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-div324" type="section" level="3" n="9">
              <pb o="130" rhead="IO. BAPT. BENED." n="142" file="0142" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0142"/>
              <p>
                <s xml:id="echoid-s1584" xml:space="preserve">Sed ſi fortè punctum
                  <var>.b.</var>
                eſſet in aliquo
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0142-01a" xlink:href="fig-0142-01"/>
                laterum, puta
                  <var>.q.u.</var>
                volo vt in rectangulo per-
                  <lb/>
                fecto
                  <var>.q.d.a.u.</var>
                ducta ſit vna diagonalis quam
                  <lb/>
                volueris puta
                  <var>.q.a.</var>
                deinde à puncto
                  <var>.b.</var>
                ad reli-
                  <lb/>
                quum angulum oppoſiti lateris ducta ſit recta
                  <var>.
                    <lb/>
                  b.d.</var>
                ita quod à diagonali ſecetur in puncto
                  <var>.ω.</var>
                  <lb/>
                per quod punctum demum à reliquo angulo la
                  <lb/>
                teris
                  <var>.q.u.</var>
                ducta ſit
                  <var>.u.ω.</var>
                vſque ad latus
                  <var>.q.d.</var>
                in
                  <reg norm="pum" type="context">pũ</reg>
                  <lb/>
                cto
                  <var>.f.</var>
                quo facto, ita faciendum erit in rectangu
                  <lb/>
                lo degradato, hoc eſt ducenda erit diagonalis
                  <var>.
                    <lb/>
                  q.r.</var>
                quę correſpondet diagonali
                  <var>.q.a.</var>
                perfecti
                  <lb/>
                deinde
                  <var>.f.e.</var>
                quæ correſpondet rectæ
                  <var>.f.u.</var>
                perfe-
                  <lb/>
                cti, quæ etiam interſecabitur à diagonali
                  <var>.q.r.</var>
                  <lb/>
                in puncto
                  <var>.o.</var>
                correſpondens
                  <var>.ω.</var>
                perfecti, per
                  <reg norm="quem" type="context">quẽ</reg>
                  <var>.
                    <lb/>
                  o.</var>
                à puncto
                  <var>.d.</var>
                cum ducta fuerit
                  <var>.d.o.</var>
                vſque ad
                  <var>.t.</var>
                  <lb/>
                in latere
                  <var>.q.e.</var>
                hoc
                  <reg norm="punctum" type="context">punctũ</reg>
                  <var>.t.</var>
                correſpondebit pun
                  <lb/>
                cto
                  <var>.b.</var>
                perfecti.</s>
              </p>
              <div xml:id="echoid-div324" type="float" level="4" n="1">
                <figure xlink:label="fig-0142-01" xlink:href="fig-0142-01a">
                  <image file="0142-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0142-01"/>
                </figure>
              </div>
              <p>
                <s xml:id="echoid-s1585" xml:space="preserve">Idem eueniet ſi loco diametri
                  <var>.q.a.</var>
                ſumpta
                  <lb/>
                fuerit diameter
                  <var>.u.d.</var>
                & loco
                  <var>.b.d.</var>
                protracta fue
                  <lb/>
                rit
                  <var>.b.a.</var>
                deinde loco
                  <var>.u.ω.f.</var>
                ducta fuerit
                  <var>.q.ω.f.</var>
                vn-
                  <lb/>
                de punctum correſpondens ipſi
                  <var>.f.</var>
                in figura de-
                  <lb/>
                gradata erit in latere ſupremo
                  <var>.e.r.</var>
                correſpon-
                  <lb/>
                dens lateri
                  <var>.u.a.</var>
                & ita ducenda erit diameter
                  <var>.d.
                    <lb/>
                  e.</var>
                correſpondens diametro
                  <var>.d.u.</var>
                et
                  <var>.q.f.</var>
                ſurſum
                  <lb/>
                verſus correſpondens
                  <var>.q.f.</var>
                imum verſus deinde
                  <var>.
