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
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
241 229
242 230
243 231
244 232
245 233
246 234
247 235
248 236
249 237
250 238
< >
page |< < (329) 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-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div630" type="section" level="3" n="26">
              <div xml:id="echoid-div634" type="letter" level="4" n="2">
                <p>
                  <s xml:id="echoid-s3992" xml:space="preserve">
                    <pb o="329" rhead="EPISTOL AE." n="341" file="0341" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0341"/>
                  rem, quæ ita reperientur, efficiemus primo anguium coni, qui ſit
                    <var>.i.A.b.</var>
                  quem diui-
                    <lb/>
                  demus per æqualia mediante
                    <var>.A.q.</var>
                  conſtituendo
                    <var>.A.i.</var>
                  huius anguli æqualem
                    <var>.A.i.</var>
                  ſu-
                    <lb/>
                  perficiei conicæ et
                    <var>.A.q.</var>
                  diuidentem, æqualem parti
                    <var>.A.q.</var>
                  axis coni, ducendo poſtea
                    <lb/>
                  ab
                    <var>.i.</var>
                  per
                    <var>.q.</var>
                  lineam vnam quouſque concurrat
                    <var>.A.b.</var>
                  in puncto
                    <var>.b.</var>
                  habebimus
                    <var>.i.b.</var>
                  pro
                    <lb/>
                  maiori axi ipſi ellipſis, quod per ſe clarum eſt, cuius medietas ſit
                    <var>.i.c.</var>
                  ſed
                    <var>.i.q.</var>
                  ipſius
                    <var>.i.
                      <lb/>
                    b.</var>
                  æqualis eſt ipſi
                    <var>.q.i.</var>
                  ipſius coni, ex quarta primi Eucli. et
                    <var>.q.b.</var>
                  ipſius
                    <var>.i.b.</var>
                  æqualis alte
                    <lb/>
                  ri parti inuiſibili. </s>
                  <s xml:id="echoid-s3993" xml:space="preserve">Reliquum eſt, vt reperiamus minorem axem, quem vocabimus
                    <var>.
                      <lb/>
                    f.r.</var>
                  ducatur ergo primum
                    <var>.q.a.u.n.</var>
                  ad rectos cum
                    <var>.i.b.</var>
                    <reg norm="æqualisque" type="simple">æqualisq́;</reg>
                  ei quæ eſt coni, & diui
                    <lb/>
                  ſa ſimiliter in
                    <var>.a.</var>
                  quæ
                    <var>.u.n.</var>
                  ipſius coni nobis cognita eſt ex lateribus
                    <var>.A.u.</var>
                  et
                    <var>.A.n.</var>
                  & ex
                    <lb/>
                  angulo coni, et
                    <var>.a.q.</var>
                  æqualis eſt
                    <var>.e.p.</var>
                  ex .34. primi. </s>
                  <s xml:id="echoid-s3994" xml:space="preserve">Nunc certi erimus ex .21. primi
                    <lb/>
                  Pergei, quod eadem proportio erit quadrati
                    <var>.u.q.</var>
                  ad quadratum ipſius
                    <var>.f.c.</var>
                  quæ pro-
                    <lb/>
                  ducti ipſius
                    <var>.i.q.</var>
                  in
                    <var>.q.b.</var>
                  ad productum ipſius
                    <var>.i.c.</var>
                  in
                    <var>.c.b.</var>
                  & cum cognita nobis ſint
                    <lb/>
                  hæc tria producta hoc eſt
                    <var>.i.q.</var>
                  in
                    <var>.q.b.</var>
                  et
                    <var>.i.c.</var>
                  in
                    <var>.c.b.</var>
                  et
                    <var>.u.q.</var>
                  in ſeipſa, cognoſcemus
                    <reg norm="etiam" type="context">etiã</reg>
                    <lb/>
                  quartum ipſius
                    <var>.f.c.</var>
                  & fic
                    <var>.f.c.</var>
                    <reg norm="eiuſque" type="simple">eiuſq́;</reg>
                  duplum
                    <var>.f.r.</var>
                  cogniti nobis itaque cum ſint hi duo
                    <lb/>
                  axes
                    <var>.i.b.</var>
                  et
                    <var>.f.r.</var>
                  formabimus ellipſim. </s>
                  <s xml:id="echoid-s3995" xml:space="preserve">Deinde producemus axim
                    <var>.b.i.</var>
                  à part
                    <var>e.i.</var>
                  quo-
                    <lb/>
                  uſque
                    <var>.i.o.</var>
                  æqualis ſit ei quæ extra conum eſt, dein-
                    <lb/>
                    <figure xlink:label="fig-0341-01" xlink:href="fig-0341-01a" number="364">
                      <image file="0341-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0341-01"/>
                    </figure>
                  de ducemus
                    <var>.o.a.</var>
                  quæ circunferentiam ellipticam
                    <lb/>
                  ſecabit in puncto
                    <var>.K.</var>
                  vnde habebimus quantita-
                    <lb/>
                  tem ipſius
                    <var>.o.K.</var>
                  et
                    <var>.K.i.</var>
                  rectam. </s>
                  <s xml:id="echoid-s3996" xml:space="preserve">inde mediante cir-
                    <lb/>
                  cino ſi acceperimus rectam diſtantiam ab
                    <var>.i.</var>
                  ad
                    <var>.K.</var>
                    <lb/>
                  in ellipſi, </s>
                  <s xml:id="echoid-s3997" xml:space="preserve">deinde firmando pedem circini in pun-
                    <lb/>
                  cto
                    <var>.i.</var>
                  in ſuperficie conica, & cum alio ſignando
                    <lb/>
                  lineam vnam curuam ad partem
                    <var>.K.</var>
                  in ſuperficie
                    <lb/>
                  conica, ſumendo poſtea interuallum
                    <var>.o.K.</var>
                  extra el
                    <lb/>
                  lipſim, </s>
                  <s xml:id="echoid-s3998" xml:space="preserve">deinde firmando vnum pedem circini in
                    <lb/>
                  extre mitate gnomonis, cum alio poſtea ſignan-
                    <lb/>
                  do aliam lineam curuam in ſuperficie ipſius coni,
                    <lb/>
                  quæ primam ſe cet in puncto
                    <var>.K.</var>
                  hoc erit punctum
                    <lb/>
                  quæſitum horę propoſitæ in ſuperficie conica
                    <lb/>
                  propoſita.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3999" xml:space="preserve">Sed ſi talis ſectio fuerit parabole, vel hyperbo
                    <lb/>
                  le, tunc mediante ſuo diametro
                    <var>.i.q.</var>
                  cum baſi
                    <var>.u.
                      <lb/>
                    q.n.</var>
                  cognita, deſignabimus ipſam ſectionem
                    <var>.u.i.</var>
                  n
                    <lb/>
                  ope mei
                    <reg norm="inſtrumenti" type="context">inſtrumẽti</reg>
                  in calce meę gnomonicæ de
                    <lb/>
                  ſcripti, </s>
                  <s xml:id="echoid-s4000" xml:space="preserve">deinde diuiſa
                    <var>.u.q.</var>
                  in
                    <var>.a.</var>
                    <reg norm="pro" type="simple">ꝓ</reg>
                    <reg norm="ductaque" type="simple">ductaq́;</reg>
                    <var>q.i.</var>
                    <reg norm="vſque" type="simple">vſq;</reg>
                    <lb/>
                    <figure xlink:label="fig-0341-02" xlink:href="fig-0341-02a" number="365">
                      <image file="0341-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0341-02"/>
                    </figure>
                  ad
                    <var>.o.</var>
                    <reg norm="ductaque" type="simple">ductaq́;</reg>
                    <var>.o.a.</var>
                  habebimus punctum
                    <var>.K</var>
                  . </s>
                  <s xml:id="echoid-s4001" xml:space="preserve">Reli-
                    <lb/>
                  qua facienda ſunt, vt dictum eſt de ellipſi.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4002" xml:space="preserve">Inuenta modo cum fuerint duo puncta eiuſ-
                    <lb/>
                  dem horæ propoſitę, ducemus ab vno ad a-
                    <lb/>
                  liud, lineam horariam mediante circino trium
                    <lb/>
                  crurum, quem tibi ſcripſi nudius tertius pro cyl
                    <lb/>
                  lindro, quæ
                    <reg norm="quidem" type="context">quidẽ</reg>
                  linea crit portio gyri ellipſis,
                    <lb/>
                  ſeu hyperbolę, vel parabolę, vt à te ipſo cogi-
                    <lb/>
                  tare potes.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum