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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          <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-s3982" xml:space="preserve">
                    <pb o="328" rhead="IO. BAPT. BENED." n="340" file="0340" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0340"/>
                  zonte; </s>
                  <s xml:id="echoid-s3983" xml:space="preserve">cogitemus etiam lineam
                    <var>.A.t.i.x.</var>
                  illud coni latus eſſe, qu od à ſummitate ver­
                    <lb/>
                  ſus baſim tranſit per medium latitudinis ipſius gnomonis, concipiamus etiam mente
                    <lb/>
                    <var>e.a.</var>
                  communem ſectionem eſſe trianguli ſupra dicti cum azimut horæ, necnon pun-
                    <lb/>
                  ctum
                    <var>.K.</var>
                  eſſe commune radio Solis
                    <var>.o.a.</var>
                  & ſuperficiei conicæ, quod quidem eſt illud
                    <lb/>
                  quod quæritur, hoc ſcilicet modo. </s>
                  <s xml:id="echoid-s3984" xml:space="preserve">Primum cognoſcimus angulum
                    <var>.p.A.t.</var>
                  vt medie
                    <lb/>
                  tas anguli totius coni, & angulum
                    <var>.p.</var>
                  rectum, vnde
                    <var>.t.</var>
                  tam intrinſecus, quam extrinſe-
                    <lb/>
                  custrianguli
                    <var>.A.p.t.</var>
                  nobis cognitus erit. </s>
                  <s xml:id="echoid-s3985" xml:space="preserve">Nunc cum angulus
                    <var>.A.t.o.</var>
                  cognoſcatur, ſi
                    <lb/>
                  gnomon
                    <var>t.o.</var>
                  fixus fuerit in ſuperficie conica, ita qd cum latere
                    <var>.A.t.</var>
                  eſſiciat
                    <reg norm="angulum" type="context">angulũ</reg>
                    <lb/>
                    <var>A.t.o.</var>
                  & lateraliter faciat angulosrectos cum ſuperficie conica, ad quod efficiendum
                    <lb/>
                  nulla eſt difficultas, cognoſcendo deinde
                    <var>.A.t.</var>
                  ſimul cum angulis
                    <var>.A.</var>
                  et
                    <var>.t.</var>
                  intrinſecis
                    <lb/>
                  trianguli ortogonij
                    <var>.A.p.t.</var>
                  cognoſcemus
                    <var>.p.t.</var>
                  et
                    <var>.A.p.</var>
                  vnde etiam tota
                    <var>.o.p.</var>
                  ſed cogno
                    <lb/>
                  ſcendo
                    <var>.o.p.</var>
                  cum angulo
                    <var>.p.o.e.</var>
                  (angulus enim
                    <var>.p.o.e.</var>
                  cognoſcitur ex hypotheſi cum
                    <lb/>
                  ſit inter azimut Solis & azimut gnomonis) cum angulo
                    <var>.o.p.e.</var>
                  recto cognoſcemus
                    <var>.p.
                      <lb/>
                    e.</var>
                  et
                    <var>.o.e.</var>
                  </s>
                  <s xml:id="echoid-s3986" xml:space="preserve">deinde cum nobis nota ſit
                    <var>.o.e.</var>
                  cum angulo altitudinis Solis
                    <var>.e.o.a.</var>
                  & angu-
                    <lb/>
                  lo
                    <var>.o.e.a.</var>
                  recto cognoſc emus longitudinem azimutalis
                    <var>.e.a.</var>
                  necnon quantitatem
                    <var>.a.o.</var>
                    <lb/>
                  Imaginata poſtea
                    <var>.a.q.</var>
                  æquidiſtante
                    <var>.e.p.</var>
                  habebimus
                    <var>.p.q.</var>
                  æqualem
                    <var>.a.e.</var>
                  ex .34. primi
                    <lb/>
                  Eucli. </s>
                  <s xml:id="echoid-s3987" xml:space="preserve">Vnde duabus
                    <var>.o.p.</var>
                  et
                    <var>.p.q.</var>
                  mediantibus,
                    <reg norm="cognitiſque" type="simple">cognitiſq́;</reg>
                  cum angulo recto
                    <var>.p.</var>
                  cogno
                    <lb/>
                  ſcemus
                    <var>.o.q.</var>
                  nec non angulum
                    <var>.o.q.