                    <lb/>
                  r.o.</var>
                reſpondens
                  <var>.a.ω.</var>
                quæ terminabicur ab
                  <reg norm="eodem- met" type="context">eodẽ-
                    <lb/>
                  met</reg>
                puncto
                  <var>.t.</var>
                vt prius.</s>
              </p>
            </div>
            <div xml:id="echoid-div326" type="section" level="3" n="10">
              <head xml:id="echoid-head186" xml:space="preserve">CAP.X.</head>
              <p>
                <s xml:id="echoid-s1586" xml:space="preserve">
                  <emph style="sc">Ex</emph>
                mea figura
                  <var>.F.</var>
                ſuperficiali perſpectiuæ facillimum modum locandi quoduis
                  <lb/>
                punctum in perſpectiua elicui. </s>
                <s xml:id="echoid-s1587" xml:space="preserve">Iuſſi enim vt aptaretur tabula quædam rectan-
                  <lb/>
                gula exactè plana, triplo aut quadruplo, aut quanto volueris maioris longitu-
                  <lb/>
                dinis, quàm latitudinis protenſa, quæ quidem latitudo erat ad duos circiter pedes
                  <lb/>
                deſignata ab
                  <var>.A.B.C.D.</var>
                cuius duobus lateribus
                  <var>.A.B.</var>
                et
                  <var>.B.C.</var>
                iuſſi, vt duæ regulæ affi
                  <lb/>
                gerentur, quæ ſuperficiem eiuſdem tabulæ excederent, vt
                  <reg norm="vnum" type="context">vnũ</reg>
                ex lateribus alicuius
                  <lb/>
                anguli recti materialis, qui
                  <reg norm="appellatur" type="simple">appellat̃</reg>
                norma (vt inferius dicam) ei adherere poſſit, cu-
                  <lb/>
                raui poſtea, ut iuxta angulum
                  <var>.D.</var>
                in puncto
                  <var>.o.</var>
                fixo mobilis regula
                  <var>.o.Q.</var>
                affigeretur
                  <lb/>
                tantæ longitudinis, aut paulò minoris, quantam occupabat latus
                  <var>.D.A.</var>
                quæ circum
                  <var>.
                    <lb/>
                  o.</var>
                volueretur, in rectitudine poſteà.
                  <var>o.i.</var>
                parallela ipſi
                  <var>.D.A.</var>
                in puncto
                  <var>.i.</var>
                duobus pedi-
                  <lb/>
                bus longè à latere
                  <var>.A.B.</var>
                aliam quoque mobilem appendere feci
                  <var>.i.M.</var>
                in tantam ferè
                  <lb/>
                longitudinem extenſam, quanta conſtat
                  <var>.A.B.</var>
                  <reg norm="conſtitui" type="context">cõſtitui</reg>
                etiam, vt
                  <reg norm="quoddam" type="context">quoddã</reg>
                angulum re
                  <lb/>
                ctum materiale tantæ magnitudinis, quanta nobis vſui eſſe poterat ſuper eadem ta-
                  <lb/>
                bula; </s>
                <s xml:id="echoid-s1588" xml:space="preserve">necnon regula quædam materialis neceſſariæ longitudinis
                  <reg norm="ſtatuerentur" type="simple">ſtatuerent̃</reg>
                ,
                  <reg norm="atque" type="simple">atq;</reg>
                hæc
                  <lb/>
                omnia tenuiſſima, vt fierent curaui. </s>
                <s xml:id="echoid-s1589" xml:space="preserve">Quandam deinde lineam ad
                  <var>.o.i.</var>
                parallelam,
                  <lb/>
                ideſt
                  <var>.p.E.</var>
                ſuper eadem tabula adeò diſtantem ab
                  <var>.o.i.</var>
                vt inter
                  <var>.E.p.</var>
                et
                  <var>.B.c.</var>
                perfe-
                  <lb/>
                ctæ res, quæ degradari debebant, locari poſſent, ſignaui. </s>
                <s xml:id="echoid-s1590" xml:space="preserve">Hæc autem diſtantia, quæ </s>
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