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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            <div xml:id="echoid-div622" type="section" level="3" n="25">
              <div xml:id="echoid-div626" type="letter" level="4" n="3">
                <p>
                  <s xml:id="echoid-s3922" xml:space="preserve">
                    <pb o="323" rhead="EPISTOL AE." n="335" file="0335" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0335"/>
                    <reg norm="ducatur" type="simple">ducat̃</reg>
                  .
                    <var>r.V.</var>
                  ad rectos cum
                    <var>.H.I.</var>
                  vſque ad circunferentiam, in qua accipiatur
                    <var>.r.n.</var>
                  æqua
                    <lb/>
                  lis ei quæ eſt in parallelo, ducatur poſtea
                    <var>.o.n.M.</var>
                  & habe bimus triangulum
                    <var>.o.r.n.</var>
                  ſi-
                    <lb/>
                  milem
                    <reg norm="æqualemque" type="simple">æqualemq́;</reg>
                  triangulo iam ſupradicto. </s>
                  <s xml:id="echoid-s3923" xml:space="preserve">Vnde angulus
                    <var>.H.o.M.</var>
                  ei æqualis erit,
                    <lb/>
                  quem azimut facit cum meridiano, & angulus
                    <var>.M.o.k.</var>
                  ei ęqualis, quem azimut con-
                    <lb/>
                  ſtituit cum verticali, ita quod ſi talis circulus
                    <var>.H.k.I.</var>
                  eſſet planum horologij orizon-
                    <lb/>
                  talis, ſuppoſito
                    <var>.o.</var>
                  pro pede gnomonis, ſecando poſtea
                    <var>.o.M.</var>
                  in puncto
                    <var>.i.</var>
                  ita vt
                    <var>.o.i.</var>
                    <lb/>
                  æqualis eſſet
                    <var>.s.a.</var>
                  dato quod
                    <var>.o.M.</var>
                  ducta ſit ad partem ſibi conuenientem, reſpectu
                    <var>.o.
                      <lb/>
                    k.</var>
                  ipſa pro verticali ſuppoſita, quod tibirelinquo, cum hoc facillimum ſit, tunc pun
                    <lb/>
                  ctum
                    <var>.i.</var>
                  eſſet quod quærebamus. </s>
                  <s xml:id="echoid-s3924" xml:space="preserve">Quod verò de vno puncto dico, idem de omni-
                    <lb/>
                  bus infero.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3925" xml:space="preserve">Vbi verò mihi ſignificas Chriſtophorum Clauium, me duobus in locis meæ gno
                    <lb/>
                  monicæ redarguere, iam vidi. </s>
                  <s xml:id="echoid-s3926" xml:space="preserve">Circa primum locum igitur, qui eſt in pagin .161.
                    <lb/>
                  ita inquit.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s3927" xml:space="preserve">Non enim deſunt, qui vel omninò negent, inter quos eſt Ioannes Baptiſta Be-
                    <lb/>
                  nedictus in ſua gnomonica cap .70. et .71. vbialia, & multo longiore ratione cona-
                    <lb/>
                  tur arcus ſignorum deſcribere, vel certe dubitent, hoc modo rectè poſſe deſcribi ar-
                    <lb/>
                  cus ſignorum, cum rationem non videant, qua hæc noſtra deſcriptio quam quidem
                    <lb/>
                  omnes ſcriptores ſine vlla demonſtratione tradunt nitatur.</s>
                </quote>
                <p>
                  <s xml:id="echoid-s3928" xml:space="preserve">Abſque dubio raptim tranſcurrit illa capita .70. 71. </s>
                  <s xml:id="echoid-s3929" xml:space="preserve">Reuerendus Clauius alio quin
                    <lb/>
                  non ſcripſiſſet, quòd ego alia & multo longiore ratione conatus ſim arcus ſignorum
                    <lb/>
                  deſcribere & c. præſertim cum eadem prorſus ratio, quæ ibi à me tradita eſt, illa ſit,
                    <lb/>
                  quam ip ſe ſuis ſcriptis inſeruit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3930" xml:space="preserve">Meus igitur modus in dictis capitibus traditus, minime diſcrepat ab eo, ſed ab il-
                    <lb/>
                  lorum modo, quorum opinio eſt interualla
                    <var>.e.h</var>
                  :
                    <var>h.u</var>
                  : u. n; </s>
                  <s xml:id="echoid-s3931" xml:space="preserve">n.m. et
                    <var>.m.d.</var>
                  meæ figuræ in
                    <lb/>
                  pagi .75. poſitæ, æqualia eſſe interuallis
                    <var>.e.h</var>
                  :h.u:u.n:n.m. et
                    <var>.m.d.</var>
                  præcedentis figuræ,
                    <lb/>
                  qui etiam ſupponunt
                    <var>.t.e.</var>
                  meæ figuræ .75. eſſe directè coniuncta cum linea
                    <var>.e.h.u.n.
                      <lb/>
                    m.d.</var>
                  & propterea verſus finem .73. pag. dixi.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s3932" xml:space="preserve">Aduertat autem quam diligentiſſime quiſque ne ſe decipi patiatur à ſubſcripta fi
                    <lb/>
                  gura ſemicirculi
                    <var>.Q.æ.m.</var>
                  cum reliquis lineis ductis, ex antiquorum more, & c.</s>
                </quote>
                <p>
                  <s xml:id="echoid-s3933" xml:space="preserve">Eo quod non defuerunt aliqui, ex vetuſtioribus (quorum ſcripta ad meas manus
                    <lb/>
                  peruenerunt) qui ſumentes interualla
                    <var>e.h</var>
                  :h.u. & c. figuræ. pag .75. æqualia illis figu-
                    <lb/>
                  ræ pag .74.
                    <reg norm="putauerunt" type="context">putauerũt</reg>
                  lineam
                    <var>.t.e.</var>
                  directè coniunctam eſſe cum
                    <var>.e.h.</var>
                  & c. quod quidem
                    <lb/>
                  maximi erroris cauſa erat, </s>
                  <s xml:id="echoid-s3934" xml:space="preserve">& propterea cap .71. verum modum oſtendi, ſeruando il
                    <lb/>
                  lam eandem ſuppoſitionem, hoc eſt quod interſtitia
                    <var>.e.h</var>
                  :
                    <var>h.u</var>
                  : & c. figurę pag .75. æqua
                    <lb/>
                  lia ſint interſtitijs
                    <var>.e.h</var>
                  :
                    <var>h.u.</var>
                  & c. præcedentis figuræ, & ideò in dicto cap .71. dixi.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s3935" xml:space="preserve">Suppoſito deinde
                    <var>.f.e.b.</var>
                  lineam meridianam eſſe in plano orizontali, cęterę lineę
                    <lb/>
                  horarię erunt prędictę.</s>
                </quote>
                <p>
                  <s xml:id="echoid-s3936" xml:space="preserve">Stantibus igitur his ſuppoſitis, vt habeantur omnia ſcientificè, volui, vt intellige-
                    <lb/>
                  retur pyra mis qua drilatera, eo modo quo dixi, cap .71. vbi clarè patet eandem pyra
                    <lb/>
                  midem eſſe, quam Pater Clauius (tacitè) poſuit in figura horologij, vt ipſe docuit
                    <lb/>
                  propoſitione ſecunda, lib. ſecundi, cuius baſis eſt triangulum
                    <var>.H.I.F.</var>
                  ſuæ figurę (exem
                    <lb/>
                  pli gratia pro quinta hora poſt meridiana) Alterum verò triangulum à me cogita-
                    <lb/>
                  tum, terminatum ab
                    <var>.t.e</var>
                  :
                    <var>e.d</var>
                  : et. ab
                    <var>.t.d.</var>
                  eleuata in mea figura, eſt in ſua
                    <reg norm="triangulum" type="context">triãgulum</reg>
                    <var>.D.
                      <lb/>
                    I.F.</var>
                  & propterea dixi.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s3937" xml:space="preserve">Nam
                    <var>.t.e.</var>
                  et
                    <var>.e.d.</var>
                    <reg norm="vtræque" type="simple">vtræq;</reg>
                  in plano horologii non ſunt, quamuis in plano æquatoris
                    <lb/>
                  tres ſint, & c.</s>
                </quote>
                <p>
                  <s xml:id="echoid-s3938" xml:space="preserve">Angulus verò
                    <var>.e.</var>
                  quem dico rectum eſſe, in ſua figura eſt angulus
                    <var>.D.I.F.</var>
                  & mea </s>
                </p>
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