Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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IO. BAPT. BENED.
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          <div xml:id="echoid-div308" type="chapter" level="2" n="2">
            <div xml:id="echoid-div318" type="section" level="3" n="6">
              <pb o="128" rhead="IO. BAPT. BENED." n="140" file="0140" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0140"/>
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            <div xml:id="echoid-div320" type="section" level="3" n="7">
              <head xml:id="echoid-head183" xml:space="preserve">CAP. VII.</head>
              <p>
                <s xml:id="echoid-s1564" xml:space="preserve">ALiarn tamen inueni viam breuiorem vt in figura
                  <var>.H.H.</var>
                in qua ſit punctus
                  <var>.
                    <lb/>
                  b.</var>
                perfecti, &
                  <var>.k.</var>
                degradati plani. </s>
                <s xml:id="echoid-s1565" xml:space="preserve">Nunc ducatur
                  <var>.b.c.s.</var>
                ad rectos cum
                  <var>.
                    <lb/>
                  p.m.</var>
                indefinitè, quæ quidem abſcindatur in puncto
                  <var>.s.</var>
                ita quòd
                  <var>.c.s.</var>
                æqualis ſit alti
                  <lb/>
                tudini perfectæ, deinde coniungatur rectà. s. cum
                  <var>.i</var>
                . </s>
                <s xml:id="echoid-s1566" xml:space="preserve">Tunc ſi ab
                  <var>.k.</var>
                vſque ad
                  <reg norm="protractam" type="context">protractã</reg>
                  <lb/>
                  <var>i.s.</var>
                ducta fuerit
                  <var>.k.R.</var>
                parallela li-
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0140-01a" xlink:href="fig-0140-01"/>
                neę
                  <var>.c.s.</var>
                hæc
                  <var>.R.k.</var>
                erit altitudo
                  <lb/>
                quæſita ſeu degradata.</s>
              </p>
              <div xml:id="echoid-div320" type="float" level="4" n="1">
                <figure xlink:label="fig-0140-01" xlink:href="fig-0140-01a">
                  <image file="0140-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0140-01"/>
                </figure>
              </div>
              <p>
                <s xml:id="echoid-s1567" xml:space="preserve">Quod ita probo. </s>
                <s xml:id="echoid-s1568" xml:space="preserve">Iam nulli du
                  <lb/>
                bium eſt quin
                  <var>.f.V.</var>
                ſit æqualis alti-
                  <lb/>
                tudini quęſitæ ſeu degradatę, quo
                  <lb/>
                  <reg norm="tieſcunque" type="simple">tieſcunq;</reg>
                ergo
                  <reg norm="probauerimus" type="simple">ꝓbauerimus</reg>
                  <var>.k.R.</var>
                  <lb/>
                æqualem eſſe lineæ
                  <var>.f.V.</var>
                habebi-
                  <lb/>
                mus propoſitum. </s>
                <s xml:id="echoid-s1569" xml:space="preserve">Quare certum
                  <lb/>
                nobis erit eandem proportionem
                  <lb/>
                eſſe lineæ
                  <var>.c.s.</var>
                ad
                  <var>.k.R.</var>
                quam
                  <var>.c.i.</var>
                ad
                  <lb/>
                  <var>k.i.</var>
                et
                  <var>.c.i.</var>
                ad
                  <var>.k.i.</var>
                vt
                  <var>.x.i.</var>
                ad
                  <var>.f.i.</var>
                et
                  <var>.x.
                    <lb/>
                  i.</var>
                ad
                  <var>.f.i.</var>
                vt
                  <var>.m.o.</var>
                ad
                  <var>.f.o.</var>
                et
                  <var>.m.o.</var>
                ad
                  <var>.
                    <lb/>
                  f.o.</var>
                vt
                  <var>.m.T.</var>
                ad
                  <var>.f.V.</var>
                ex ſimilitudine
                  <lb/>
                triangulorum. </s>
                <s xml:id="echoid-s1570" xml:space="preserve">Ergo
                  <var>.m.T.</var>
                ad
                  <var>.f.V.</var>
                  <lb/>
                erit vt
                  <var>.c.s.</var>
                ad
                  <var>.k.R.</var>
                ex .11. quinti,
                  <lb/>
                ſed
                  <var>.c.s.</var>
                ſumpta fuit æqualis
                  <var>.m.T</var>
                .
                  <lb/>
                </s>
                <s xml:id="echoid-s1571" xml:space="preserve">quare
                  <var>.c.s.</var>
                ad
                  <var>.f.V.</var>
                erit, vt
                  <var>.m.T.</var>
                ad
                  <lb/>
                  <reg norm="eandem" type="context context">eãdẽ</reg>
                  <var>.f.V.</var>
                ex .7.
                  <reg norm="quinti" type="simple">ꝗnti</reg>
                , & ex .11. eiuſ-
                  <lb/>
                dem
                  <var>.c.s.</var>
                ad
                  <var>.f.V.</var>
                erit vt
                  <var>.c.s.</var>
                ad
                  <var>.k.R.</var>
                  <lb/>
                quapropter ex .9. eiuſdem
                  <var>.k.R.</var>
                æqualis erit
                  <var>.f.V</var>
                .</s>
              </p>
            </div>
            <div xml:id="echoid-div322" type="section" level="3" n="8">
              <head xml:id="echoid-head184" xml:space="preserve">CAP. VIII.</head>
              <p>
                <s xml:id="echoid-s1572" xml:space="preserve">MOdus ab antiquis philoſophis obſeruatus, eſt etiam vtilis,
                  <reg norm="compendioſaque" type="simple">compendioſaq́;</reg>
                via
                  <lb/>
                progreditur, cuius ſpeculationem, in ſubſcripta figura, quadam ex parte
                  <reg norm="ſecun- dum" type="context">ſecũ-
                    <lb/>
                  dum</reg>
                morem antiquum, quadam etiam ex parte ſecundum ingenij mei vires
                  <reg norm="conſtru- cta" type="context">cõſtru-
                    <lb/>
                  cta</reg>
                , cognoſcemus. </s>
                <s xml:id="echoid-s1573" xml:space="preserve">In qua ego diuiſi
                  <var>.x.i.</var>
                in puncto
                  <var>.s.</var>
                ab
                  <var>.x.</var>
                ita eleuato, quanta eſt
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0140-02a" xlink:href="fig-0140-02"/>
                </s>
              </p>
            </div>
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