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

Page concordance

< >
Scan Original
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
< >
page |< < of 145 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="063/01/025.jpg"/>
              les FM, PA. </s>
              <s>Cùm
                <expan abbr="itaq;">itaque</expan>
              angulus OMF ſit grad. 33. prim. 30.
                <lb/>
              ſemiſſis nimirum anguli externi NOM grad. 67: & angulus
                <lb/>
              OMA grad: 78. prim: 30; quòd æquales ſint arcus AM. FC:
                <lb/>
              ablato angulo OMF ex OMA, erit angulus reliquus FMA,
                <lb/>
              hoc eſt illi æqualis FPA grad: 45. </s>
              <s>Cùm
                <expan abbr="itaq;">itaque</expan>
              angulus FIC ſit
                <lb/>
                <expan abbr="quoq;">quoque</expan>
              oſtenſus grad. 45, erit angulus FIC externus æqualis
                <lb/>
              angulo interno FPI: quod eſt abſurdum. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              THEOREMA III.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
                <emph type="italics"/>
              Lapſus grauium in ſegmento
                <lb/>
              Circuli minore, quàm grad: 90. eſt velocior per duas chordas, quàm per
                <lb/>
              unam chordam.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Moueatur graue ex B in F per arcum grad: 45. </s>
              <s>Dico veloci­
                <lb/>
              ùs moueri per duas chordas BC. CF, quàm per unam chordam
                <lb/>
              BF. </s>
              <s>Supponatur BC æqualis CF: & ducatur FQ parallela BC:
                <lb/>
              in productâ verò BC ſumatur BT æqualis
                <expan abbr="Fq.">Fque</expan>
              erit
                <expan abbr="itaq;">itaque</expan>
              BT
                <lb/>
              partium 11111400, & BC partium 3901806. </s>
              <s>Quâ ablatâ ex
                <lb/>
              BT manet CT partium 7209594. </s>
              <s>Adde Logaritmum huius
                <lb/>
              logaritmo anguli CTH grad. 67. prim. 30; qui per lemma eſt
                <lb/>
              complementum anguli FCT grad: 22. prim. 30.
                <expan abbr="eritq;">eritque</expan>
              aggre­
                <lb/>
              gatum logaritmus lateris CH partium 6659688. </s>
              <s>Eſt autem
                <lb/>
              CH maius latere BC, ſeu CF partium 3901806. </s>
              <s>Cùm
                <expan abbr="itaq;">itaque</expan>
              ,
                <lb/>
              motus ex C in H ſit æqualis duratione motui ex C in T, per pri:
                <lb/>
              theorema huius; erit mot
                <emph type="sup"/>
              9
                <emph.end type="sup"/>
              in CF minor duratione motu in CH:
                <lb/>
              additoque communi motu in BC, motus in BC, CF minor du­
                <lb/>
              ratione motu in BT ſeu
                <expan abbr="Fq.">Fque</expan>
              hoc eſt per prop. 15. illi æquali
                <lb/>
              motu in BF. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              THEOREMA IV.
                <emph.end type="center"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum