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 |< < (364) 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-div703" type="section" level="3" n="35">
              <div xml:id="echoid-div703" type="letter" level="4" n="1">
                <pb o="364" rhead="IO. BAPT. BENED." n="376" file="0376" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0376"/>
              </div>
            </div>
            <div xml:id="echoid-div708" type="section" level="3" n="36">
              <div xml:id="echoid-div708" type="letter" level="4" n="1">
                <head xml:id="echoid-head536" xml:space="preserve">DE AVGMENTO PONDERIS CORPORIS
                  <lb/>
                ad ſtateram appenſi, & quadam alia demonſtratione,
                  <lb/>
                & quibuſdam erroribus Tartaleæ.</head>
                <head xml:id="echoid-head537" style="it" xml:space="preserve">Mutio Groto.</head>
                <p>
                  <s xml:id="echoid-s4350" xml:space="preserve">SI ea quæ à me audiuiſti non credis, conſidera quæſo libram ſeu ſtateram
                    <lb/>
                    <var>o.a.</var>
                  cuius centrum non longitudinis ſed ponderum ſit
                    <var>.i.</var>
                  quę ſtatera, vt ori
                    <lb/>
                  zontaliter conſiſtat, oportebit pondus extremitatis
                    <var>.o.</var>
                  ita ſe habere
                    <lb/>
                  ad pondus extremitatis
                    <var>.a.</var>
                  ut
                    <var>.a.i.</var>
                  ſe habet ad
                    <var>.o.i.</var>
                  quod te ſcire puto, ima
                    <lb/>
                  ginemur nunc d uas lineas
                    <var>.a.e.</var>
                  et
                    <var>.o.n.</var>
                  paralle las
                    <reg norm="infinitasque" type="simple">infinitasq́;</reg>
                  & à puncto
                    <var>.n.</var>
                  immobili,
                    <lb/>
                  & fixo extra ſtateram, tranſeat per
                    <var>.i.</var>
                  linea
                    <var>.n.i.e</var>
                  . </s>
                  <s xml:id="echoid-s4351" xml:space="preserve">Cogitemus etiam punctum
                    <var>.e.</var>
                  inter
                    <lb/>
                  ſectionis ipſius
                    <var>.n.i.e.</var>
                  cum
                    <var>.a.e.</var>
                  progredi vniformiter
                    <reg norm="continuòque" type="simple">continuòq́;</reg>
                  ab
                    <var>.a.</var>
                  per lineam
                    <var>.a.e.</var>
                    <lb/>
                  vnde punctum
                    <var>.i.</var>
                  interſectionis ipſius
                    <var>.n.i.e.</var>
                  cum
                    <var>.a.i.o.</var>
                  ſemper vicinius fiet puncto
                    <var>.o.</var>
                    <lb/>
                  nec unquam cum illo vnum erit, quamuis moueatur tempore infinito. </s>
                  <s xml:id="echoid-s4352" xml:space="preserve">Nunc autem
                    <lb/>
                  dico, quod cum ſtateram
                    <var>.o.i.a.</var>
                  oporteat ſemper orizontalem eſſe virtute ponderis,
                    <lb/>
                  o. oportebit pundus
                    <var>.o.</var>
                  in infinitum etiam augeri,
                    <reg norm="quotieſcunque" type="simple">quotieſcunq;</reg>
                  pondus
                    <var>.a.</var>
                  nunquam
                    <lb/>
                  diminui voluerimus vel econtra hoc in infinitum diminui, ſi illud nunquam augeri
                    <lb/>
                  voluerimus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4353" xml:space="preserve">Sedre vera non putabam te indigere aliqua demonſtratione, quod linea
                    <var>.b.h.</var>
                  di-
                    <lb/>
                  uiſa ſit per æqualia à
                    <unsure/>
                  linea
                    <var>.c.a.</var>
                  cum hæc perpendicularis ſit ab
                    <var>.a.</var>
                  ad baſim
                    <var>.g.d.</var>
                  in
                    <reg norm="triam" type="context">triã</reg>
                    <lb/>
                  gulo orthogonio
                    <var>.g.a.d.</var>
                  & cum ſit
                    <var>.b.h.</var>
                  perpendicularis ad
                    <var>.a.o.</var>
                  ex ſuppoſito quæ
                    <var>.a.
                      <lb/>
                    o.</var>
                  in ſe habet punctum medium baſis
                    <var>.g.d.</var>
                  nec
                    <reg norm="non" type="context">nõ</reg>
                  illud anguli recti
                    <var>.a.</var>
                  quod per ſe cla
                    <lb/>
                  riſſimum eſt, cum iam ſcis
                    <var>.o.</var>
                  eſſe centrum circuli circundantis triangulum
                    <var>.g.a.d.</var>
                  or-
                    <lb/>
                  thogonium, et
                    <var>.g.d.</var>
                  eius diameter, vnde
                    <var>.o.a.</var>
                  æquabitur ipſi
                    <var>.o.g.</var>
                  quapropter angulus
                    <lb/>
                  o.
                    <reg norm="am" type="context">ã</reg>
                  . g. æquabitur angulo
                    <var>.g.</var>
                  ex quinta primi, </s>
                  <s xml:id="echoid-s4354" xml:space="preserve">deinde ex .32. eiuſdem, angulus
                    <var>.h.</var>
                  æqua
                    <lb/>
                  bitur angulo
                    <var>.d.</var>
                  eo quod an gulus
                    <var>.e.</var>
                  rectus eſt, quemadmodum et
                    <var>.a.</var>
                  ſed angulus
                    <var>.d.</var>
                    <lb/>
                  æqualis eſt angulo
                    <var>.g.a.c</var>
                  . </s>
                  <s xml:id="echoid-s4355" xml:space="preserve">& propterea angulus
                    <var>.h.</var>
                  erit etiam æqualis angulo
                    <var>.h.a.u.</var>
                    <lb/>
                  vnde
                    <var>.h.u.</var>
                  æqualis erit ipſi
                    <var>.u.
                      <lb/>
                    a.</var>
                  ex .6. primi, cum poſtea angulus
                    <var>.
                      <lb/>
                      <figure xlink:label="fig-0376-01" xlink:href="fig-0376-01a" number="417">
                        <image file="0376-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0376-01"/>
                      </figure>
                    o.a.d.</var>
                  æqualis ſitangulo
                    <var>.d.</var>
                  ex quin­
                    <lb/>
                  ta primi erit angulus
                    <var>.a.b.e.</var>
                  æqua-
                    <lb/>
                  lis angulo
                    <var>.g.</var>
                  ex .32. dicta, eo quod
                    <lb/>
                  e. rectus eſt, & ex eadem æqualis
                    <lb/>
                  erit angulo
                    <var>.d.a.c.</var>
                  vnde
                    <var>.u.b.</var>
                  erit
                    <lb/>
                  æqualis ipſi
                    <var>.u.a.</var>
                  ex .6. dicti, & ideo
                    <lb/>
                  æqualis eric ipſi
                    <var>.u.h</var>
                  . </s>
                  <s xml:id="echoid-s4356" xml:space="preserve">Reliqua ve-
                    <lb/>
                  rò illius propoſitionis credo ex te
                    <lb/>
                  omnia poſſe
                    <reg norm="intelligere" type="context">ĩtelligere</reg>
                  , excepto,
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  vt tibi ſignificaui ſi à
                    <reg norm="puncto" type="context">pũcto</reg>
                    <var>.i.</var>
                  com-
                    <lb/>
                  muni ipſi
                    <var>.a.c.u.</var>
                  & circunferentiæ,
                    <lb/>
                  ducta fuerit
                    <var>.i.x.</var>
                  ad
                    <reg norm="punctum" type="context">pũctum</reg>
                    <var>.x.</var>
                  com
                    <lb/>
                  mune vni parallelæ à
                    <reg norm="puncto" type="context">pũcto</reg>
                    <var>.g.</var>
                  ipſi
                    <lb/>
                    <var>h.b.</var>
                  & circunferentiæ, quod di-
                    <lb/>
                  cta
                    <var>.i.x.</var>
                  ad rectos erit ipſi
                    <var>.a.b.d.</var>
                  eo
                    <lb/>
                  quod cum angulus
                    <var>.a.g.x.</var>
                  æqualis </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>