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]
page |< < (305) of 445 > >|
EPISTOLAE.
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div591" type="section" level="3" n="22">
              <div xml:id="echoid-div591" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s3766" xml:space="preserve">
                    <pb o="305" rhead="EPISTOLAE." n="317" file="0317" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0317"/>
                  eo quod tam proportio producti
                    <var>.n.o.</var>
                  in
                    <var>.o.u.</var>
                  ad productum
                    <var>.m.o.</var>
                  in
                    <var>.o.x.</var>
                  quam pro-
                    <lb/>
                  portio trianguli
                    <var>.n.o.u.</var>
                  ad triangulum
                    <var>.m.o.x.</var>
                  componitur ex proportione
                    <var>.u.o.</var>
                  ad
                    <var>.o.
                      <lb/>
                    x.</var>
                  & ex proportion
                    <var>e.n.o.</var>
                  ad
                    <var>.m.o.</var>
                  vnde proportio dictorum productorum nobis co-
                    <lb/>
                  gnita erit, eo quod cum nobis cognita ſit proportio
                    <var>.A.</var>
                  ad
                    <var>.B.</var>
                  vt data, cognita etiam
                    <lb/>
                  nobis erit coniuncta, hoceſt
                    <var>.A.B.</var>
                  ad
                    <var>.B</var>
                  . </s>
                  <s xml:id="echoid-s3767" xml:space="preserve">& propterea ea quæ trianguli
                    <var>.n.o.u.</var>
                  ad
                    <reg norm="trian- gulum" type="context">triã-
                      <lb/>
                    gulum</reg>
                    <var>.m.o.x.</var>
                  & ſimiliter productorum. </s>
                  <s xml:id="echoid-s3768" xml:space="preserve">Quæſiui poſtea modum inueniendi duas
                    <lb/>
                  dictas lineas
                    <var>.m.o.</var>
                  et
                    <var>.o.x.</var>
                  & cognoui quod ſi producta fuerit
                    <var>.p.i.</var>
                  æquidiſtans li-
                    <lb/>
                  neæ
                    <var>.o.x.</var>
                    <reg norm="producendoque" type="simple">producendoq́</reg>
                    <var>.o.n.</var>
                  quouſque cum
                    <var>.p.i.</var>
                  ſe interſecarent in puncto
                    <var>.i.</var>
                  inuenien
                    <lb/>
                  do poſtea lineam quandam, quæ ducta cum
                    <var>.p.i.</var>
                  efficeret rectangulum æquale rectan
                    <lb/>
                  gulo cognito quod ex
                    <var>.m.o.</var>
                  in
                    <var>.o.x.</var>
                  poteſt fieri, quod cognitum dico, eo quod nobis
                    <lb/>
                  cognita eſt proportio data, & rectangulum etiam
                    <var>.n.o.</var>
                  in
                    <var>.o.u.</var>
                  deinde ſecando ab
                    <var>.o.
                      <lb/>
                    n.</var>
                  partem æqualem lineæ iam inuentæ, quæ ſit
                    <var>.o.t</var>
                  . </s>
                  <s xml:id="echoid-s3769" xml:space="preserve">Inueniendo poſtea, ex .28. ſexti
                    <lb/>
                  lineam
                    <var>.o.m.</var>
                  cuius productum in
                    <var>.m.t.</var>
                  æquale ſit producto
                    <var>.t.o.</var>
                  in
                    <var>.o.i.</var>
                  vnde ex .15. eiuſ
                    <lb/>
                  dem proportio
                    <var>.o.i.</var>
                  ad
                    <var>.m.o.</var>
                  eadem eſſet, quæ
                    <var>.m.t.</var>
                  ad
                    <var>.o.t.</var>
                  & componendo, ita ſe ha-
                    <lb/>
                  beret
                    <var>.m.i.</var>
                  ad
                    <var>.m.o.</var>
                  vt
                    <var>.m.o.</var>
                  ad
                    <var>.o.t.</var>
                  ſed ex .4. ſexti, ita eſſet
                    <var>.p.i.</var>
                  ad
                    <var>.o.x.</var>
                  vt
                    <var>.m.i.</var>
                  ad
                    <var>.m.o</var>
                  .
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3770" xml:space="preserve">quare ex .11. quinti, ita eſſet
                    <var>.p.i.</var>
                  ad
                    <var>.o.x.</var>
                  vt
                    <var>.m.o.</var>
                  ad
                    <var>.o.t.</var>
                  vnde ex .15. ſexti productum
                    <var>.