                      <lb/>
                    p.</var>
                  quo mediante, necnon median-
                    <lb/>
                  te angulo
                    <var>.q.A.t.</var>
                  et
                    <var>.A.q.</var>
                  cognita, co
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0340-01a" xlink:href="fig-0340-01"/>
                  gnoſcemus
                    <var>.A.i.</var>
                  et
                    <var>.q.i.</var>
                  quę
                    <var>.q.i.</var>
                  dem
                    <lb/>
                  pta à
                    <var>.q.o.</var>
                  relinquet nobis
                    <reg norm="cognitam" type="context">cognitã</reg>
                    <lb/>
                    <var>i.o</var>
                  . </s>
                  <s xml:id="echoid-s3988" xml:space="preserve">Et quia
                    <var>.o.i.q.</var>
                  et
                    <var>.o.K.a.</var>
                  ſemper
                    <lb/>
                  ſunt in eadem ſuperficie ſecante co
                    <lb/>
                  num, quæ etiam ſecat ſuperficiem
                    <lb/>
                  trianguli
                    <var>.A.q.x.</var>
                  ad rectos ex .18. vn
                    <lb/>
                  decimi, cum linea
                    <var>.u.n.</var>
                  perpendicu
                    <lb/>
                  laris ſit ſuperficiei trianguli
                    <var>.A.q.i.</var>
                    <lb/>
                  ex .8. dicti, quia parallela eſt
                    <var>.l.p.</var>
                  quę
                    <lb/>
                  perpendicularis eſt ſuperficiei
                    <reg norm="trian- guli" type="context">triã-
                      <lb/>
                    guli</reg>
                    <var>.o.p.q.</var>
                  ex .4. eiuſdem, ſequitur,
                    <lb/>
                  quod talis ſectio ( quæ intelligatur
                    <lb/>
                  per
                    <var>.u.K.i.n.</var>
                  ) ſemper erit elliptica,
                    <lb/>
                  vel parabole, ſeu hyperbole,
                    <reg norm="prout" type="simple">ꝓut</reg>
                    <lb/>
                  linea
                    <var>.o.i.q.</var>
                  ſecabit latus coni, oppo
                    <lb/>
                  ſitum lateri
                    <var>.A.i.</var>
                  diſtento in ipſa ſuperficie conica, ſeu ad ſuperiorem partem produ
                    <lb/>
                  ctum, velipſi parallelum.</s>
                </p>
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                  <figure xlink:label="fig-0339-02" xlink:href="fig-0339-02a">
                    <image file="0339-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0339-02"/>
                  </figure>
                  <figure xlink:label="fig-0340-01" xlink:href="fig-0340-01a">
                    <image file="0340-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0340-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s3989" xml:space="preserve">Supponamus nunc dictam lineam
                    <var>.o.q.</var>
                  ſecare dictum oppoſitum latus lateri
                    <var>.A.i.</var>
                    <lb/>
                  verſus baſim, vnde ſectio
                    <var>.u.K.i.n.</var>
                  erit elliptica. </s>
                  <s xml:id="echoid-s3990" xml:space="preserve">quod facile cognitu eſt
                    <reg norm="mediante" type="context">mediãte</reg>
                  com
                    <lb/>
                  paratione angulorum
                    <var>.A.q.i.</var>
                  et
                    <var>.q.A.i.</var>
                  interſe, eo quod ſi eſſent ęquales, dicta ſect o
                    <lb/>
                  barabola eſſet ex .27. primi Eucli. et .11. primi Pergei, ſed ſi angulus
                    <var>.A.q.i.</var>
                  maior eſ-
                    <lb/>
                  ſet angulo
                    <var>.q.A.i.</var>
                  ſectio eſſet ellipſis, ex ultimo poſtulato primi Euclid. </s>
                  <s xml:id="echoid-s3991" xml:space="preserve">& ex .13. pri-
                    <lb/>
                  mi Pergei, ſed ſi dictus angulus
                    <var>.A.q.i.</var>
                  minor eſſet angulo
                    <var>.A.</var>
                  tunc ſectio eſſet hyper-
                    <lb/>
                  bole ex dicto poſtulato & ex .12. primi Pergei. </s>
                  <s xml:id="echoid-s3992" xml:space="preserve">Sit ergo primum vt
                    <reg norm="dictum" type="context">dictũ</reg>
                  eſt, hoc
                    <lb/>
                  eſt, quod ſectio eſſet oxygonia, ideſt elliptica, ſeu defectio (quod idem eſt,) ſepa-
                    <lb/>
                  ratim oportebit nos ellipſim deſignare
                    <reg norm="ſimilem" type="context">ſimilẽ</reg>
                    <reg norm="ęqualemque" type="context simple">ęqualẽq́;</reg>
                  ei, quæ eſt
                    <var>.u.K.i.n.</var>
                    <reg norm="quod" type="wordlist">qđ</reg>
                    <reg norm="quidem" type="context">quidẽ</reg>
                    <lb/>
                  difficile non erit, quotieſcunque ſuos axes inuenerimus, maiorem ſcilicet, & mino- </s>
                </p>
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