Monantheuil, Henri de, Aristotelis Mechanica, 1599

Page concordance

< >
Scan Original
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
< >
page |< < of 252 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <pb xlink:href="035/01/081.jpg" pagenum="41"/>
              <p type="main">
                <s id="id.000740">Deter.
                  <emph type="italics"/>
                Dico D I eſſe maiorem ipſa A K quæ eſt ſegmentum in
                  <lb/>
                maiori circulo. </s>
                <s id="id.000741">Ante huius fabricam hoc problema eſt
                  <expan abbr="aſſumẽdum">aſſumendum</expan>
                .
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="id.000742">
                  <emph type="italics"/>
                Deſcribere circulum minorem qui alterum datum maiorem
                  <lb/>
                interius tangat.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="id.000743">
                  <emph type="italics"/>
                Sit datus circulus A B K C maior, ab A per D centrum reper­
                  <lb/>
                tum prop. 1. lib. 3. </s>
                <s>ducatur A k diameter. </s>
                <s id="id.000744">Deſcribendus autem ſit eo
                  <lb/>
                minor, cuius accipiatur E
                  <expan abbr="centrũ">centrum</expan>
                  <emph.end type="italics"/>
                  <lb/>
                  <figure id="id.035.01.081.1.jpg" xlink:href="035/01/081/1.jpg" number="16"/>
                  <lb/>
                  <emph type="italics"/>
                inter A & D, & interuallo
                  <lb/>
                E A deſcribatur A F G. </s>
                <s>hic
                  <lb/>
                tanget interius circulum A B k
                  <lb/>
                C datum in puncto A. </s>
                <s id="id.000745">Nam ſi
                  <lb/>
                & ſecet, vt in puncto H, ducta
                  <lb/>
                H E. </s>
                <s>erit æqualis ipſi E A def.
                  <lb/>
                15. lib. 1. non erit igitur E A mi­
                  <lb/>
                nima omnium quæ ab E puncto
                  <lb/>
                extra D centrum circuli A B
                  <lb/>
                K C cadunt in eius concauam pe­
                  <lb/>
                ripheriam, quod eſt contra prop.
                  <lb/>
                7. lib. 3. </s>
                <s>non erat igitur H punctum commune vtrique circulo, &
                  <lb/>
                ſic de alijs. </s>
                <s id="id.000748">Circulus igitur A F G, tangit circulum A B K C
                  <lb/>
                in puncto A prop. 11. lib. 3. </s>
                <s>quod oportuit facere.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="id.000749">
                  <emph type="italics"/>
                Iam nunc de A G maiori ſemidiametro detrahatur portio A H
                  <lb/>
                æqualis D H minori prop. 3. lib. 1. centro H interuallo A H deſ­
                  <lb/>
                cribatur circulus A M L poſtul. 3. qui erit æqualis dato D E F.
                  <lb/>
                def. 1. lib. 3. </s>
                <s>Et tanget intus circulum A B C in puncto A ex probl.
                  <lb/>
                præſumpto. </s>
                <s>per punctum B
                  <expan abbr="ducaeur">ducatur</expan>
                parallela B M prop. 31. lib. 1.
                  <lb/>
                & per eandem parallela M N quæ per 34. lib. eiuſdem cum ſit
                  <lb/>
                æqualis ipſi B K erit & æqualis ipſi. </s>
                <s id="id.000754">E I ax. 1. connectantur M H,
                  <lb/>
                E H poſt. 1.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="id.000757">Demonſt. </s>
                <s>
                  <emph type="italics"/>
                Poſtquam ax. 3. A N, D I æquales ſunt quia reli­
                  <lb/>
                quæ ex æqualibus A H, D H ex fab. demptis æqualibus N H,
                  <lb/>
                I H quæ latera ſunt ſub æqualibus angulis duorum triangulorum
                  <lb/>
                M N H & I E H habentium duos angulos duobus angulis
                  <lb/>
                æquales, & latus lateri æquale vt eſt in 26. prop. lib. 1. </s>
                <s>nempe angu­
                  <lb/>
                lus qui ad N rectus eſt prop. 29. lib. 1. & qui ad I, rectus ex hypoth.
                  <lb/>
                ideo æquales ax. 10. </s>
                <s>tum angulus M H N ad centrum conſtitutus
                  <emph.end type="italics"/>
                </s>
              </p>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum