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]

Table of handwritten notes

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            <div xml:id="echoid-div328" type="section" level="3" n="12">
              <p>
                <s xml:id="echoid-s1641" xml:space="preserve">
                  <pb o="136" rhead="IO. BAPT. BENED." n="148" file="0148" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0148"/>
                cere oportet. </s>
                <s xml:id="echoid-s1642" xml:space="preserve">Ratio verò ab ipſo adducta propter quam
                  <var>.E.</var>
                repreſentatur oculo al-
                  <lb/>
                tius quam
                  <var>.b.</var>
                nempe eo quod
                  <var>.A.</var>
                ſuperſtet ipſi
                  <var>.E.</var>
                nihil valet, quia ſi inferius eſſet,
                  <lb/>
                idem contingeret, ſed hoc euenit eo quod
                  <var>.E.</var>
                altius eſt ipſo
                  <var>.b</var>
                . </s>
                <s xml:id="echoid-s1643" xml:space="preserve">Idem dico de
                  <var>.h.</var>
                  <lb/>
                vbi ſimiliter decipitur. </s>
                <s xml:id="echoid-s1644" xml:space="preserve">Idem etiam in .7. cap. fallitur in ſecundo modo, quem oſten
                  <lb/>
                dit pro ſecundo quadrato aliquo degradato à parallelogrammo degradato magis
                  <lb/>
                longo quàm lato, cum ducat parallelam
                  <var>.l.m.</var>
                ad
                  <var>.b.c.</var>
                à puncto
                  <var>.l.</var>
                interſection is ipſius
                  <var>.
                    <lb/>
                  o.c.</var>
                id, quod non rectè efficitur quemadmodum ex rationibus à me allegatis circa
                  <lb/>
                meas figuras
                  <var>.A.A.</var>
                facilè innoteſcit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1645" xml:space="preserve">Nono deinde cap. contrario planè ordine, quam oporteret proceſsit, quia
                  <reg norm="cum" type="context">cũ</reg>
                  <lb/>
                angulus .2. trianguli perfecti magis diſtet à plano ſuper quod degradari debet
                  <lb/>
                triangulum, quàm latus .1. 3. oppoſitum dicto angulo .2. & per confequens longère
                  <lb/>
                motior ſit ab oculo, ipſe in degradato,
                  <reg norm="eum" type="context">eũ</reg>
                magis propinquum eſſe facit, è con-
                  <lb/>
                tra eap .10. rectè fecit contra id, quod capite .9. tradiderat.</s>
              </p>
              <p>
                <s xml:id="echoid-s1646" xml:space="preserve">Quod autem deinceps in prima parte .11. & vltimi capitis aſſerit eſt,
                  <reg norm="admittendum" type="context">admittendũ</reg>
                .
                  <lb/>
                </s>
                <s xml:id="echoid-s1647" xml:space="preserve">Quod verò in ſecunda parte ab eo traditur, ideſt alius quidam modus quem de
                  <reg norm="tranſ" type="context">trãſ</reg>
                  <lb/>
                ferendis punctis à perfecto in degradato proponit, non eſt modus vniuerſalis; </s>
                <s xml:id="echoid-s1648" xml:space="preserve">quia
                  <lb/>
                ſi altitudo
                  <var>.T.Q.</var>
                oculi à plano orizontali, non eſſet æqualis medietati lateris
                  <var>.B.D.</var>
                  <lb/>
                perfecti, interualla
                  <var>.a.b.c.d.e.</var>
                lateris
                  <var>B.D.</var>
                admittenda non eſſent.</s>
              </p>
              <p>
                <s xml:id="echoid-s1649" xml:space="preserve">Pro cuius rei intelligentia ſit in ſubſcripta hic figura corporea
                  <var>.ω.</var>
                parallelogram-
                  <lb/>
                mum rectangulum
                  <var>A.B.C.D.</var>
                in plano orizontali, & linea
                  <var>.Q.H.</var>
                illud per medium
                  <lb/>
                diuidat, quæ ſit parallela duobus lateribus
                  <var>.A.B.</var>
                et
                  <var>.C.D.</var>
                in cuius quolibet puncto
                  <var>.
                    <lb/>
                  Q.</var>
                ſit infimus terminus altitudinis oculi, & in
                  <var>.
                    <lb/>
                    <figure xlink:label="fig-0148-01" xlink:href="fig-0148-01a" number="202">
                      <image file="0148-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0148-01"/>
                    </figure>
                  T.</var>
                ad perpendiculum ipſius
                  <var>.Q.</var>
                ſit verus ſitus
                  <lb/>
                eiuſdem, tantum eleuatus à
                  <var>.Q.</var>
                quanta eſt
                  <lb/>
                medietas ipſius
                  <var>.D.B.</var>
                ſitq́ue figura corpo-
                  <lb/>
                rea finita ſimilis meæ
                  <var>.A.</var>
                vnde
                  <var>.Q.T.</var>
                æqualis
                  <lb/>
                erit ipſi
                  <var>.Q.æ.</var>
                & planum perpendiculare
                  <reg norm="orizon- ti" type="context">orizõ-
                    <lb/>
                  ti</reg>
                , ſuper quod punctum
                  <var>.k.</var>
                perfecti duci debet
                  <lb/>
                ſit
                  <var>.R.D.B.</var>
                ſintq́ue ductæ per imaginationem
                  <lb/>
                lineæ
                  <var>.T.K</var>
                :
                  <var>Q.K.</var>
                et ſit
                  <var>.K.N.</var>
                perpendicularis la-
                  <lb/>
                teri
                  <var>.C.D.</var>
                à quo puncto
                  <var>.N.</var>
                imaginatione ſit
                  <reg norm="con" type="context">cõ</reg>
                  <lb/>
                præhenſa linea
                  <var>.N.Q.</var>
                at que hæ tres lineæ ſectæ
                  <lb/>
                ſint à plano in punctis
                  <var>.c.i.</var>
                et .2. quorum
                  <reg norm="punctum" type="context">punctũ</reg>
                .
                  <lb/>
                2. erit quæſitum plani. </s>
                <s xml:id="echoid-s1650" xml:space="preserve">Imaginemur nunc duos
                  <lb/>
                triangulos
                  <var>.K.T.Q.</var>
                et
                  <var>.N.Q.æ.</var>
                qui ſecti
                  <reg norm="erunt" type="context">erũt</reg>
                  <lb/>
                à plano
                  <var>.R.B.D.</var>
                quorum communes ſectiones
                  <lb/>
                erunt .1. 2. et
                  <var>.D.c.</var>
                & quia
                  <var>.N.K.D.i.</var>
                et
                  <var>.æ.Q.</var>
                  <lb/>
                inuicem ſunt parallelæ, ſequitur eandem pro-
                  <lb/>
                portionem futuram ipſius
                  <var>.Q.K.</var>
                ad
                  <var>.K.i.</var>
                quæ eſt
                  <lb/>
                ipſius
                  <var>.æ.N.</var>
                ad
                  <var>.N.D.</var>
                imaginatione concipien
                  <lb/>
                do a puncto
                  <var>.K.</var>
                vſque ad
                  <var>.æ.Q.</var>
                quandam paral-
                  <lb/>
                lelam ipſi
                  <var>.N.æ.</var>
                quemadmo dum ex te ipſo intel
                  <lb/>
                ligere potes. </s>
                <s xml:id="echoid-s1651" xml:space="preserve">Sed ratione ſimilitudinis trian-
                  <lb/>
                gulorum ita ſe res habet de
                  <var>.æ.Q.</var>
                ad
                  <var>.D.c.</var>
                vt de
                  <var>.
                    <lb/>
                  æ.N.</var>
                ad
                  <var>.N.D.</var>
                vt quoque de
                  <var>.T.Q.</var>
                ad .2. 1. quemadmodum ipſius
                  <var>.Q.K.</var>
                ad
                  <var>.K.i.</var>
                vn-
                  <lb/>
                de ex .11. quinti, idem erit de
                  <var>.Q.T.</var>
                ad .1. 2. quod de
                  <var>.Q.æ.</var>
                ad
                  <var>.c.D.</var>
                & ex .16. eiuſdem
                  <lb/>
                de
                  <var>.Q.T.</var>
                ad
                  <var>.Q.æ.</var>
                quod de .1. 2. ad
                  <var>.c.D.</var>
                & exiſtente
                  <var>.æ.Q.</var>
                ex ſuppoſito æquali ipſi.</s>
              </p>
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