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-div564" type="section" level="3" n="17">
              <div xml:id="echoid-div564" type="letter" level="4" n="1">
                <pb o="294" rhead="IO. BAPT. BENED." n="306" file="0306" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0306"/>
                <p>
                  <s xml:id="echoid-s3642" xml:space="preserve">Vel ſi tibi placet, accipe hanc aliam methodum à me excogitatum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3643" xml:space="preserve">Duplicetur
                    <reg norm="triangulum" type="context">triangulũ</reg>
                    <var>.a.b.c.</var>
                    <reg norm="orthogonium" type="context">orthogoniũ</reg>
                  , & fiat
                    <reg norm="rectangulum" type="context">rectangulũ</reg>
                    <var>.b.u.</var>
                  vt in mea figura
                    <lb/>
                  ſecundi exempli hic vides. </s>
                  <s xml:id="echoid-s3644" xml:space="preserve">
                    <reg norm="producaturque" type="simple">producaturq́;</reg>
                    <var>.b.c.</var>
                  quouſque
                    <var>.c.f.</var>
                  æqualis ſit
                    <var>.c.u.</var>
                  vnde
                    <var>.b.f.</var>
                    <lb/>
                  cognita nobis erit ex hypotheſi, </s>
                  <s xml:id="echoid-s3645" xml:space="preserve">quare cognoſcemus etiam quadratum
                    <var>.g.f.</var>
                  à quo
                    <lb/>
                    <reg norm="demptum" type="context">demptũ</reg>
                  cum fuerit
                    <reg norm="aggregatum" type="context">aggregatũ</reg>
                  quadratorum
                    <var>.g.u.</var>
                  et
                    <var>.u.f.</var>
                  nobis
                    <reg norm="cognitum" type="context">cognitũ</reg>
                  (nam quadra
                    <lb/>
                  ta
                    <var>.g.u.</var>
                  et
                    <var>.u.f.</var>
                  æqualia ſunt quadrato ipſius
                    <var>.a.c.</var>
                  diagonalis datę) remanebit aggrega-
                    <lb/>
                  tum
                    <reg norm="ſupplementorum" type="context context">ſupplemẽtorũ</reg>
                  cognitum, </s>
                  <s xml:id="echoid-s3646" xml:space="preserve">quare eius medietas cognoſcetur ideſt
                    <var>.b.u.</var>
                  vndæ ex
                    <num value="5">.
                      <lb/>
                    5.</num>
                  ſecundi Eucli. vt ſuperius diximus cognoſcetur etiam
                    <var>.b.c.</var>
                  et
                    <var>.c.f.</var>
                  diſtinctæ.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3647" xml:space="preserve">Idem aſſero de
                    <reg norm="exemplo" type="context">exẽplo</reg>
                  Gemmæ Friſij à Stifelio citato in Appendice regulæ falſi.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3648" xml:space="preserve">Sit gratia exempli rectangulum hicſubſcriptum
                    <var>.a.b.</var>
                  datæ ſuperficiei data etiam
                    <lb/>
                  nobis ſit proportio
                    <var>.a.e.</var>
                  ad
                    <var>.e.b.</var>
                  laterum producentium,
                    <reg norm="cogitemusque" type="simple">cogitemusq́;</reg>
                    <var>.a.e.</var>
                  producta
                    <lb/>
                  vſque ad
                    <var>.o.</var>
                  ita vt
                    <var>.e.o.</var>
                  æqualis ſit ipſi
                    <var>.e.b.</var>
                  imagine
                    <lb/>
                    <figure xlink:label="fig-0306-01" xlink:href="fig-0306-01a" number="329">
                      <image file="0306-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0306-01"/>
                    </figure>
                  mus
                    <reg norm="etiam" type="context">etiã</reg>
                  perfectum eſſe quadratum
                    <var>.b.o.</var>
                  vnde ex
                    <lb/>
                  prima ſexti ſeu .18. vel .19. ſeptimi vel .15. quinti
                    <lb/>
                  eadem proportio erit ipſius
                    <var>.a.b.</var>
                  ad
                    <var>.b.o.</var>
                  vt
                    <var>.a.e.</var>
                  ad
                    <lb/>
                    <var>e.o.</var>
                  vel ad
                    <var>.e.b.</var>
                  </s>
                  <s xml:id="echoid-s3649" xml:space="preserve">quare ex regula de tribus, cogno-
                    <lb/>
                  ſcemus quadratum
                    <var>.b.o.</var>
                  & eius
                    <reg norm="radicem" type="context">radicẽ</reg>
                    <var>.e.o.</var>
                  & ex ea
                    <lb/>
                  demregula cognoſcemus
                    <var>.a.e.</var>
                  cum cognita nobis ſit
                    <var>.e.o.</var>
                  ſimul cum proportione
                    <var>.e.o.</var>
                    <lb/>
                  ad
                    <var>.e.a</var>
                  .</s>
                </p>
              </div>
              <div xml:id="echoid-div568" type="letter" level="4" n="2">
                <head xml:id="echoid-head432" style="it" xml:space="preserve">Quod circulus ſit figura infinitorum angulorum hoc eſt
                  <lb/>
                ultima poligoniarum.</head>
                <head xml:id="echoid-head433" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3650" xml:space="preserve">SEd quod idem Stifelius in Appendice ſecundi libri dicat circulum eſſe figuram
                    <lb/>
                  poligoniam, non eſt ita mirandum, nam & alij multi doctiſſimi viri hanc
                    <lb/>
                  veritatem cognouerunt, de Leone Baptiſta Alberto nihil dicam, cum ipſe fateatur
                    <lb/>
                  hoc accepiſſe à philoſophis, vt etiam refert Ariſt. de ſphæratertio de cœlo. </s>
                  <s xml:id="echoid-s3651" xml:space="preserve">conſi-
                    <lb/>
                  dera quæſo in circulo, quod cum angulus contingentiæ ſit angulus, quamuis
                    <reg norm="omnium" type="context">omniũ</reg>
                    <lb/>
                  acutorum rectilineorum anguſtiſſimus, vnde ex communi ratione ſequitur reliquum
                    <lb/>
                  ex duobus rectis rectilineis eſſe angulum, & ſi omnium obtuſorum rectilineorum ſit
                    <lb/>
                  ampliſſimum, tanto magis igitur erit angulus, id quod remanet ex duobus rectis re
                    <lb/>
                  ctilineis, detractis
                    <reg norm="cum" type="context">cũ</reg>
                  fuerint duobus angulis contingentiæ, qui quidem angulus erit
                    <lb/>
                  in quouis puncto circunferentiæ ipſius circuli, idem intelligendum eſt de ſphæra,
                    <lb/>
                  cuius angulus eſt reſiduum ex quatuor rectis ſolidis, detractis cum fuerint quatuor
                    <lb/>
                  angulis contingentiæ
                    <reg norm="ſolidisque" type="simple">ſolidisq́;</reg>
                  .</s>
                </p>
              </div>
              <div xml:id="echoid-div569" type="letter" level="4" n="3">
                <head xml:id="echoid-head434" style="it" xml:space="preserve">Explanatio .25. Problematis lib. 2. Monteregij.</head>
                <head xml:id="echoid-head435" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3652" xml:space="preserve">QVod in .25. problemate .2. lib. de triangulis Monteregium non intelligas, mi-
                    <lb/>
                  rum non eſt, eo quod quandoque bonus dormitat Homerus. </s>
                  <s xml:id="echoid-s3653" xml:space="preserve">Puto enim il-
                    <lb/>
                  lud problema ab ipſo Monteregio non fuiſſe viſitatum. </s>
                  <s xml:id="echoid-s3654" xml:space="preserve">Sed ne me aliquo modo
                    <lb/>
                  culpes, accipe hanc
                    <reg norm="aliam" type="context">aliã</reg>
                    <reg norm="methodum" type="context">methodũ</reg>
                  a me aliter
                    <reg norm="etiam" type="context">etiã</reg>
                    <reg norm="excogitatam" type="context">excogitatã</reg>
                  in eadem ipſius figura.</s>
                </p>
              </div>
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