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 concordance

< >
Scan Original
261 249
262 250
263 251
264 252
265 253
266 254
267 255
268 256
269 259
270 258
271 259
272 260
273 261
274 222
275 263
276 264
277 265
278 266
279 267
280 268
281 269
282 270
283 271
284 272
285 273
286 274
287 275
288 276
289 277
290 278
< >
page |< < (254) of 445 > >|
    <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-div495" type="section" level="3" n="5">
              <div xml:id="echoid-div505" type="letter" level="4" n="5">
                <p>
                  <s xml:id="echoid-s3195" xml:space="preserve">
                    <pb o="254" rhead="IO. BABPT. BENED." n="266" file="0266" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0266"/>
                  cundam verò ex .37. et .38. eiuſdem, </s>
                  <s xml:id="echoid-s3196" xml:space="preserve">propterea quod in .37. probat mediante maiori
                    <lb/>
                  diametro ipſius hyperbolis & defectionis, In .38. autem mediante minori diametro
                    <lb/>
                  ordinatè ad maiorem.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3197" xml:space="preserve">Tertia autem paſſio, non niſi circulo conuenit; </s>
                  <s xml:id="echoid-s3198" xml:space="preserve">pace ipſius Cardani dictum ſit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3199" xml:space="preserve">Quapropter ſit circulus
                    <var>.q.o.b.</var>
                  cuius diameter ſit
                    <var>.q.b.</var>
                  contingentes vero ab extre
                    <lb/>
                  mitate diametri ſint
                    <var>.d.b.</var>
                  et
                    <var>.q.g.</var>
                  per punctum autem
                    <var>.o.</var>
                  quoduis, ipſius
                    <reg norm="circunferentiæ" type="context">circũferentiæ</reg>
                  ,
                    <lb/>
                  tranſeant
                    <var>.b.o.g.</var>
                  et
                    <var>.q.o.d</var>
                  . </s>
                  <s xml:id="echoid-s3200" xml:space="preserve">tunc dico productum
                    <var>.q.o.</var>
                  in
                    <var>.q.d.</var>
                  vel
                    <var>.b.o.</var>
                  in
                    <var>.b.g.</var>
                  ęquale eſ-
                    <lb/>
                  ſe quadrato
                    <var>.q.b.</var>
                  quod ita probo.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3201" xml:space="preserve">Nam angulus
                    <var>.q.b.d.</var>
                  ſeu
                    <var>.b.q.g.</var>
                  rectus eſt ex .17. tertij Eucli. et
                    <var>.b.o.q.</var>
                  ſimiliter re-
                    <lb/>
                  ctus ex .30. ipſius lib. angulus verò
                    <var>.b.q.d.</var>
                  ſeu
                    <var>.q.b.g.</var>
                  communis eſt. </s>
                  <s xml:id="echoid-s3202" xml:space="preserve">quare
                    <var>.b.q.</var>
                  media
                    <lb/>
                  proportionalis erit inter dictas lineas
                    <var>.q.d.</var>
                  et
                    <var>.q.o.</var>
                  & inter
                    <var>.b.g.</var>
                  et
                    <var>.b.o</var>
                  . </s>
                  <s xml:id="echoid-s3203" xml:space="preserve">Vnde ſequetur
                    <lb/>
                  propoſitum ex .16.6. Eucli.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3204" xml:space="preserve">Sed ſi circa diametrum
                    <var>.q.b.</var>
                  mente fingamus aliquam elipſim, quætangat ipſum
                    <lb/>
                    <figure xlink:label="fig-0266-01" xlink:href="fig-0266-01a" number="299">
                      <image file="0266-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0266-01"/>
                    </figure>
                  circulum duobus punctis me-
                    <lb/>
                  diantibus
                    <var>.q.</var>
                  et
                    <var>.b.</var>
                  (nam pluribus
                    <lb/>
                  eſſet impoſſibile, ex .27. quarti
                    <lb/>
                  Pergei) clarè patebit, quod
                    <reg norm="pum" type="context">pũ</reg>
                    <lb/>
                  ctus
                    <var>.o.</var>
                  erit extra
                    <reg norm="circunferentiam" type="context">circunferentiã</reg>
                    <lb/>
                  ipſius defectionis, </s>
                  <s xml:id="echoid-s3205" xml:space="preserve">quare ipſa cir
                    <lb/>
                  cunferentia ſecabit
                    <var>.b.g.</var>
                  vel
                    <var>.q.
                      <lb/>
                    d.</var>
                  in alio puncto, vnde ipſi non
                    <lb/>
                  occurret id quod probauimus
                    <lb/>
                  de circulo.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3206" xml:space="preserve">Admiratus etiam ſum, ipſum
                    <lb/>
                  Cardanum dicere hyperbolem
                    <lb/>
                  ita vocari, eo quod angulus con
                    <lb/>
                  tentus ab axe ipſius figuræ, & à
                    <lb/>
                  latere trigoni in hyperbole ma-
                    <lb/>
                  ior ſit quam in parabole, quod
                    <lb/>
                  eriam confirmat paulo inferius,
                    <lb/>
                  nam hoc verum non eſt, imo fal
                    <lb/>
                  ſiſſimum. </s>
                  <s xml:id="echoid-s3207" xml:space="preserve">Talis enim ſectio ita
                    <lb/>
                  nominata fuit, hoc eſt hyperbo
                    <lb/>
                  les, ſimili ratione, qua elipſis ſeu
                    <lb/>
                  defectio etiam vocata fuit, nam
                    <lb/>
                  ſicut in ipſa defectione quadra-
                    <lb/>
                  tum ordinatę
                    <var>.l.m.</var>
                  minor eſt pro
                    <lb/>
                  ducto lineæ
                    <var>.e.m.</var>
                  in
                    <var>.e.t.</var>
                  per figu
                    <lb/>
                  ram ſimilcm producto
                    <var>.d.e.</var>
                  in
                    <var>.e.
                      <lb/>
                    t.</var>
                  quæ eandem obtineat
                    <reg norm="altitu- dinem" type="context">altitu-
                      <lb/>
                    dinẽ</reg>
                  ipſius
                    <var>.e.m.</var>
                  vt ipſe Pergeus
                    <lb/>
                  monſtrat in .13. primi lib. ita in
                    <lb/>
                  hyperbole
                    <reg norm="dictum" type="context">dictũ</reg>
                  quadratum ex
                    <lb/>
                  cedit quantitatem illius figuræ,
                    <lb/>
                  per ſimilem dictæ vt in .12.
                    <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                    <lb/>
                  Pergei facilè videre eſt. </s>
                  <s xml:id="echoid-s3208" xml:space="preserve">ſed
                    <reg norm="prae­ ter" type="simple">prę­
                      <lb/>
                    ter</reg>
                  illas paſſiones, quas notat </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum