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 |< < (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