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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              <p>
                <s xml:id="echoid-s1626" xml:space="preserve">
                  <pb o="135" rhead="DE PERSPECT." n="147" file="0147" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0147"/>
                quam iudicio. </s>
                <s xml:id="echoid-s1627" xml:space="preserve">Tibi quoque conſiderandum relinquo; </s>
                <s xml:id="echoid-s1628" xml:space="preserve">cum rationabilis degrada-
                  <lb/>
                tio eſſe debeat, qua ratione neceſſarium ſit, vt diſtantiæ reſq́ue, in vna &
                  <reg norm="eadem" type="context">eadẽ</reg>
                pro-
                  <lb/>
                portione cum altitudine oculi ad rem degradatam exiſtant? </s>
                <s xml:id="echoid-s1629" xml:space="preserve">Cum poſtea degrada-
                  <lb/>
                uerit
                  <reg norm="quadratum" type="context">quadratũ</reg>
                , is ſcriptor, in figura
                  <var>.d.b.c.e.</var>
                eum bene & ex perſpectiuæ optimis
                  <lb/>
                legibus degradatum fuiſſe probare nititur; </s>
                <s xml:id="echoid-s1630" xml:space="preserve">ſolum probans
                  <var>.d.e.</var>
                æqualem eſſe ipſi
                  <var>.
                    <lb/>
                  E.h.</var>
                  <reg norm="qua" type="wordlist">q̃</reg>
                  <var>.E.h.</var>
                  <reg norm="ſecundum" type="context">ſecundũ</reg>
                ipſum eſt degra datio lateris
                  <var>.c.g.</var>
                &
                  <reg norm="cum" type="context">cũ</reg>
                ſuperius dixerit, ſetria
                  <lb/>
                quadrati plana degradauiſſe, quia
                  <var>.b.E.</var>
                degradat
                  <var>.b.c.</var>
                et
                  <var>.E.h.</var>
                degradat
                  <var>.c.g.</var>
                et
                  <var>.f.
                    <lb/>
                  h.</var>
                degradat
                  <var>.f.g.</var>
                nec quidem de lateribus
                  <var>.b.d.</var>
                et
                  <var>.c.e.</var>
                loquitur, quia ſi
                  <var>.c.g.</var>
                  <lb/>
                perfecti, degradatum eſt in
                  <var>.E.h</var>
                : et
                  <var>.d.e.</var>
                rectè protracta exiſtit, cum ſit æqua-
                  <lb/>
                lis ipſi
                  <var>.E.h.</var>
                cum etiam
                  <var>.b.d.</var>
                et
                  <var>.c.e.</var>
                rectè protractæ eſſe debeant: </s>
                <s xml:id="echoid-s1631" xml:space="preserve">qua de cau-
                  <lb/>
                ſa ipſis
                  <var>.b.E.</var>
                et
                  <var>.f.h.</var>
                quæ, ex ipſo, ſunt degradationes
                  <var>.b.c.</var>
                et
                  <var>.f.g.</var>
                æquales eſſe non de-
                  <lb/>
                bent? </s>
                <s xml:id="echoid-s1632" xml:space="preserve">Poſſet is mihi quidem reſpondere,
                  <reg norm="quod" type="simple">ꝙ</reg>
                hoc pacto nulla ſuperficies clauderetur.
                  <lb/>
                </s>
                <s xml:id="echoid-s1633" xml:space="preserve">Ergo tria latera
                  <var>.b.c</var>
                :
                  <var>c.g.</var>
                et
                  <var>.g.f.</var>
                  <reg norm="non" type="context">nõ</reg>
                benè ſunt degradata,
                  <reg norm="eiusque" type="simple">eiusq́;</reg>
                  <reg norm="proportionalitates" type="simple">ꝓportionalitates</reg>
                ma
                  <lb/>
                lè intellectæ nil probant. </s>
                <s xml:id="echoid-s1634" xml:space="preserve">quia ſi dictæ proportionalitates, nobis tutò promitterent
                  <lb/>
                degradationes, ab eo primum effectas, in linea
                  <var>.b.f.</var>
                eſſe bonas, ergo duæ
                  <var>.b.d.</var>
                et
                  <var>.e.c.</var>
                  <lb/>
                falſæ exiſterent, quarum quælibet maior eſt
                  <var>.b.E.</var>
                et
                  <var>.f.h.</var>
                ex .18. primi Eucli. </s>
                <s xml:id="echoid-s1635" xml:space="preserve">Omitta-
                  <lb/>
                mus etiam quod vbi is ſcribit eam eſſe rationem, aut comparationem ab
                  <var>.A.d.</var>
                ad
                  <var>.b.
                    <lb/>
                  E.</var>
                quæ eſt ab
                  <var>.d.c.</var>
                ad
                  <var>.b.c.</var>
                eandemq́ue eſſe ab
                  <var>.E.h.</var>
                ad
                  <var>.c.g.</var>
                quæ eſt ab
                  <var>.A.E.</var>
                ad
                  <var>.A.c.</var>
                nil
                  <lb/>
                probet; </s>
                <s xml:id="echoid-s1636" xml:space="preserve">nec ſimilitudinem triangulorum, nec aliquam propoſitionem Eucli. citans.
                  <lb/>
                </s>
                <s xml:id="echoid-s1637" xml:space="preserve">In quo excuſari non poteſt, quòd non ſoleat Euclidem, aut alium quemuis autorem
                  <lb/>
                citare, cum vel in ipſo operis principio capite .3. primæ partis, A pollonium
                  <reg norm="Pergeum" type="context">Pergeũ</reg>
                  <lb/>
                  <reg norm="Euclidemque" type="simple">Euclidemq́;</reg>
                , & ſi etiam præter rem, citet. </s>
                <s xml:id="echoid-s1638" xml:space="preserve">Deinde
                  <reg norm="quum" type="context">quũ</reg>
                idem probare vult
                  <var>.d.e.</var>
                æqua
                  <lb/>
                lem eſſe ipſi
                  <var>.E.h.</var>
                eandem inquit eſſe proportionem
                  <var>.a.b.</var>
                ad
                  <var>.a.d.</var>
                quæ eſt ipſius
                  <var>.A.c.</var>
                  <lb/>
                ad
                  <var>.A.E.</var>
                quod & ſi verum ſit, hic tamen modus ratiocinandi nullo ordine nititur,
                  <lb/>
                quia rectius dixiſſet pro clariori intelligentia ipſius
                  <var>.a.c.</var>
                ad
                  <var>.a.e.</var>
                eandem proportio-
                  <lb/>
                nem eſſe, quæ eſt
                  <var>.A.c.</var>
                ad
                  <var>.A.E.</var>
                propter ſimilitudinem, quæ inter duos triangulos
                  <var>.A.
                    <lb/>
                  c.a.</var>
                et
                  <var>.E.c.e.</var>
                intercedit, cum
                  <var>.E.e.</var>
                ſupponatur parallela ipſi
                  <var>.A.a.</var>
                quod etiam vt de-
                  <lb/>
                monſtraretur longiori oratione ei opus fuiſſet ſi voluiſſet intellectum eorum, qui pa
                  <lb/>
                rum ſunt exercitati, perduci ad
                  <reg norm="cognoſcendum" type="context">cognoſcendũ</reg>
                idem planè futurum de
                  <var>.a.c.</var>
                ad
                  <var>.a.e.</var>
                vt
                  <lb/>
                eſt ipſius
                  <var>.A.c.</var>
                ad
                  <var>.A.E.</var>
                in hunc modum, ideſt probando primùm duos triangulos
                  <var>.A.
                    <lb/>
                  c.a.</var>
                et
                  <var>.E.c.e.</var>
                æquiangulos eſſe, mediante .29. primi Eucli. cum
                  <var>.A.a.</var>
                et
                  <var>.E.e.</var>
                inuicem
                  <lb/>
                ſint parallelæ. </s>
                <s xml:id="echoid-s1639" xml:space="preserve">Vnde ex .4. ſexti. idem extitiſſet de
                  <var>.A.c.</var>
                ad
                  <var>.E.c.</var>
                vt
                  <var>.a.c.</var>
                ad
                  <var>.e.c.</var>
                et. ex
                  <lb/>
                16. quinti idem de
                  <var>.A.c.</var>
                ad
                  <var>.a.c.</var>
                vt ipſius
                  <var>.E.c.</var>
                ad
                  <var>.e.c.</var>
                & ex .19. eiuſdem de
                  <var>.A.E.</var>
                ad
                  <var>.a.
                    <lb/>
                  e.</var>
                vt ipſius
                  <var>.A.c.</var>
                ad
                  <var>.a.c.</var>
                & ex .16. iam dicta de
                  <var>.A.E.</var>
                ad
                  <var>.A.c.</var>
                vt ipſius
                  <var>.a.e.</var>
                ad
                  <var>.a.c.</var>
                ideſt
                  <lb/>
                ipſius
                  <var>.A.c.</var>
                ad
                  <var>.A.E.</var>
                vt eſt ipſius
                  <var>.a.c.</var>
                ad
                  <var>.a.e</var>
                : Aut hoc alio modo, qui breuior eſt pro-
                  <lb/>
                cedendum, incipiendo ſcilicet à ſecunda ſexti Eucli. dicendo
                  <reg norm="quod" type="simple">ꝙ</reg>
                exiſtente
                  <var>.E.e.</var>
                paral
                  <lb/>
                lela ipſi
                  <var>.A.a</var>
                : ex dicta .2. lib. 6. erit idem de
                  <var>.c.E.</var>
                ad
                  <var>.E.A.</var>
                vt de
                  <var>.c.e.</var>
                ad
                  <var>.e.a.</var>
                vnde ex
                  <num value="18">.
                    <lb/>
                  18.</num>
                quinti innotuiſſet ſtatim quod de
                  <var>.c.A.</var>
                ad
                  <var>.E.A.</var>
                vt de
                  <var>.c.a.</var>
                ad
                  <var>.e.a.</var>
                extitiſſet. </s>
                <s xml:id="echoid-s1640" xml:space="preserve">Nunc
                  <lb/>
                mediantibus ſupradictis duabus propoſitionibus ideſt .29. primi, & 4. ſexti, cogno-
                  <lb/>
                ſcitur idem planè eſſe de
                  <var>.b.c.</var>
                ad
                  <var>.d.e.</var>
                quod ipſius
                  <var>.a.c.</var>
                ad
                  <var>.a.e.</var>
                & ex eiſdem idem eſſe
                  <lb/>
                de
                  <var>.c.g.</var>
                ad
                  <var>.E.h.</var>
                quod ipſius
                  <var>.A.c.</var>
                ad
                  <var>.A.E.</var>
                vnde ex .11. quinti bis repetita idem erit de
                  <lb/>
                  <var>b.c.</var>
                ad
                  <var>.d.e.</var>
                quod de
                  <var>.c.g.</var>
                ad
                  <var>.E.h.</var>
                ſed cum ex ſuppoſito
                  <var>.c.g.</var>
                ſit æqualis ipſi
                  <var>.c.b.</var>
                idem
                  <lb/>
                erit de
                  <var>.c.g.</var>
                ad
                  <var>.e.d.</var>
                quod ipſius
                  <var>.c.b.</var>
                ad eandem ex .7. quinti, vnde ex .11. idem erit de
                  <lb/>
                  <var>c.g.</var>
                ad
                  <var>.E.h.</var>
                quod eiuſdem
                  <var>.c.g.</var>
                ad
                  <var>.e.d.</var>
                ex .9. igitur eiuſdem
                  <var>.d.e.</var>
                æqualis erit ipſi
                  <var>.E.
                    <lb/>
                  h.</var>
                atque hic verus eſt modus ducendi intellectum parum exercitatum in cognicio-
                  <lb/>
                nis campum. </s>
                <s xml:id="echoid-s1641" xml:space="preserve">quem quidem mihi obſeruandum proponerem ſi onus ſcribendi ſu-
                  <lb/>
                ſciperem ijs, qui in ſcientijs parum verſati ſunt, quos tanquam puerulos manu du- </s>
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