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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DE PERSPECT.
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            <div xml:id="echoid-div328" type="section" level="3" n="12">
              <p>
                <pb o="137" rhead="DE PERSPECT." n="149" file="0149" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0149"/>
                <s xml:id="echoid-s1652" xml:space="preserve">1. 2. </s>
                <s xml:id="echoid-s1653" xml:space="preserve">Vnde huiuſmodi regula tunc bona redditur, quando
                  <var>T.Q.</var>
                æqualis eſt ipſi .œ.
                  <lb/>
                Q. ideſt medietati ipſius
                  <var>.D.B.</var>
                at verò ſi æqualis non eſſet hoc minime ſequeretur,
                  <lb/>
                vt facilè patet. </s>
                <s xml:id="echoid-s1654" xml:space="preserve">Quòd verò .2.
                  <var>R.Z.</var>
                &. ſint benè diſpoſita, dubitandum non eſt, quia
                  <lb/>
                punctum
                  <var>.i.</var>
                meæ hic ſubſcriptæ figuræ, quod coreſpondet K. eius ſiguræ adeò diſtat
                  <lb/>
                a medio
                  <var>.R.X.</var>
                trianguli
                  <var>.R.B.D.</var>
                vt .2. cum .1. 2. dicto medio
                  <var>.R.X.</var>
                ex .6. </s>
                <s xml:id="echoid-s1655" xml:space="preserve">Vndecimi fit
                  <lb/>
                parallela. </s>
                <s xml:id="echoid-s1656" xml:space="preserve">Idem de reliquis dico. quod manifeſtè cognoſci poteſt, ab eo, quod in
                  <lb/>
                ſuperius poſitis figuris corporeis dixi. </s>
                <s xml:id="echoid-s1657" xml:space="preserve">Huiuſmodi modus ducendi res in perſpectiua,
                  <lb/>
                non ſolum à Gallis, ſed à Germanis etiam in vſum reducitur. </s>
                <s xml:id="echoid-s1658" xml:space="preserve">Sed quia ad hæc
                  <reg norm="vſque" type="simple">vſq;</reg>
                  <lb/>
                tempora eiuſdem perfectionis ratio, quam ego ſuperius propoſui,
                  <reg norm="nondum" type="context">nõdum</reg>
                in lucem
                  <lb/>
                emerſit, factum fuit, vt
                  <reg norm="errorum" type="context">errorũ</reg>
                laqueis irretirentur, ſumentes
                  <var>.T.Q.</var>
                modo maiorem,
                  <lb/>
                modo minorem medietate lateris
                  <var>.D.B</var>
                . </s>
                <s xml:id="echoid-s1659" xml:space="preserve">Cum hunc igitur modum hic Autor
                  <lb/>
                vniuerſalem eſſe putet, labitur in errorem, cum debuiſſet longitudinem ipſius
                  <var>.T.Q.</var>
                  <lb/>
                debere eſſe æqualem medietati ipſius
                  <var>.D.B.</var>
                proferre. </s>
                <s xml:id="echoid-s1660" xml:space="preserve">Aſſerit deinde diſtantiam ip-
                  <lb/>
                ſius
                  <var>.T.Q.</var>
                à latere
                  <var>.B.D.</var>
                æ qualem eſſe debere lateri
                  <var>.C.D.</var>
                quod neceſſarium non eſt,
                  <lb/>
                quia in quibuslibet diſtantijs, iuſta operatio fieri poteſt, quemadmodum in ſubſcri-
                  <lb/>
                pta hîc figura facile patet, ideſt, quòd quibuſcunque modis
                  <var>.c.D.</var>
                æqualis remaneat
                  <lb/>
                ipſi .1. 2. & ſic interualla, quæ
                  <reg norm="per" type="simple">ꝑ</reg>
                tranſuerſum aguntur
                  <reg norm="vſque" type="simple">vſq;</reg>
                ad
                  <reg norm="medium" type="context">mediũ</reg>
                trianguli
                  <var>.D.R.B.</var>
                  <lb/>
                Neque etiam probandus eſt auctor ille, cum pro oculo, ſuum
                  <var>.T.</var>
                loco
                  <var>.Q.</var>
                à me poſi-
                  <unsure/>
                  <lb/>
                ti, ponit, cum is locus ſit verus ſitus pedis eius quireſpicit, & non oculi. </s>
                <s xml:id="echoid-s1661" xml:space="preserve">Quòd
                  <reg norm="autem" type="context">autẽ</reg>
                  <lb/>
                Auctor iſte, modo vniuerſali intelligat, vt iam diximus,
                  <reg norm="conſideretur" type="context">cõſideretur</reg>
                figura tertij mo
                  <lb/>
                di primi cap. tertiæ partis, in qua ſuum oculum (vt ita dicam) ponit in
                  <var>.o.</var>
                altius ſeu
                  <lb/>
                diſtans à rectitudine lateris
                  <var>.c.d.</var>
                plus quam ſit totum latus
                  <var>.d.b</var>
                .</s>
              </p>
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                <figure xlink:label="fig-0148-01" xlink:href="fig-0148-01a">
                  <image file="0148-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0148-01"/>
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            <div xml:id="echoid-div331" type="section" level="3" n="13">
              <head xml:id="echoid-head191" xml:space="preserve">AD EVNDEM IACOBVM.
                <lb/>
              CAP. XIII.</head>
              <p>
                <s xml:id="echoid-s1662" xml:space="preserve">
                  <emph style="sc">TVas</emph>
                accepiliteras omnis humanitatis & officij plenas, in quibus requiris cau-
                  <lb/>
                ſam, quæ me in alijs meis literis impulit ad
                  <reg norm="dicendum" type="context">dicendũ</reg>
                ,
                  <reg norm="angulum" type="context">angulũ</reg>
                  <var>.q.o.u.</var>
                modo ma-
                  <lb/>
                iorem, modo verò minorem futurum angulo
                  <var>.q.p.u.</var>
                meæ figuræ corporeæ
                  <var>.A.</var>
                hanc
                  <lb/>
                igitur ob cauſam imagineris in ſubſcripta hîc figura duo triangula
                  <var>.q.o.u.</var>
                et
                  <var>.q.p.u.</var>
                  <lb/>
                quorum
                  <var>.q.p.u.</var>
                perpendiculariter ſit ſuper ſuperficie trianguli
                  <var>.q.o.p.</var>
                collocatum,
                  <lb/>
                præcisè vt in mea figura corporea
                  <var>.A.</var>
                ſuperficies verò trianguli
                  <var>.q.o.p.</var>
                ſit exempli-
                  <lb/>
                gratia
                  <var>.V.M.</var>
                & trian-
                  <lb/>
                guli
                  <var>.u.o.p.</var>
                ſit
                  <var>.V.D.</var>
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0149-01a" xlink:href="fig-0149-01"/>
                quarum
                  <reg norm="communis" type="context">cõmunis</reg>
                ſe-
                  <lb/>
                ctio ſit
                  <var>.V.p.o.x.</var>
                non
                  <lb/>
                eſt enim
                  <reg norm="dubitandum" type="context">dubitãdum</reg>
                  <lb/>
                quin triangulum
                  <var>.q.
                    <lb/>
                  p.u.</var>
                ſit perpendicula-
                  <lb/>
                re triangulo
                  <var>.q.o.p.</var>
                  <lb/>
                  <reg norm="cum" type="context">cũ</reg>
                hoc ex .18. lib. 11.
                  <lb/>
                Eucli. perpendicula-
                  <lb/>
                re ſit ſuperficiei
                  <var>.a.s.</var>
                  <lb/>
                in qua reperitur
                  <reg norm="trian- gulum" type="context">triã-
                    <lb/>
                  gulum</reg>
                  <var>.q.p.u.</var>
                & hoc
                  <lb/>
                ex linea
                  <var>.o.p.</var>
                perpendiculari dictæ ſuperficiei
                  <var>.a.s</var>
                . </s>
                <s xml:id="echoid-s1663" xml:space="preserve">Nunc dico angulum
                  <var>.q.o.u.</var>
                modo
                  <lb/>
                maiorem, modo minorem eſſe angulo
                  <var>.q.p.u</var>
                . </s>
                <s xml:id="echoid-s1664" xml:space="preserve">Notiſſimum igitur primum nobis </s>
              </p>
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