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]

Table of Notes

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            <div xml:id="echoid-div720" type="section" level="3" n="38">
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                <p>
                  <s xml:id="echoid-s4397" xml:space="preserve">
                    <pb o="370" rhead="IO. BAPT. BENED." n="382" file="0382" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0382"/>
                  e
                    <unsure/>
                  tiam collectus cum angulo
                    <var>.o.a.c.</var>
                  grad .15. hi tres anguli efficient angulum
                    <var>.d.a.c.
                      <lb/>
                    d.</var>
                  ctum grad .108. min .22.</s>
                </p>
                <head xml:id="echoid-head548" style="it" xml:space="preserve">Examinatio anguli
                  <var>.u.</var>
                </head>
                <p>
                  <s xml:id="echoid-s4398" xml:space="preserve">Ducatur
                    <var>.d.n.</var>
                  quam quidem
                    <var>.d.n.</var>
                  cognoſcemus vt ſinus anguli
                    <var>.d.o.n.</var>
                  gra .45. nam
                    <lb/>
                  angulus ei contrapoſitus
                    <var>.q.o.p.</var>
                  eſt dimidium recti, </s>
                  <s xml:id="echoid-s4399" xml:space="preserve">quare
                    <var>.d.n.</var>
                  erit partium .70710.
                    <lb/>
                  talium qualium
                    <var>.d.o.</var>
                  fuerit .100000. ſed
                    <var>.d.o.</var>
                  eſt partium .115270. qualium
                    <var>.a.d.</var>
                  eſt
                    <num value="100000">.
                      <lb/>
                    100000.</num>
                  nam
                    <var>.e.d.</var>
                  vt ſinus anguli
                    <var>.e.a.d.</var>
                  gra .63. min .22. eſt partium .89389.
                    <var>o.e.</var>
                  ve-
                    <lb/>
                  ro eſt partium .50000. talium qualium
                    <var>.a.o.</var>
                  eſt .100000. vt ſinus anguli
                    <var>.e.a.o.</var>
                  gra .30.
                    <lb/>
                  ſed vt
                    <var>.a.o.</var>
                  eſt
                    <reg norm="partium" type="context">partiũ</reg>
                  .51762. </s>
                  <s xml:id="echoid-s4400" xml:space="preserve">hoc eſt vt
                    <var>.a.d.</var>
                  eſt .100000. ipſa
                    <var>.o.e.</var>
                  erit
                    <reg norm="partium" type="context">partiũ</reg>
                  .25881
                    <lb/>
                  quæ iuncta cum fuerit cum
                    <var>.e.d.</var>
                  efficiet
                    <var>.d.o.</var>
                  partium .115270. vt dictum eſt, quapro-
                    <lb/>
                  pter cum
                    <var>.d.n.</var>
                  ſit partium .70710. talium qualium
                    <var>.d.o.</var>
                  fuerit .100000. ipſa
                    <var>.d.n.</var>
                  erit
                    <lb/>
                  partium .81507. talium qualium
                    <var>.d.o.</var>
                  erit .115270. ideſt qualium
                    <var>.d.a.</var>
                  vel
                    <var>.d.u.</var>
                  erit
                    <lb/>
                  100000. quæ quidem
                    <var>.d.n.</var>
                  eſt ſinus anguli
                    <var>.d.u.n.</var>
                  graduum ſcilicet .54. 36. cuius du-
                    <lb/>
                  plum erit gra .109. mi .12. debebattamen eſſe .108.
                    <var>m.o</var>
                  .</s>
                </p>
                <head xml:id="echoid-head549" style="it" xml:space="preserve">Examinatio anguli
                  <var>.d.</var>
                </head>
                <p>
                  <s xml:id="echoid-s4401" xml:space="preserve">Accipe angulum
                    <var>.a.d.o.</var>
                  gra .26.
                    <lb/>
                    <figure xlink:label="fig-0382-01" xlink:href="fig-0382-01a" number="424">
                      <image file="0382-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0382-01"/>
                    </figure>
                  min .38. vt ſupra, cui applica angu-
                    <lb/>
                  lum
                    <var>.o.d.n.</var>
                  gra .45. min
                    <var>.o.</var>
                  ſimul cum
                    <lb/>
                  angulo
                    <var>.u.d.n.</var>
                  reſiduo ex recto gra
                    <lb/>
                  duum .35. minu .24. & conficies an-
                    <lb/>
                  gulum
                    <var>.a.d.u.</var>
                  grad .107. minu .2. &
                    <lb/>
                  habebis propoſitum, quem tamen
                    <lb/>
                  oportebat eſſe gra .108. min
                    <var>.o</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4402" xml:space="preserve">Quod autem omnia rectè ſuppu-
                    <lb/>
                  tata ſint, ex ſumma omnium angulo
                    <lb/>
                  rum patere poteſt. </s>
                  <s xml:id="echoid-s4403" xml:space="preserve">nam collectis om
                    <lb/>
                  nibus quinque angulis
                    <var>.a.c.d.f.u.</var>
                  ſi-
                    <lb/>
                  mul, hoc eſt grad .108. minu .22. cum
                    <lb/>
                  gra .107. min .2. cum grad .12. effi-
                    <lb/>
                  cient grad .540. min
                    <var>.o.</var>
                  ſumma æqua
                    <lb/>
                  lis ſex angulis rectis.</s>
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