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
221 209
222 210
223 211
224 212
225 213
226 214
227 215
228 216
229 217
230 218
231 219
232 220
233 221
234 222
235 223
236 224
237 225
238 226
239 227
240 228
241 229
242 230
243 231
244 232
245 233
246 234
247 235
248 236
249 237
250 238
< >
page |< < (305) 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-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>
                <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/>
                    <figure xlink:label="fig-0317-01" xlink:href="fig-0317-01a" number="339">
                      <image file="0317-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0317-01"/>
                    </figure>
                  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>