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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                <s xml:id="echoid-s1615" xml:space="preserve">
                  <pb o="134" rhead="IO. BAPT. BENED." n="146" file="0146" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0146"/>
                minis vſque ad planiſitum in quo degradatio facta ſit: </s>
                <s xml:id="echoid-s1616" xml:space="preserve">ſtatim altitudo
                  <var>.A.</var>
                oculi à pe
                  <lb/>
                de, quæ tanta ſemper eſſe debet quanta eſt altitudo trianguli
                  <var>.b.n.m.</var>
                qui clauditur,
                  <lb/>
                protrahendo
                  <var>.m.l.</var>
                et
                  <var>.b.h.</var>
                vſque ad concurſum in
                  <var>.n.</var>
                in lucem prodibit. </s>
                <s xml:id="echoid-s1617" xml:space="preserve">Oporter
                  <lb/>
                deinde erigere lineam
                  <var>.b.o.</var>
                perpendicularem lineæ
                  <var>.d.b.m.</var>
                & vſque ad eandem pro
                  <lb/>
                ducere lineam
                  <var>.l.h.</var>
                in puncto
                  <var>.E.</var>
                et à puncto
                  <var>.A.</var>
                per
                  <var>.E.</var>
                vſque ad
                  <var>.c.</var>
                ipſius
                  <var>.d.b.m.</var>
                produ
                  <lb/>
                ctæ ducere
                  <var>.A.E.c.</var>
                atque deinde protrahere lineam
                  <var>.o.b.</var>
                vſque ad
                  <var>.T.</var>
                ita vt
                  <var>.b.T.</var>
                ęqua
                  <lb/>
                lis ſit ipſi
                  <var>.b.c.</var>
                & ad ipſam à puncto
                  <var>.m.</var>
                ducere parallelam
                  <var>.m.R.</var>
                & à puncto
                  <var>.T.</var>
                ducere
                  <var>.
                    <lb/>
                  T.R.</var>
                parallelam ipſi
                  <var>.b.m</var>
                . </s>
                <s xml:id="echoid-s1618" xml:space="preserve">Vnde ex .34. primi Eucli
                  <var>.m.R.</var>
                æqualis erit ipſi
                  <var>.b.T.</var>
                et
                  <var>.R.
                    <lb/>
                  T.</var>
                ipſi
                  <var>.m.b.</var>
                & anguli in rectos euadent, atque hoc parallelo grammum rectangulum
                  <lb/>
                erit verum perfectum degradati
                  <var>.b.m.l.h.</var>
                obrationes à me circa
                  <reg norm="figuram" type="context">figurã</reg>
                  <var>.A.</var>
                adductas.
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0146-01a" xlink:href="fig-0146-01"/>
                </s>
                <s xml:id="echoid-s1619" xml:space="preserve">Sed eſt hic quod magis nos commoueat, quia cum ex linea
                  <var>.b.c.</var>
                quadratum
                  <var>.b.g.</var>
                pro
                  <lb/>
                duxerit, vult eum poſtea degradare. </s>
                <s xml:id="echoid-s1620" xml:space="preserve">Quod vt faciat (hanc figuram videbis in cap
                  <num value="4">.
                    <lb/>
                  4.</num>
                ſecundæ partis Danielis Barbari) oculum
                  <var>.A.</var>
                in eadem ſuperficie extenſa,
                  <lb/>
                quadrati
                  <var>.b.g.</var>
                collocat. </s>
                <s xml:id="echoid-s1621" xml:space="preserve">Quod rectè fieti non poteſt, quia oculum hoc mo-
                  <lb/>
                do locantes, viſualesq́ue radios beneficio vnius plani ſituati in
                  <var>.b.f.</var>
                ſecantes in ipſo
                  <lb/>
                plano, nihil aliud quam
                  <reg norm="dictam" type="context">dictã</reg>
                  <reg norm="lineam" type="context">lineã</reg>
                  <var>.b.f.</var>
                &
                  <reg norm="nullam" type="context">nullã</reg>
                  <reg norm="degradationem" type="context">degradationẽ</reg>
                  <reg norm="inuenient" type="context">inueniẽt</reg>
                . </s>
                <s xml:id="echoid-s1622" xml:space="preserve">Id quod, & ſi
                  <lb/>
                natura ſua ſit omnibus notum, ponit
                  <reg norm="tantum" type="wordlist/context">tñ</reg>
                id ipſum Vitelio pro quinta propoſitione
                  <lb/>
                quarti libri de perſpectiua. </s>
                <s xml:id="echoid-s1623" xml:space="preserve">Præter hæc, credit latera
                  <var>.b.d.</var>
                et
                  <var>.c.e.</var>
                quadrati degra-
                  <lb/>
                dati ſemper videri mediantibus angulis
                  <var>.b.A.c.</var>
                et
                  <var>.f.A.g.</var>
                quod fieri
                  <reg norm="non" type="context">nõ</reg>
                poteſt, quem-
                  <lb/>
                a dmodum ex mea figura corporea
                  <var>.A.</var>
                facilè cognoſcere poſſumus, </s>
                <s xml:id="echoid-s1624" xml:space="preserve">propterea quòd
                  <lb/>
                latera
                  <var>.d.r.</var>
                et
                  <var>.q.e.</var>
                meæ figuræ, mediantibus angulis
                  <var>.d.o.r.</var>
                et
                  <var>.q.o.e.</var>
                qui extra ſuperfi-
                  <lb/>
                ciem
                  <var>.s.a.</var>
                exiſtunt videntur, vnde ſi quis imaginaretur in puncto
                  <var>.p.</var>
                oculum eſſe, &
                  <lb/>
                ab ipſo ad
                  <var>.u.</var>
                et
                  <var>.q.</var>
                duas lineas duceret, angulus
                  <var>.q.o.u.</var>
                nunc maior, nunc minor eſſet
                  <lb/>
                angulo
                  <var>.q.p.u.</var>
                aliquando etiam æqualis, quamuis rariſſime; </s>
                <s xml:id="echoid-s1625" xml:space="preserve">Sub diuerſis igitur an-
                  <lb/>
                gulis, pro maiori parte, deteguntur latera, à partibus quadrati tam degradati, quàm
                  <lb/>
                perfecti, quæ non ſunt anguli
                  <var>.b.A.c.</var>
                et
                  <var>.f.A.G</var>
                . </s>
                <s xml:id="echoid-s1626" xml:space="preserve">Quod vero idem poſtea dicat eam
                  <lb/>
                proportionem eſſe ab
                  <var>.b.E.</var>
                ad
                  <var>.f.h.</var>
                & ſimul ad
                  <var>.c.g.</var>
                quæ eſt ab
                  <var>.a.g.</var>
                ad
                  <var>.h.g.</var>
                id tuo relin­ </s>
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