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

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          <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">
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            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-
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            fectario clarum ſatis ac manifeſtum eſſet.</s>
            <s xml:id="echoid-s1186" xml:space="preserve"/>
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        <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,
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            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"/>
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