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]

Page concordance

< >
Scan Original
211 199
212 200
213 201
214 202
215 203
216 204
217 205
218 206
219 207
220 208
221 209
222 210
223 211
224 212
225 213
226 214
227 215
228 216
229 217
230 218
231 219
232 220
233 221
234 222
235 223
236 224
237 225
238 226
239 227
240 228
< >
page |< < (134) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div308" type="chapter" level="2" n="2">
            <div xml:id="echoid-div328" type="section" level="3" n="12">
              <p>
                <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/>
                  <figure xlink:label="fig-0146-01" xlink:href="fig-0146-01a" number="201">
                    <image file="0146-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0146-01"/>
                  </figure>
                </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>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>