc diagonalis eſſe vel æqualis alteri laterum, vel ma-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum