Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              <s id="N299F0">
                <emph type="center"/>
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              Theorema
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              11.
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              </s>
            </p>
            <p id="N299FC" type="main">
              <s id="N299FE">
                <emph type="italics"/>
              Si
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              triangulum BIG voluatur circa CA, in quam BH cadit perpendi­
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              culariter, ſitque BH axis per centrum grauitatis ductus, diuiſuſque in
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              4.
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              partes æquales B.F.E.D.H. centrum percuſſionis eſt in D
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              ; quod facilè de­
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              monſtratur; </s>
              <s id="N29A18">nam IG in iſto motu deſcribit ſuperficiem cylindri, &
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              triangulum GBI deſcribit, vt ſic loquar, ſectorem cylindri; </s>
              <s id="N29A1E">igitur im­
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              petus in IG eſt ad impetum in NM, vt ſuperficies curua terminata in I
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              G, ad ſuperficiem terminatam in NM, ſub eodem ſcilicet angulo; </s>
              <s id="N29A26">vel vt
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              baſis pyramidis IG, ad baſim NM; igitur perinde ſe habet IG, ac ſi
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              incumberet prædicta baſis, itemque NM, &c. </s>
              <s id="N29A2E">igitur ac ſi eſſet ſolida
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              pyramis quadrilatera; ſed pyramidis centrum grauitatis eſt D, per
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              Theorema 4. </s>
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            <p id="N29A37" type="main">
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                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              12.
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              </s>
            </p>
            <p id="N29A45" type="main">
              <s id="N29A47">
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              Si idem triangulum GIB voluatur circa IG, centrum percuſſionis eſt in
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              E, quod diuidit HB bifariam æqualiter
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              ; </s>
              <s id="N29A52">quod vt demonſtretur, perinde
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              ſe habet triangulum BGI circumactum, atque ſi ſingulis partibus in­
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              cumberent perpendiculares, quæ eſſent vt earumdem partium motus; </s>
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              ſit autem triangulum BAC æquale priori; </s>
              <s id="N29A5F">baſis cunei ABHKDC; </s>
              <s id="N29A63">
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              ducatur planum DBA, quod dirimat cuneum in duo ſolida, ſcilicet in
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              pyramidem ABHKD, & ſolidum ABDC; </s>
              <s id="N29A6A">pyramis continet 2/3 totius
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              cunei, vt conſtat; </s>
              <s id="N29A70">eſt enim prædictus cuneus ſubduplus priſmatis, cuius
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              baſis ſit HA, & altitudo ID; </s>
              <s id="N29A76">cuius pyramis prædicta continet 1/3; </s>
              <s id="N29A7A">igitur
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              ſi priſma ſit vt 6. pyramis erit vt 2. & cuneus vt 3. igitur pyramis conti­
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              net 2/3 cunci; </s>
              <s id="N29A82">igitur alterum ſolidum ABDC eſt 1/3 cunei; </s>
              <s id="N29A86">cunei cen­
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              trum grauitatis idem eſt, quod trianguli HKD, per Corol. 1. Th.3.igi­
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              tur eſt in linea directionis MF.ita vt IM ſit 1/3 totius ID, per Th 3. py­
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              ramidis verò centrum grauitatis eſt in linea NG, ita vt IN ſit 1/4 totius
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              ID, per Th.4. igitur ſi eſt NM ad ML, vt ſolidum ABDC ad pyra­
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              midem AHD, id eſt vt 1.ad 2. certè NI, & NL erunt æquales; </s>
              <s id="N29A96">ſed IN
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              eſt 1/4 totius ID; igitur IL 1/2 ergo L dirimit æqualiter ID, quod erat
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              demonſtr. </s>
              <s id="N29A9E">ſit ID 12.IN 3.IM 4. IL 6. </s>
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            <p id="N29AA2" type="main">
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                <emph type="center"/>
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              Theorema
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              13.
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              </s>
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              Si voluatur ſector circa axem parallelum ſubtenſæ, determinari poteſt cen­
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              trum percuſſionis, dato centro grauitatis ſectoris, quod tantum hactenus in­
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              uentum eſt ex ſuppoſita circuli quadratura
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              : </s>
              <s id="N29ABF">ſit enim ſector AKHM, ſub­
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              tenſa KM; </s>
              <s id="N29AC5">diuidatur AI in tres partes æquales ADFI, item AH, in
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              tres æquales AEGH, centrum grauitatis ſectoris non eſt in F, quod eſt
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              centrum grauitatis trianguli AMK, ſed propiùs accedit ad H; </s>
              <s id="N29ACD">nec
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              etiam eſt in G, quod eſt centrum grauitatis trianguli ALN, ſed propiùs
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              accedit ad A; </s>
              <s id="N29AD5">ergo eſt inter FG, v.g. in R, ita vt AH ſit ad AR vt arcus
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              MHK ad 2/3 ſubtenſæ MK; </s>
              <s id="N29ADD">id eſt ad MP; </s>
              <s id="N29AE1">vt demonſtrat La Faille Prop.
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              34. poteſt etiam haberi centrum grauitatis ſegmenti circuli; </s>
              <s id="N29AE8">ſit enim
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              ſegmentum FCHI cuius centrum ſit B; </s>
              <s id="N29AF0">ſint BC. BI. BH. diuidens æ-</s>
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