Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

Page concordance

< >
Scan Original
31 31
32 32
33 33
34 34
35 35
36 36
37 37
38 38
39 39
40 40
41 41
42 42
43 43
44 44
45 45
46 46
47 47
48 48
49 49
50 50
51 51
52
53
54
55 55
56 56
57 57
58 58
59 59
60 60
< >
page |< < (39) of 197 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div191" type="section" level="1" n="140">
          <p>
            <s xml:id="echoid-s1179" xml:space="preserve">
              <pb o="39" file="527.01.039" n="39" rhead="*DE* S*TATICÆ ELEMENTIS*."/>
            deto, ſub duplum æquilibris ponderis ejuſdĕ
              <lb/>
              <figure xlink:label="fig-527.01.039-01" xlink:href="fig-527.01.039-01a" number="67">
                <image file="527.01.039-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.039-01"/>
              </figure>
            columnæ, ſublatoq́ue triangulo A B C, co-
              <lb/>
            lumna D E quieſcat in H, ut hîc vides. </s>
            <s xml:id="echoid-s1180" xml:space="preserve">Ob
              <lb/>
            cauſas jam nunc cõmem oratas, quemadmo-
              <lb/>
            dum T I ad IV: </s>
            <s xml:id="echoid-s1181" xml:space="preserve">ita R eritad X. </s>
            <s xml:id="echoid-s1182" xml:space="preserve">neque hoc
              <lb/>
            tantũ quando I V perpĕdicularis eſt & </s>
            <s xml:id="echoid-s1183" xml:space="preserve">recta
              <lb/>
            ad axem F G, verum etiam quando contin-
              <lb/>
            gĕter obliqua. </s>
            <s xml:id="echoid-s1184" xml:space="preserve">Cujus rei argumĕta documĕ-
              <lb/>
            taq; </s>
            <s xml:id="echoid-s1185" xml:space="preserve">ſpeciatim dari poſſent, niſi hoc è 6 con-
              <lb/>
            fectario clarum ſatis ac manifeſtum eſſet.</s>
            <s xml:id="echoid-s1186" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div193" type="section" level="1" n="141">
          <head xml:id="echoid-head153" xml:space="preserve">9 C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s1187" xml:space="preserve">8 Confectario proportio declarata fuit, ubi I mobile punctum ſupra H fuir
              <lb/>
            punctum fixum, & </s>
            <s xml:id="echoid-s1188" xml:space="preserve">linea IV obliquè extollens H firmum punctum verſus
              <lb/>
            inclinata: </s>
            <s xml:id="echoid-s1189" xml:space="preserve">eadem proportio in alio quovis ſitu demonſtranda eſt, & </s>
            <s xml:id="echoid-s1190" xml:space="preserve">primum
              <lb/>
            quidem in illis, ubi mobile punctum infra fixum eſt, lineaq́ue obliquè extol-
              <lb/>
            lens à firmo inclinata eſt. </s>
            <s xml:id="echoid-s1191" xml:space="preserve">& </s>
            <s xml:id="echoid-s1192" xml:space="preserve">quidem iſto pacto.</s>
            <s xml:id="echoid-s1193" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1194" xml:space="preserve">A B columna eſto, ejusq́ue axis C D, punctum firmum E, mobile vero F,
              <lb/>
              <figure xlink:label="fig-527.01.039-02" xlink:href="fig-527.01.039-02a" number="68">
                <image file="527.01.039-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.039-02"/>
              </figure>
            pondus obliquè extollens G, cujus
              <lb/>
            obliqua linea FH, FI verò linea re-
              <lb/>
            ctè attollens, cujus rectum pondus K.
              <lb/>
            </s>
            <s xml:id="echoid-s1195" xml:space="preserve">Etiam L M columna æqualis & </s>
            <s xml:id="echoid-s1196" xml:space="preserve">ſimi-
              <lb/>
            lis eſto A B columnæ, ejusq́ue axis
              <lb/>
            N O, punctum firmum E, mobile F,
              <lb/>
            ut E N æquetur E D, E F verò E P,
              <lb/>
            pondus obliquè extollens Q æquale
              <lb/>
            G, cujus linea obliqua ſit parallela ad
              <lb/>
            F H: </s>
            <s xml:id="echoid-s1197" xml:space="preserve">pondus rectè extollens S æqua-
              <lb/>
            le ponderi K, & </s>
            <s xml:id="echoid-s1198" xml:space="preserve">linea illius recta P T. </s>
            <s xml:id="echoid-s1199" xml:space="preserve">His ita poſitis & </s>
            <s xml:id="echoid-s1200" xml:space="preserve">conceſſis A B & </s>
            <s xml:id="echoid-s1201" xml:space="preserve">L M
              <lb/>
            addantur, fiantq́ue una columna AM, cujus centrum gravitatis erit E, ex theſi-
              <lb/>
            Ponderibus K, G, S, Q, amotis, columna A M quemvis datũ ſitum ſervabit
              <lb/>
            in E puncto, per 7 propoſit. </s>
            <s xml:id="echoid-s1202" xml:space="preserve">eritq́ columna A B cõtra L M columnam æquili-
              <lb/>
            bris. </s>
            <s xml:id="echoid-s1203" xml:space="preserve">Rurſus pondera Q, G æquiponderantia æquipõderantibus & </s>
            <s xml:id="echoid-s1204" xml:space="preserve">quidem
              <lb/>
            ſimili ſitu appendamus, Q & </s>
            <s xml:id="echoid-s1205" xml:space="preserve">G, per 13 propoſitionem, in A M columnam
              <lb/>
            cjuſdem potentiæ ſunt, ideoq́ue quantum potentiæ eſt ponderi Q in L M
              <lb/>
            columnam, tantundem quoque & </s>
            <s xml:id="echoid-s1206" xml:space="preserve">G fueritin ſuam A B. </s>
            <s xml:id="echoid-s1207" xml:space="preserve">Atqui potentia G
              <lb/>
            eſt, in ſitu ſuo retinere A B, per 6 confect. </s>
            <s xml:id="echoid-s1208" xml:space="preserve">eadem igitur & </s>
            <s xml:id="echoid-s1209" xml:space="preserve">Q erit in L M. </s>
            <s xml:id="echoid-s1210" xml:space="preserve">
              <lb/>
            Conſimiliter eadem potentia K eſt in A B, eadem igitur S fuerit in L M. </s>
            <s xml:id="echoid-s1211" xml:space="preserve">
              <lb/>
            Quemadmodum itaque IF ad FH ita K ad G per 8 conſectar. </s>
            <s xml:id="echoid-s1212" xml:space="preserve">atqui TP
              <lb/>
            æquatur IF, & </s>
            <s xml:id="echoid-s1213" xml:space="preserve">PR, ipſi FH, item pondus S ponderi, K, pondusq́ue Q
              <lb/>
            ponderi G: </s>
            <s xml:id="echoid-s1214" xml:space="preserve">ut igitur TP ad PR ita S ad Q. </s>
            <s xml:id="echoid-s1215" xml:space="preserve">Quapropter iſta proportio,
              <lb/>
            ut diximus, non minus conſtans eſt in exemplis, ubi mobile punctum P in-
              <lb/>
            fra E firmum eſt, quam ubi ſupra, ubiq́ue linea P R rectè extollens à latere
              <lb/>
            firmi puncti E declinat, quam ubiſupra eſt, & </s>
            <s xml:id="echoid-s1216" xml:space="preserve">obliquè extollens linea idem
              <lb/>
            firmum punctum verſus inclinat.</s>
            <s xml:id="echoid-s1217" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum