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-div670" type="section" level="3" n="29">
              <div xml:id="echoid-div670" type="letter" level="4" n="1">
                <pb o="348" rhead="IO. BAPT. BENED." n="360" file="0360" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0360"/>
                <p>
                  <s xml:id="echoid-s4213" xml:space="preserve">Verum eſt igitur quod
                    <var>.a.b.</var>
                  cum
                    <var>.a.c.</var>
                  longiores ſint ipſa
                    <var>.b.c.</var>
                  per latus terrago.
                    <lb/>
                  nicum quadrupli eius quod fit. ex
                    <var>.a.e.</var>
                  in
                    <var>.a.i.</var>
                  quod fuit propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4214" xml:space="preserve">Illud etiam non eſt ſpernendum, quod quotieſcunque data fuerint omnia latera
                    <lb/>
                  alicuius trianguli, illicò poſſumus cognoſcere puncta
                    <var>.u.n.s.</var>
                  contingentiæ circuli in
                    <lb/>
                  ſcripti, ope vltimæ partis penultimæ tertij, eo quod ex illa iam ſcimus, quod de-
                    <lb/>
                  trahendo
                    <var>.b.c.</var>
                  ex aggregato aliorum duorum laterum, remanebit
                    <var>.u.a.</var>
                  et
                    <var>.a.n.</var>
                  qua-
                    <lb/>
                  rum vnaquęque nota erit, cum illarum quælibet, medietas ſit reſidui cogniti, detra
                    <lb/>
                  hendo poſtea vnam
                    <reg norm="illarum" type="context">illarũ</reg>
                  ab altero
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0360-01a" xlink:href="fig-0360-01"/>
                  duorum laterum
                    <var>.a.b.</var>
                  vel
                    <var>.a.c.</var>
                  rema
                    <lb/>
                  nebit
                    <var>.u.b.</var>
                  vel
                    <var>.c.n.</var>
                  ęqualis
                    <var>.b.s.</var>
                  vel
                    <var>.c.
                      <lb/>
                    s.</var>
                  vnde ſimiliter nobis innoteſcet
                    <lb/>
                  punctum
                    <var>.s.</var>
                  cum duobus punctis
                    <var>.u.</var>
                    <lb/>
                  ct
                    <var>.n.</var>
                  à quibus duobus punctis, ſi
                    <lb/>
                  duę perpendiculares ad talia latera
                    <lb/>
                  ductæ fuerint, vbi hæe perpendicu
                    <lb/>
                  lares ſeinuicem ſecabunt, ibi
                    <reg norm="cen- trum" type="context">cen-
                      <lb/>
                    trũ</reg>
                  circuli inſcriptibilis erit in trian
                    <lb/>
                  gulo propoſito.</s>
                </p>
                <div xml:id="echoid-div671" type="float" level="5" n="2">
                  <figure xlink:label="fig-0360-01" xlink:href="fig-0360-01a">
                    <image file="0360-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0360-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s4215" xml:space="preserve">Inter alia, quæ tibi dixi de Iride, quod memoria non tenes, nihil aliud eſt niſi
                    <lb/>
                  quod cum Iris videtur, non eodem loco ab omnibus videtur, quia reflexio eſt, &
                    <lb/>
                  vt reflexio luminis à ſpeculo non omnibus ab eodem puncto fit, ita etiam tibi dixi
                    <lb/>
                  de Iride.</s>
                </p>
              </div>
              <div xml:id="echoid-div673" type="letter" level="4" n="2">
                <head xml:id="echoid-head513" style="it" xml:space="preserve">De Inſtrumento oxygonio, ſeu elliptico.</head>
                <head xml:id="echoid-head514" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4216" xml:space="preserve">QVod aliquando à me audiuiſti falſum non eſt, ſcilicet poſſibile eſſe (vt
                    <lb/>
                  ſpeculatus ſum) particulare inſtrumentum fabricari ad deſignandum oxy-
                    <lb/>
                  goniam, ſeu ellipticam ſectionem, quæ à Pergeo defectio appellatur, quod quidem
                    <lb/>
                  inſtrumentum valde diuerſum eſt ab alijs, quę aliàs inueni, pro ipſis conicis ſectio
                    <lb/>
                  nibus delineandis. </s>
                  <s xml:id="echoid-s4217" xml:space="preserve">Occaſionem
                    <reg norm="autem" type="wordlist">aũt</reg>
                  huiuſimodi inſtrumenti inueniendi mihi præ
                    <lb/>
                  buit
                    <reg norm="ſecunda" type="context">ſecũda</reg>
                  dubij ſolutio
                    <reg norm="quam" type="context">quã</reg>
                  feci ann .1568. grauiſſ. philoſopho Franciſco Vimer
                    <lb/>
                  cato,
                    <reg norm="nam" type="context">nã</reg>
                    <reg norm="cum" type="context">cũ</reg>
                  viderim in ea figura
                    <var>.f.a.</var>
                  ſemper
                    <reg norm="æqualem" type="context">æqualẽ</reg>
                  eſſe
                    <var>.o.i.</var>
                  ſuæ parallelæ ſcilicet,
                    <lb/>
                  vnde cum recta linea fuerit protracta per
                    <var>.o.</var>
                  et
                    <var>.f.</var>
                  ipſa foret ſemper
                    <reg norm="ęquidiſtans" type="context">ęquidiſtãs</reg>
                    <var>.d.p.</var>
                  ex
                    <lb/>
                  33. primi Eucli. </s>
                  <s xml:id="echoid-s4218" xml:space="preserve">Venit mihi in mentem modus conſtruendi hoc ſubſcriptum inſtru-
                    <lb/>
                  mentum, tali ordine, videlicet,
                    <reg norm="coniungendo" type="context">coniungẽdo</reg>
                  ſeptem hic ſubnotatas lineas materia-
                    <lb/>
                  les
                    <var>.z.r</var>
                  :
                    <var>u.n</var>
                  :
                    <var>e.h</var>
                  :
                    <var>e.c</var>
                  :
                    <var>c.l</var>
                  :
                    <var>l.s.</var>
                  et
                    <var>.s.e.</var>
                  ſimul, hoc modo, ſcilicet
                    <reg norm="ſabricando" type="context">ſabricãdo</reg>
                  quadrila-
                    <lb/>
                  terum æquilaterum
                    <var>.c.e.s.l.</var>
                  hac conditione, quod immobili exiſtente puncto
                    <var>.c.</var>
                  in li
                    <lb/>
                  nea
                    <var>.z.r.</var>
                  reliqua omnia mobilia exiſtant, hoc eſt quod
                    <reg norm="punctum" type="context">punctũ</reg>
                    <var>.s.</var>
                  moueatur per di-
                    <lb/>
                  ctam lineam
                    <var>.z.r.</var>
                  & immobili exiſtente puncto
                    <var>.e.</var>
                  vt extremum lineæ
                    <var>.e.h.</var>
                  hoc eſt
                    <lb/>
                  coniuncto extremo
                    <var>.e.</var>
                  lineæ
                    <var>.e.h.</var>
                  cum angulo
                    <var>.c.e.s.</var>
                  reliqua puncta lineæ ipſius
                    <var>.e.h.</var>
                    <lb/>
                  moueantur per
                    <var>.l.</var>
                  & per duas parallelas
                    <var>.u.n.</var>
                  et
                    <var>.z.r.</var>
                  longitudo vero
                    <var>.e.h.</var>
                  ſit compo-
                    <lb/>
                  ſita ex duplo vnius lateris ipſius quadrilateris. </s>
                  <s xml:id="echoid-s4219" xml:space="preserve">Oportet deinde quod punctum
                    <var>.f.</var>
                    <lb/>
                  ſemper vnum, & idem ſit ipſius parallelæ
                    <var>.u.n.</var>
                  moueatur tamen per
                    <var>.e.h.</var>
                  quod qui-
                    <lb/>
                  dem punctum illud erit, quod vnam
                    <reg norm="portionem" type="context">portionẽ</reg>
                  circunferentiæ oxygoniæ ſectonis </s>
                </p>
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