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
211 199
212 200
213 201
214 202
215 203
216 204
217 205
218 206
219 207
220 208
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
< >
page |< < (275) 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-div533" type="section" level="3" n="11">
              <div xml:id="echoid-div538" type="letter" level="4" n="4">
                <p>
                  <s xml:id="echoid-s3435" xml:space="preserve">
                    <pb o="275" rhead="EPISTOL AE." n="287" file="0287" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0287"/>
                  ſit quadratum ipſius
                    <var>.D.B</var>
                  . </s>
                  <s xml:id="echoid-s3436" xml:space="preserve">Nunc ſupponendo
                    <var>.A.B.</var>
                  ſimile
                    <var>.a.b.</var>
                  clarum erit ex diffini-
                    <lb/>
                  tione ſimilium figurarum, quod eadem proportio erit
                    <var>.A.D.</var>
                  ad
                    <var>.D.B.</var>
                  quę
                    <var>.a.d.</var>
                  ad
                    <var>.d.
                      <lb/>
                    b.</var>
                  hoc eſt
                    <var>.A.D.</var>
                  ad
                    <var>.D.C.</var>
                  vt
                    <var>.a.d.</var>
                  ad
                    <var>.d.c.</var>
                  hoc eſt
                    <var>.A.B.</var>
                  ad
                    <var>.B.c.</var>
                  vt
                    <var>.a.b.</var>
                  ad
                    <var>.b.c.</var>
                  ex prima
                    <lb/>
                  ſexti, vel .18. ſeu .19. ſeptimi, </s>
                  <s xml:id="echoid-s3437" xml:space="preserve">tunc cum dixerimus ſi
                    <var>.a.b.</var>
                  ita reſpondet ad
                    <var>.b.c.</var>
                  ergo
                    <var>.A.
                      <lb/>
                    B.</var>
                  correſpondet etiam ita ad
                    <var>.B.C.</var>
                  </s>
                  <s xml:id="echoid-s3438" xml:space="preserve">quare ex regula de tribus rectè fit multiplicando
                    <var>.
                      <lb/>
                    A.B.</var>
                  per
                    <var>.b.c.</var>
                  productum verò diuidendo per
                    <var>.a.b.</var>
                  ex .15. ſexti vel .20. ſeptimi, cuius
                    <lb/>
                  prouentus radix quadrata erit quod quærebatur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3439" xml:space="preserve">Sed aliter idem poſſe fieri ſpeculatus ſum, hoc eſt multiplicando numerum .49.
                    <lb/>
                  ordinis .1000. hominum
                    <reg norm="cum" type="context">cũ</reg>
                  radice quadrata numeri .3500. propoſiti, productum ve-
                    <lb/>
                  rò diuidere per radicem quadratam ipſius .1000. vnde prouentus .91. erit numerus
                    <lb/>
                  vnius ordinis .3500. numeri
                    <reg norm="propoſiti" type="simple">ꝓpoſiti</reg>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3440" xml:space="preserve">Cuius
                    <reg norm="operationis" type="simple">oꝑationis</reg>
                  ſpeculatio eſt iſta.
                    <lb/>
                    <figure xlink:label="fig-0287-01" xlink:href="fig-0287-01a" number="314">
                      <image file="0287-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0287-01"/>
                    </figure>
                  </s>
                  <s xml:id="echoid-s3441" xml:space="preserve">Sit
                    <var>.a.b.</var>
                  quadratum .1000. et
                    <var>.a.c.</var>
                  ſua
                    <lb/>
                  radix et
                    <var>.a.d.</var>
                  rectangulum propoſi-
                    <lb/>
                  tum ipſius .1000. et
                    <var>.a.e.</var>
                  vnus ordo.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3442" xml:space="preserve">Sit etiam
                    <var>.A.B.</var>
                  quadratum .3500. &
                    <lb/>
                    <var>A.C.</var>
                  eius radix et
                    <var>.A.D.</var>
                    <reg norm="rectangulum" type="context">rectangulũ</reg>
                    <lb/>
                  ipſius numeri .3500. propoſiti, ſimile
                    <lb/>
                  tamen rectangulo
                    <var>.a.d.</var>
                  et
                    <var>.A.E.</var>
                  eius
                    <lb/>
                  vnus ordo. </s>
                  <s xml:id="echoid-s3443" xml:space="preserve">
                    <reg norm="Cum" type="context">Cũ</reg>
                  enim
                    <var>.a.b.</var>
                  æquale ſit
                    <lb/>
                    <var>a.d.</var>
                  et
                    <var>.A.B</var>
                  :
                    <var>A.D.</var>
                    <reg norm="tunc" type="context">tũc</reg>
                    <var>.a.c.</var>
                  erit media
                    <lb/>
                  proportionalis inter
                    <var>.a.e.</var>
                  et
                    <var>.e.d.</var>
                  & ſic
                    <lb/>
                    <var>A.C.</var>
                  erit etiam media proportiona
                    <lb/>
                  lis inter
                    <var>.A.E.</var>
                  et
                    <var>.E.D.</var>
                  per .16. ſexti,
                    <lb/>
                  ſeu .20. ſeptimi, & quia proporrio. A
                    <lb/>
                  E. ad
                    <var>.E.D.</var>
                  æqualis eſt proportioni
                    <var>.
                      <lb/>
                    a.e.</var>
                  ad
                    <var>.e.d.</var>
                  cum
                    <var>.A.D.</var>
                  ſupponatur ſi-
                    <lb/>
                  mile
                    <var>.a.d.</var>
                  ergo proportio
                    <var>.A.E.</var>
                  ad
                    <var>.A
                      <lb/>
                    C.</var>
                  ęqualis erit proportioni
                    <var>.a.e.</var>
                  ad
                    <var>.a.
                      <lb/>
                    c.</var>
                  quę medietates ſunt
                    <reg norm="totorum" type="context">totorũ</reg>
                  æqua-
                    <lb/>
                  lium, rectè igitur fiet ſi procedamus
                    <lb/>
                  ex regula de tribus, dicendo ſi
                    <var>.a.c.</var>
                    <lb/>
                    <reg norm="correſpondet" type="context">correſpõdet</reg>
                    <var>.a.e.</var>
                  tùc
                    <var>.A.C.</var>
                    <reg norm="correſpon" type="context">correſpõ</reg>
                    <lb/>
                  det
                    <var>.A.E.</var>
                  ex ſupradictis .15. ſexti. vel
                    <lb/>
                  20. ſeptimi.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3444" xml:space="preserve">Ratio verò quarti quæſiti per ſe
                    <lb/>
                  patet, quod eſt inuenire
                    <reg norm="pauimentum" type="context">pauimentũ</reg>
                    <lb/>
                  ſeu aream quadratam, in qua poſſint
                    <lb/>
                  locari quot homines volueris, ita in
                    <lb/>
                  ter ſe ſiti, ut vnuſquiſque occupet
                    <num value="7">.
                      <lb/>
                    7.</num>
                  pedes ipſius areę in longitudinem
                    <lb/>
                  et .3. per latitudinem à lateribus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3445" xml:space="preserve">Seu ex propoſito hominum nume
                    <lb/>
                  ro inuenire numerum ipſorum loca-
                    <lb/>
                  bilem in aliqua area quadrata, ita,
                    <lb/>
                  vt vnuſquiſque occupet .21. pedes
                    <lb/>
                  quadratos ipſius areæ.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum