Marci of Kronland, Johannes Marcus, De proportione motus figurarum recti linearum et circuli quadratura ex motu, 1648

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 145 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="063/01/069.jpg"/>
            <p type="main">
              <s>
                <emph type="center"/>
              THEOREMA XI.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
                <emph type="italics"/>
              Si ne〈qué〉 motus Quadrati, ne〈que〉 huius diameter ad angulos rectos ſe­
                <lb/>
              cet planum, ad angulos inæquales reflectit.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Motus Quadrati
                <emph type="italics"/>
              abcd
                <emph.end type="italics"/>
              obliquè ſecans planum
                <emph type="italics"/>
              gr,
                <emph.end type="italics"/>
              habeat
                <lb/>
              latus
                <emph type="italics"/>
              ad
                <emph.end type="italics"/>
              eidem plano parallelum: & ſit linea hypomochlij
                <emph type="italics"/>
              dg.
                <emph.end type="italics"/>
                <lb/>
              ad eam verò perpendicularis
                <emph type="italics"/>
              eh;
                <emph.end type="italics"/>
              |cuius quadratum grauitas
                <lb/>
              movens centri,
                <expan abbr="atq;">atque</expan>
              huius complementum quadratum
                <emph type="italics"/>
              fi,
                <emph.end type="italics"/>
              pla­
                <lb/>
              ga eiuſdem centri. </s>
              <s>Quod quidem quadratum in ſemicirculo
                <lb/>
                <emph type="italics"/>
              fie
                <emph.end type="italics"/>
              conſtituit chorda reliqua, in quo chorda
                <emph type="italics"/>
              ie
                <emph.end type="italics"/>
              ſit ſumpta æ­
                <lb/>
              qualis
                <emph type="italics"/>
              eh.
                <emph.end type="italics"/>
              Et quia plaga fit per lineas
                <emph type="italics"/>
              ea. ef. ed:
                <emph.end type="italics"/>
              per 4. theo. 2 part.
                <lb/>
              erit per 3 theor: huius, motus reflexus in lineâ
                <emph type="italics"/>
              ek;
                <emph.end type="italics"/>
              motus
                <lb/>
              autem centri in lineâ plano
                <emph type="italics"/>
              qr
                <emph.end type="italics"/>
              parallelâ, ſeu tangente cir culi
                <lb/>
              centro
                <emph type="italics"/>
              f,
                <emph.end type="italics"/>
              & interuallo
                <emph type="italics"/>
              fe
                <emph.end type="italics"/>
              deſcripti. quòd ſi ergo fiat ut
                <emph type="italics"/>
              ci
                <emph.end type="italics"/>
              ad
                <lb/>
                <emph type="italics"/>
              if,
                <emph.end type="italics"/>
              ita
                <emph type="italics"/>
              em
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              ek,
                <emph.end type="italics"/>
              erit per prop: 32 motus medius
                <emph type="italics"/>
              el
                <emph.end type="italics"/>
              diameter
                <lb/>
              parallelogrammi
                <emph type="italics"/>
              kelm:
                <emph.end type="italics"/>
              dico angulum reflexionis
                <emph type="italics"/>
              lem
                <emph.end type="italics"/>
              eſſe in
                <lb/>
              æqualem angulo
                <emph type="italics"/>
              adg.
                <emph.end type="italics"/>
              Quia enim angulus
                <emph type="italics"/>
              afi
                <emph.end type="italics"/>
              externus ma­
                <lb/>
              ior eſt angulo interno
                <emph type="italics"/>
              adh,
                <emph.end type="italics"/>
              æqualis autem angulo
                <emph type="italics"/>
              ief
                <emph.end type="italics"/>
              per 9.
                <lb/>
              theor:
                <expan abbr="atq;">atque</expan>
              huic æquatur angulus
                <emph type="italics"/>
              lem,
                <emph.end type="italics"/>
              propterea quòd ſimilia
                <lb/>
              ſint triangula
                <emph type="italics"/>
              ief, mel:
                <emph.end type="italics"/>
              erit
                <expan abbr="quoq;">quoque</expan>
              æqualis angulo externo
                <lb/>
                <emph type="italics"/>
              afi,
                <emph.end type="italics"/>
              maior verò angulo interno
                <emph type="italics"/>
              fdh
                <emph.end type="italics"/>
              angulo nimirum inci­
                <lb/>
              dentiæ. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              THEOREMA XII.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
                <emph type="italics"/>
              Motus Pentagoni ſecans obliquè planum, ſi latus oppoſitum habeat
                <lb/>
              eidem plano par allelum, ad angulos æquales reflectit.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Pentagonum
                <emph type="italics"/>
              abcde
                <emph.end type="italics"/>
              habeat latus
                <emph type="italics"/>
              cd
                <emph.end type="italics"/>
              plano
                <emph type="italics"/>
              op
                <emph.end type="italics"/>
              parallelum
                <lb/>
              & oppoſitum: dico ad angulos reflecti æquales. </s>
              <s>Sit enim </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum