Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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        <div xml:id="echoid-div282" type="section" level="1" n="104">
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              <pb o="144" file="0208" n="228" rhead="CHRISTIANI HUGENII"/>
            rum autem ſumma quadratorum data erit, ſi detur diſtantia
              <lb/>
              <note position="left" xlink:label="note-0208-01" xlink:href="note-0208-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">O@CILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            centri gravitatis figuræ S Y T Z ab recta B Y vel D Z;
              <lb/>
            </s>
            <s xml:id="echoid-s3273" xml:space="preserve">nec non diſtantia indidem centri gravitatis cunei ſui abſciſſi
              <lb/>
            plano per eandem rectam . </s>
            <s xml:id="echoid-s3274" xml:space="preserve">Vel, figura S Y T Z
              <note symbol="*" position="left" xlink:label="note-0208-02" xlink:href="note-0208-02a" xml:space="preserve">Prop. 9.
                <lb/>
              huj.</note>
            exiſtente, ut S T ſit axis ejus, eadem quadratorum ſumma da-
              <lb/>
            bitur, ſi detur diſtantia centri gravitatis figuræ dimidiæ S Z T
              <lb/>
            ab axe S T, item centri gravitatis cunei, ſuper eadem di-
              <lb/>
            midia figura, abſciſſi plano per axem ducto . </s>
            <s xml:id="echoid-s3275" xml:space="preserve">Ergo,
              <note symbol="*" position="left" xlink:label="note-0208-03" xlink:href="note-0208-03a" xml:space="preserve">Prop. 11.
                <lb/>
              huj.</note>
            datis, dabitur quoque ſumma quadratorum à perpendicula-
              <lb/>
            ribus quæ, à particulis omnibus ſolidi A B C D, ductæ
              <lb/>
            intelliguntur in planum E A C. </s>
            <s xml:id="echoid-s3276" xml:space="preserve">Invenimus autem & </s>
            <s xml:id="echoid-s3277" xml:space="preserve">ſum-
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            mam quadratorum, à perpendicularibus omnibus in planum
              <lb/>
            per E G ductis. </s>
            <s xml:id="echoid-s3278" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s3279" xml:space="preserve">aggregatum utriuſque ſummæ ha-
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            bebitur, hoc eſt, per ſuperius oſtenſa, ſumma quadratorum
              <lb/>
            perpendicularium quæ, à particulis omnibus ſolidi A B C D,
              <lb/>
            cadunt in rectam datam per E tranſeuntem, & </s>
            <s xml:id="echoid-s3280" xml:space="preserve">ad paginæ
              <lb/>
            hujus planum erectam. </s>
            <s xml:id="echoid-s3281" xml:space="preserve">quod erat faciendum.</s>
            <s xml:id="echoid-s3282" xml:space="preserve"/>
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        <div xml:id="echoid-div286" type="section" level="1" n="105">
          <head xml:id="echoid-head131" xml:space="preserve">PROPOSITIO XV.</head>
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            <s xml:id="echoid-s3283" xml:space="preserve">IIsdem poſitis, ſi ſolidum A B C D ſit ejusmodi, ut
              <lb/>
              <note position="left" xlink:label="note-0208-04" xlink:href="note-0208-04a" xml:space="preserve">TAB. XXI.
                <lb/>
              Fig. 1. & 2.</note>
            figura plana S Y T Z, ipſi proportionalis, non ha-
              <lb/>
            beat notam diſtantiam centri gravitatis à tangenti-
              <lb/>
            bus B Y vel D Z, vel, ut ſubcentrica cunei ſuper ipſa
              <lb/>
            abſciſſi, plano per easdem B Y vel D Z, ignoretur;
              <lb/>
            </s>
            <s xml:id="echoid-s3284" xml:space="preserve">in figura tamen proportionali, quæ à latere eſt,
              <lb/>
            O Q P, detur diſtantia Φ P, qua centrum gravita-
              <lb/>
            tis figuræ dimidiæ O P V abeſt ab axe O P; </s>
            <s xml:id="echoid-s3285" xml:space="preserve">li-
              <lb/>
            cebit hinc invenire ſummam quadratorum à diſtan-
              <lb/>
            tiis particularum ſolidi A B C D à plano E C. </s>
            <s xml:id="echoid-s3286" xml:space="preserve">O-
              <lb/>
            portet autem ut ſectiones omnes, N N, M M, ſint
              <lb/>
            plana ſimilia; </s>
            <s xml:id="echoid-s3287" xml:space="preserve">utque per omnium centra gravitatis
              <lb/>
            transeat planum E C; </s>
            <s xml:id="echoid-s3288" xml:space="preserve">quemadmodum in prismate,
              <lb/>
            pyramide, c
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            ono, conoidibus, multisque aliis </s>
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