                      <lb/>
                    o.x.</var>
                  in
                    <var>.m.o.</var>
                  æquale eſſet producto. p, i. in
                    <var>.o.t.</var>
                  & ſic haberemus intentum.</s>
                </p>
                <div xml:id="echoid-div592" type="float" level="5" n="2">
                  <figure xlink:label="fig-0316-02" xlink:href="fig-0316-02a">
                    <image file="0316-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0316-02"/>
                  </figure>
                  <figure xlink:label="fig-0316-03" xlink:href="fig-0316-03a">
                    <image file="0316-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0316-03"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s3771" xml:space="preserve">Sed ſi punctum
                    <var>.m.</var>
                  caderet in punctum
                    <var>.n.</var>
                  idem eſſet, ſi vorò punctum
                    <var>.m.</var>
                  tranſiret
                    <lb/>
                  n. oporteret nos facere hoc in latere
                    <var>.n.u.</var>
                  ipſum quærendo in linea
                    <var>.n.u.</var>
                  ducendo pri
                    <lb/>
                  mum lineam
                    <var>.p.i.</var>
                    <reg norm="æquidiſtantem" type="context">æquidiſtantẽ</reg>
                    <var>.u.x.</var>
                  & producendo
                    <var>.u.n.</var>
                  ad partem
                    <var>.u.</var>
                  proſequendo,
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  ſuperius iam dictum eſt.</s>
                </p>
              </div>
              <div xml:id="echoid-div594" type="letter" level="4" n="2">
                <head xml:id="echoid-head459" style="it" xml:space="preserve">Idem facere de parallelogr ammo.</head>
                <head xml:id="echoid-head460" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3772" xml:space="preserve">DAtum parallelogrammum in duas partes diuidere, ſecundum aliquam datam
                    <lb/>
                  proportionem à linea tranſeunte per punctum propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3773" xml:space="preserve">Sit exempli gratia, datum parallelogrammum
                    <var>.b.u.</var>
                  datum verò punctum
                    <var>.o.</var>
                  extra
                    <lb/>
                  figuram, proportio autem ea ſit, quæ
                    <var>.A.</var>
                  ad
                    <var>.B.</var>
                  vt ſupra. </s>
                  <s xml:id="echoid-s3774" xml:space="preserve">Nunc diuidatur primò re-
                    <lb/>
                  ctangulum datum per æqualia, mediante linea
                    <var>.r.c.</var>
                  parallela ambobus lateribus
                    <var>.b.x.</var>
                    <lb/>
                  et
                    <var>.s.u.</var>
                  quæ quidem linea diuidatur in puncto
                    <var>.i.</var>
                  ita quod eadem proportio ſit
                    <var>.r.i.</var>
                  ad
                    <var>.
                      <lb/>
                    i.c.</var>
                  vt
                    <var>.A.</var>
                  ad
                    <var>.B.</var>
                  protrahatur deinde à puncto
                    <var>.o.</var>
                  linea
                    <var>.o.i.q.</var>
                  quæ ſecabit ambo duo la-
                    <lb/>
                  tera
                    <var>.b.x.</var>
                  vel
                    <var>.s.u.</var>
                  intra terminos eorum, vel tantum
                    <var>.b.x.</var>
                  reliquum verò extra termi-
                    <lb/>
                  nos
                    <var>.s.u</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3775" xml:space="preserve">Nunc autem ſi intra dictos terminos tranſibit, vt in prima figura videre potes,
                    <lb/>
                  problema ſolutum erit, eo quod
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0317-01a" xlink:href="fig-0317-01"/>
                  ſi à puncto
                    <var>.i.</var>
                  protracta fuerit
                    <var>.p.
                      <lb/>
                    d.</var>
                  pa rallela ad
                    <var>.u.x.</var>
                  habebimus
                    <lb/>
                  ex prima ſexti eandem propor-
                    <lb/>
                  tionem
                    <var>.s.d.</var>
                  ad
                    <var>.p.x.</var>
                  ut
                    <var>.r.i.</var>
                  ad
                    <var>.i.c.</var>
                    <lb/>
                  hoc eſt vt
                    <var>.A.</var>
                  ad
                    <var>.B.</var>
                  ſed
                    <reg norm="triangulus" type="context">triãgulus</reg>
                    <lb/>
                    <var>i.e.d.</var>
                  æqualis eſt triangulo
                    <var>.i.q.p.</var>
                    <lb/>
                  vt tibi facilè patebit, vnde qua-
                    <lb/>
                  drilaterum
                    <var>.e.q.u.x.</var>
                  æquale erit
                    <lb/>
                  quadrilatero
                    <var>.d.u.</var>
                  ex communi </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>