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-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div518" type="section" level="3" n="8">
              <div xml:id="echoid-div518" type="letter" level="4" n="1">
                <pb o="264" rhead="IO. BAPT. BENED." n="276" file="0276" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0276"/>
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              <div xml:id="echoid-div521" type="letter" level="4" n="2">
                <head xml:id="echoid-head394" style="it" xml:space="preserve">Figuram ſuperficialem ellipſi ſimilem, ex datis axibus cir-
                  <lb/>
                cino mediante delineari poſſe.</head>
                <head xml:id="echoid-head395" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3301" xml:space="preserve">FIguram ſuperficialem ellipſi ſimilem, ex datis axibus, circino mediante delinea
                    <lb/>
                  re cum volueris, ita facito.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3302" xml:space="preserve">Sit
                    <var>.e.c.</var>
                  ſemiaxis maior
                    <var>.a.e.</var>
                  verò minor, ad angulum rectum inuicem coniuncti,
                    <lb/>
                  tunc
                    <var>.a.e.</var>
                  producatur vſque ad
                    <var>.o</var>
                  . </s>
                  <s xml:id="echoid-s3303" xml:space="preserve">
                    <reg norm="Itaque" type="simple">Itaq;</reg>
                    <var>.a.o.</var>
                  maior ſit quam diſtantia inter
                    <var>.o.</var>
                  et
                    <var>.c.</var>
                  quę
                    <lb/>
                  quidem
                    <var>.a.o.</var>
                  poſſet etiam dari, deſcribatur poſtea circulus
                    <var>.a.d.b.</var>
                  circa centrum
                    <var>.o.</var>
                  à
                    <lb/>
                  quo puncto protrahatur ſemidiameter
                    <var>.o.b.</var>
                  quæ cum
                    <var>.a.o.</var>
                  angulum rectum conſti-
                    <lb/>
                  tuat, quę
                    <var>.o.b.</var>
                  erit æquidiſtans
                    <var>.e.c.</var>
                  ex .28. primi, ducatur poſtea
                    <var>.b.c.d.</var>
                  et
                    <var>.o.t.d.</var>
                  vnde
                    <lb/>
                  angulus
                    <var>.t.c.d.</var>
                  ęqualis erit angulo
                    <var>.o.b.d.</var>
                  ex .29. eiuſdem. </s>
                  <s xml:id="echoid-s3304" xml:space="preserve">ex quinta autem anguli
                    <var>.b.</var>
                    <lb/>
                  et
                    <var>.d.</var>
                  ſunt inuicem æquales, </s>
                  <s xml:id="echoid-s3305" xml:space="preserve">quare etiam
                    <lb/>
                  & anguli
                    <var>.d.</var>
                  et
                    <var>.c.</var>
                  inuicem ęquales erunt,
                    <lb/>
                    <figure xlink:label="fig-0276-01" xlink:href="fig-0276-01a" number="306">
                      <image file="0276-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0276-01"/>
                    </figure>
                  & ex .6. eiuſdem
                    <var>.t.c.</var>
                  ęqualis erit
                    <var>.t.d.</var>
                  duca
                    <lb/>
                  tur poſtea
                    <var>.d.x.h.</var>
                  perpendicularis lineæ
                    <var>.c.
                      <lb/>
                    e.</var>
                  ita diſtans ſub ipſa
                    <var>.c.e.</var>
                  vt arcus circula-
                    <lb/>
                  ris circa
                    <var>.t.</var>
                  delineatus ex ſemidiametro
                    <var>.t.
                      <lb/>
                    d.</var>
                  aptus ſit eam ſecare, ſumpto poſtea
                    <var>.r.</var>
                    <lb/>
                  tam diſtante ab
                    <var>.e.</var>
                  vt
                    <var>.t.</var>
                  reperitur ab ipſo
                    <lb/>
                  e. et
                    <var>.z.</var>
                  ab
                    <var>.e.</var>
                  vt
                    <var>.o.</var>
                  ab eodem, ducendo po-
                    <lb/>
                  ſtea duos alios arcus magnitudinis
                    <reg norm="priorum" type="context">priorũ</reg>
                    <lb/>
                  circa centra
                    <var>.r.</var>
                  et
                    <var>.z.</var>
                  habebimus propoſi-
                    <lb/>
                  tum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3306" xml:space="preserve">Sed cum quis voluerit prius arcus mi-
                    <lb/>
                  norum circulorum delineare circa maio-
                    <lb/>
                  rem axem, fiant cuiuſuis magnitudinis, vt
                    <lb/>
                  in ſecunda figura videre eſt, poſito tamen quod eorum diameter, minor ſit minore
                    <lb/>
                  axe ipſius figurę, quorum circulorum vnus ſit
                    <var>.c.d.</var>
                  circa
                    <var>.t.</var>
                  eius centrum, deinde in axe
                    <lb/>
                  minori ſumatur
                    <var>.a.x.</var>
                  æqualis
                    <var>.c.t.</var>
                  & protrahatur
                    <var>.t.x.</var>
                  quę per ęqualia diuidatur in pun-
                    <lb/>
                  cto
                    <var>.n.</var>
                  à quo poſtea ducatur
                    <var>.n.o.</var>
                  ad angulos rectos
                    <lb/>
                    <figure xlink:label="fig-0276-02" xlink:href="fig-0276-02a" number="307">
                      <image file="0276-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0276-02"/>
                    </figure>
                  cum
                    <var>.t.x.</var>
                  vſque ad interſectionem cum
                    <var>.a.e.</var>
                  in pun-
                    <lb/>
                  cto
                    <var>.o.</var>
                  minori axi producta cum oportuerit, quod
                    <lb/>
                  quidem punctum
                    <var>.o.</var>
                  centrum erit arcus
                    <var>.d.a.</var>
                  maio-
                    <lb/>
                  ris, eo quod
                    <var>.o.t.</var>
                  æqualis eſſet
                    <var>.o.x.</var>
                  ex .4. primi Eu-
                    <lb/>
                  cli. </s>
                  <s xml:id="echoid-s3307" xml:space="preserve">vnde
                    <var>.o.d.</var>
                  æqualis eſſet
                    <var>.o.a.</var>
                  & circuli etiam in-
                    <lb/>
                  uicem contingentes in puncto
                    <var>.d.</var>
                  ex .11. tertij tam
                    <lb/>
                  in prima, quam in ſecunda figura, ſumpto
                    <reg norm="denique" type="simple">deniq;</reg>
                    <lb/>
                  puncto
                    <var>.s.</var>
                  tam remoto ab
                    <var>.e.</var>
                  quam
                    <var>.o.</var>
                  reperitur ab
                    <lb/>
                  eodem, ipſum, centrum erit alterius arcus oppoſi-
                    <lb/>
                  ti, poſſemus etiam
                    <reg norm="abſque" type="simple">abſq;</reg>
                  diuiſione ipſius,
                    <var>t.x.</var>
                  conſti
                    <lb/>
                  tuere angulum
                    <var>.x.t.o.</var>
                    <reg norm="æqualem" type="context">æqualẽ</reg>
                  angulo
                    <var>.t.x.o.</var>
                  vnde ex
                    <lb/>
                  6. primi haberemus
                    <var>.o.t.</var>
                  æqualem
                    <var>.o.x</var>
                  .</s>
                </p>
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