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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page |< < (367) of 445 > >|
EPISTOL AE.
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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div713" type="section" level="3" n="37">
              <div xml:id="echoid-div713" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s4379" xml:space="preserve">
                    <pb o="367" rhead="EPISTOL AE." n="379" file="0379" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0379"/>
                  e
                    <unsure/>
                    <var>.g.</var>
                  vnde angulus
                    <var>.g.e.q.</var>
                  æqualis erit angulo
                    <var>.b.a.g.</var>
                  portionis, cum duplus ſit angulo
                    <lb/>
                    <var>q.p.g.</var>
                  medietati anguli ipſius portionis ex .19. tertij, ita quod angulus
                    <var>.q.e.g.</var>
                  nobis
                    <lb/>
                  cognitus erit, & ſimiliter arcus
                    <var>.g.q.</var>
                  & conſequenter ar-
                    <lb/>
                  cus
                    <var>.p.g.</var>
                  reſiduum medij circuli, & ſic
                    <var>.m.g.</var>
                  eius ſinus re
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0379-01a" xlink:href="fig-0379-01"/>
                  ctus, & etiam chorda
                    <var>.p.g.</var>
                  vt dupla ſinus dimidij arcus
                    <var>.
                      <lb/>
                    p.g.</var>
                  & ſic
                    <var>.p.m.</var>
                  eius ſinus verſus, vel vt tertium latus trian
                    <lb/>
                  guli orthogonij
                    <var>.p.g.m.</var>
                  vnde nobis cognita erit propor
                    <lb/>
                  tio ipſius
                    <var>.b.g.</var>
                  (quæ dupla eſt ipſi
                    <var>.m.g.</var>
                  ) ad
                    <var>.m.p.</var>
                  & quia
                    <lb/>
                  productum
                    <var>.p.m.</var>
                  in
                    <var>.m.q.</var>
                  æquale eſt ei, quod fit ex
                    <var>.b.m.</var>
                    <lb/>
                  in
                    <var>m.g.</var>
                  ex .34. tertij, quapropter nobis cognita erit pars
                    <lb/>
                    <var>q.m.</var>
                  quæ cum
                    <var>.p.m.</var>
                  complet totum diametrum
                    <var>.q.p.</var>
                  vn
                    <lb/>
                  de nobis cognita erit proportio ipſius
                    <var>.b.g.</var>
                  ad
                    <var>.q.p.</var>
                  qua
                    <lb/>
                  mediante cognoſcemus diametrum ſecundum partes il
                    <lb/>
                  las quibus propoſita ſuerit
                    <var>.b.g</var>
                  .</s>
                </p>
                <div xml:id="echoid-div713" type="float" level="5" n="1">
                  <figure xlink:label="fig-0379-01" xlink:href="fig-0379-01a">
                    <image file="0379-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0379-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s4380" xml:space="preserve">Hoc autem problema non in numeris ſed in continuo ab Euclid. ponitur in .32
                    <unsure/>
                  .
                    <lb/>
                  tertij.</s>
                </p>
              </div>
              <div xml:id="echoid-div715" type="letter" level="4" n="2">
                <head xml:id="echoid-head542" style="it" xml:space="preserve">De inuentione alterius trianguli conditionati.</head>
                <head xml:id="echoid-head543" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4381" xml:space="preserve">QVotieſcunque etiam inuenire voluerimus triangulum aliquem, puta
                    <var>.n.q.o.</var>
                    <lb/>
                  æqualem triangulo
                    <var>.t.</var>
                  (exempli gratia) propoſito, qui habeat angulum
                    <var>.n.</var>
                  æ-
                    <lb/>
                  qualem angalo
                    <var>.a.</var>
                  dato, latera vero continentia ipſum angulum
                    <var>.n.</var>
                  ſint inuicem pro-
                    <lb/>
                  portionata vt
                    <var>.x.</var>
                  et
                    <var>.y.</var>
                  ita faciemus, accipiemus lineam
                    <var>.n.m.</var>
                  cuius volueris magnitu-
                    <lb/>
                  dinis, ſupra quam conſtituemus triangulum
                    <var>.m.n.p.</var>
                  æqualem triangulo
                    <var>.t.</var>
                  hac metho-
                    <lb/>
                  do, hoc eſt prolungando latus
                    <var>.r.z.</var>
                  trianguli
                    <var>.t.</var>
                  quod ſit
                    <var>.r.e.</var>
                  ita vt duplum ſit ipſi
                    <var>.r.z.</var>
                    <lb/>
                  ducendo poſtea
                    <var>.c.e.</var>
                  habebimus ex .38. primi triangulum
                    <var>.t.</var>
                  eſſe dimidium totius
                    <lb/>
                  trianguli
                    <var>.r.c.e.</var>
                  deſignabimus deinde ex .44. dicti ſuperficiem
                    <var>.p.n.m.b.</var>
                  parallelo
                    <lb/>
                  grammam
                    <reg norm="æqualemque" type="simple">æqualemq́;</reg>
                  triangu
                    <lb/>
                  lo
                    <var>.r.c.e.</var>
                  habentem angulum
                    <var>.
                      <lb/>
                      <anchor type="figure" xlink:label="fig-0379-02a" xlink:href="fig-0379-02"/>
                    n.</var>
                  æqualem angulo
                    <var>.a.</var>
                  ducatur
                    <lb/>
                  poſtea
                    <var>.p.m.</var>
                  & habebimus
                    <reg norm="triam" type="context">triã</reg>
                    <lb/>
                  gulum
                    <var>.m.n.p.</var>
                  æqualem
                    <var>.t.</var>
                  cum
                    <lb/>
                  angulo
                    <var>.n.</var>
                  æquali angulo
                    <var>.a.</var>
                  pro
                    <lb/>
                  ducatur poſtea
                    <var>.n.p.</var>
                  ita vt
                    <var>.n.K.</var>
                    <lb/>
                  ſe habeat .ad
                    <var>.n.m.</var>
                  quemadmo
                    <lb/>
                  dum
                    <var>.x.</var>
                  ad
                    <var>.y.</var>
                  quod erit facilli-
                    <lb/>
                  mum producendo
                    <var>.n.m.</var>
                  et
                    <var>.n.
                      <lb/>
                    K.</var>
                  indeterminatè ſi oportuerit,
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4382" xml:space="preserve">deinde eas ad æqualitatem ſe-
                    <lb/>
                  can
                    <unsure/>
                  do ipſis
                    <var>.x.</var>
                  et
                    <var>.y.</var>
                  efficiendo
                    <lb/>
                  exempli gratia quod
                    <var>.n.i.</var>
                  ſit
                    <lb/>
                  æqualis ipſi
                    <var>.x.</var>
                  et
                    <var>.n.u.</var>
                  ipſi
                    <var>.y.</var>
                  du
                    <lb/>
                  cendo poſtea
                    <var>.u.i.</var>
                  deinde à puncto
                    <var>.m.</var>
                  ducendo
                    <var>.m.K.</var>
                  æquidiſtanter
                    <var>.u.i.</var>
                  ex .31.
                    <lb/>
                  primi. </s>
                  <s xml:id="echoid-s4383" xml:space="preserve">& ſic habebimus ex .4. ſexti proportionem
                    <var>.x.</var>
                  ad
                    <var>.y.</var>
                  eſſe inter
                    <var>.n.K.</var>
                  et
                    <var>.n.</var>
                  </s>
                </p>
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