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-div606" type="section" level="3" n="23">
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                <pb o="314" rhead="IO. BABPT. BENED." n="326" file="0326" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0326"/>
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                <head xml:id="echoid-head473" style="it" xml:space="preserve">Modus inueniendi duo triangula
                  <reg norm="varijs" type="lig">varijs</reg>
                conditionibus
                  <lb/>
                affecta.</head>
                <head xml:id="echoid-head474" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3861" xml:space="preserve">QVod etiam quæris ita ſe habet, duo ſcilicet triangula inuenire, æqualia dua-
                    <lb/>
                  bus ſuperficiebus rectilineis propoſitis, quę quidem triangula ſint eiuſdem
                    <lb/>
                  alritudinis, & quod
                    <reg norm="vnunquodque" type="context">vnũquodque</reg>
                  habeat angulum æqualem angulo pro
                    <unsure/>
                  poſito, &
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  alius angulus vnius, cum alio alterius, æquetur duobus rectis.</s>
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                <p>
                  <s xml:id="echoid-s3862" xml:space="preserve">Sint exempli gratia duæ propoſitæ ſuperflcies
                    <var>.c.y.</var>
                  duo verò anguli dati ſint
                    <var>.r.s.</var>
                    <lb/>
                  cum voluerimus inuenire duo triangula (quæ ſint
                    <var>.a.i.u.</var>
                  et
                    <var>.n.t.x.</var>
                  ) tali conditio-
                    <lb/>
                  ne prædita, quod angulus, a. æqualis ſit angulo
                    <var>.s.</var>
                  & angulus
                    <var>.t.</var>
                  angulo
                    <var>.r.</var>
                  & quod
                    <lb/>
                  angulus
                    <var>.x.</var>
                  ſimul cum angulo
                    <var>.u.</var>
                    <reg norm="æ- quentur" type="context">æ-
                      <lb/>
                    quẽtur</reg>
                  duobus rectis, & quod
                    <reg norm="triam" type="context">triã</reg>
                    <lb/>
                    <figure xlink:label="fig-0326-01" xlink:href="fig-0326-01a" number="349">
                      <image file="0326-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0326-01"/>
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                    <reg norm="gulum" type="context">gulũ</reg>
                    <var>.a.i.u.</var>
                  æquale ſit ſuperficiei
                    <var>.
                      <lb/>
                    c.</var>
                  reliquum verò ſuperficiei
                    <var>.y.</var>
                    <lb/>
                  Ex duabus ſuperficiebus
                    <var>.c.</var>
                  et
                    <var>.y.</var>
                    <lb/>
                  conſtituemus duo quadrata, per vl
                    <lb/>
                  timam ſecundi Eucli. accipiemus,
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3863" xml:space="preserve">deinde duo latera tetragonica ip-
                    <lb/>
                  ſorum quadratorum, & inuenie-
                    <lb/>
                  mus tertiam lineam in continua
                    <lb/>
                  proportionalitate cum illis lateri-
                    <lb/>
                  bus ex .10. ſexti, ſeruabimus po-
                    <lb/>
                  ſtea extremas illarum, quæ ſint
                    <var>.z.</var>
                    <lb/>
                  et
                    <var>.l.</var>
                  quarum proportio,
                    <reg norm="eadem" type="context">eadẽ</reg>
                  erit,
                    <lb/>
                  quæ inter duas propoſitas ſuperfi-
                    <lb/>
                  cies reperitur ex .18. ſexti, accipie
                    <lb/>
                  mus, deinde lineam aliquam cu-
                    <lb/>
                  inſuis longitudinis, quæ ſit
                    <var>.q.g.</var>
                  ſu-
                    <lb/>
                  pra quam conſtituemus in puncto
                    <lb/>
                  q. angulum
                    <var>.m.q.g.</var>
                  ęqualem angu-
                    <lb/>
                  lo
                    <var>.s.</var>
                  & angulum
                    <var>.m.q.K.</var>
                  æqualem
                    <lb/>
                  angulo
                    <var>.r.</var>
                  ex .23. primi, poſtea ve-
                    <lb/>
                  rò à quouis puncto ipſius lineæ
                    <var>.q.
                      <lb/>
                    m.</var>
                  puta
                    <var>.o.</var>
                  ducetur
                    <var>.o.f.</var>
                  vſque ad
                    <var>.q.
                      <lb/>
                    g.</var>
                  quorſum volueris, producendo
                    <lb/>
                  ipſam
                    <reg norm="vſque" type="simple">vſq;</reg>
                  . ad
                    <var>.d.</var>
                  ita quod propor-
                    <lb/>
                  tio
                    <var>f.o.</var>
                  ad
                    <var>.o.d.</var>
                  ſit vt
                    <var>.z.</var>
                  ad
                    <var>.l.</var>
                  ex .10.
                    <lb/>
                  ſexti, ducendo poſtea à puncto
                    <var>.d.</var>
                    <lb/>
                  lineam
                    <var>.d.h.E.</var>
                  parallelam lineæ
                    <var>.q.
                      <lb/>
                    g.</var>
                  & quia ex .2. primi Vitellionis
                    <var>.
                      <lb/>
                    h.E.</var>
                  ſecatur ab
                    <var>.q.K.</var>
                  in puncto
                    <var>.b.</var>
                    <lb/>
                  protrahemus
                    <var>.b.o.p.</var>
                  vnde ex ſimi-
                    <lb/>
                  litudine triangulorum habebimus
                    <lb/>
                  proportionem
                    <var>.p.o.</var>
                  ad
                    <var>.o.b.</var>
                  vt
                    <var>.f.o.</var>
                  </s>
                </p>
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