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-div518" type="section" level="3" n="8">
              <div xml:id="echoid-div518" type="letter" level="4" n="1">
                <pb o="263" rhead="EPISTOL AE." n="275" file="0275" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0275"/>
                <p>
                  <s xml:id="echoid-s3295" xml:space="preserve">Sed ſi circuli propoſiti ſeiuncti fuerint, ſumatur
                    <var>.b.i.</var>
                  diameter maioris, qui fiat ſe-
                    <lb/>
                  midiameter vnius circuli circa centrum
                    <var>.o.</var>
                  & hic circulus vocetur
                    <var>.h.x.</var>
                  coniunga-
                    <lb/>
                  tur deinde ſemidiameter
                    <var>.o.i.</var>
                  minoris circuli cum ſemidiametro
                    <var>.a.i.</var>
                  circuli maio-
                    <lb/>
                  ris, & ex huiuſmodi compoſita linea, fiat vnus ſemidiameter
                    <var>.a.x.</var>
                  circuli
                    <var>.x.n.</var>
                  concen
                    <lb/>
                  trici cum maiori, & à puncto
                    <var>.x.</var>
                  interſectionis horum circulorum (poſito quod ſe in-
                    <lb/>
                  uicem interſecent) ducantur per eorum centra
                    <var>.x.a.</var>
                  et
                    <var>.x.o.</var>
                  vſque ad ipſorum circun-
                    <lb/>
                  ferentias in punctis
                    <var>.d.</var>
                  et
                    <var>.f.</var>
                  duę
                    <lb/>
                  lineæ, vnde habebimus
                    <var>.x.d.</var>
                    <lb/>
                  æqualem
                    <var>.x.f.</var>
                  eo quod tam in
                    <lb/>
                    <figure xlink:label="fig-0275-01" xlink:href="fig-0275-01a" number="304">
                      <image file="0275-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0275-01"/>
                    </figure>
                    <var>x.d.</var>
                  quam in
                    <var>.x.f.</var>
                  reperiuntur
                    <lb/>
                  diametri, & ſemidiametri am-
                    <lb/>
                  borum circulorum, facto deni
                    <lb/>
                  que centro
                    <var>.x.</var>
                  vnius circuli, cu
                    <lb/>
                  ius ſemidiameter ęqualis ſit
                    <lb/>
                  vni earum
                    <var>.x.d.</var>
                  vel
                    <var>.x.f.</var>
                  folu-
                    <lb/>
                  tum erit problema, dicta ra-
                    <lb/>
                  tione.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3296" xml:space="preserve">Si verò diſtantia duorum
                    <lb/>
                  propoſitorum circulorum tanta fuerit, quod ſecundi circuli nequeant ſe inuicem
                    <lb/>
                  tangere, vel ſecare, tunc alia via incedendum erit, quę talis eſt & generalis. </s>
                  <s xml:id="echoid-s3297" xml:space="preserve">Diuida-
                    <lb/>
                  tur tota
                    <var>.q.b.</var>
                  per æqualia in puncto
                    <var>.z.</var>
                  circa quod
                    <reg norm="ſignentur" type="context">ſignẽtur</reg>
                  duo puncta ab ipſo ęquidi
                    <lb/>
                  ſtantia
                    <var>.K.</var>
                  et
                    <var>.p.</var>
                  diſtantia vero
                    <var>.a.K.</var>
                  facta ſit ſemidiameter eſſe vnius circuli
                    <var>.K.x.</var>
                  circa
                    <lb/>
                  centrum
                    <var>.a.</var>
                  diſtantia autem
                    <var>.o.p.</var>
                  ſemidiameter alterius circuli
                    <var>.p.x.</var>
                  circa cen-
                    <lb/>
                  trum
                    <var>.o.</var>
                  qui quidem circuli ſe inuicem ſecent in puncto
                    <var>.x.</var>
                  à quo cum ductę fue-
                    <lb/>
                  rinc
                    <var>.x.a.d.</var>
                  et
                    <var>.x.o.f.</var>
                  per centra dictorum circulorum, ipſe erunt
                    <reg norm="inuicem" type="context">inuicẽ</reg>
                  ęquales, eo
                    <reg norm="quod" type="wordlist">qđ</reg>
                    <lb/>
                  cum
                    <var>.b.K.</var>
                  æqualis ſit
                    <var>.q.p.</var>
                  igitur
                    <var>.x.d.</var>
                  et
                    <var>.q.p.</var>
                  erunt inuicem ęquales, ſed
                    <var>.f.x.</var>
                  æqualis eſt
                    <lb/>
                    <var>q.p</var>
                  . </s>
                  <s xml:id="echoid-s3298" xml:space="preserve">quare
                    <var>.x.f.</var>
                  æqualis erit
                    <var>.x.d.</var>
                  tunc ſi
                    <var>.x.</var>
                  centrum fuerit vnius circuli, cuius ſemidia-
                    <lb/>
                  mer ſit vna dictarum, problema ſolutum erit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3299" xml:space="preserve">Talis etiam ſoiutio commo-
                    <lb/>
                  da erit ad inueniendum dictum
                    <lb/>
                    <figure xlink:label="fig-0275-02" xlink:href="fig-0275-02a" number="305">
                      <image file="0275-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0275-02"/>
                    </figure>
                  circulum cuiuſuis magnitudinis,
                    <lb/>
                  dato tamen
                    <reg norm="quod" type="simple">ꝙ</reg>
                  eius diameter, ma
                    <lb/>
                  ior ſit
                    <var>.b.z.</var>
                  cum in noſtra poteſta
                    <lb/>
                  te ſit accipere puncta
                    <var>.K.</var>
                  et
                    <var>.p.</var>
                  pro
                    <lb/>
                  xima vel remota ab ipſo
                    <var>.z.</var>
                  ad li-
                    <lb/>
                  bitum. </s>
                  <s xml:id="echoid-s3300" xml:space="preserve">Vnde abſque vlla diuiſio
                    <lb/>
                  neipſius
                    <var>.q.b.</var>
                  per medium, ſatis
                    <lb/>
                  erit ſignare puncta
                    <var>.K.</var>
                  et
                    <var>.p.</var>
                  dua-
                    <lb/>
                  bus diſtantijs mediantibus
                    <var>.b.K.</var>
                    <lb/>
                  et
                    <var>.q.p.</var>
                  inuicem æqualibus, &
                    <lb/>
                  etiam propoſitis.</s>
                </p>
                <handwritten number="19"/>
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