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
61 49
62 50
63 51
64 52
65 53
66 54
67 55
68 56
69 57
70 58
71 59
72 60
73 61
74 62
75 63
76 64
77 65
78 66
79 67
80 70
81 71
82 70
83 71
84 72
85 73
86 74
87 75
88 76
89 77
90 78
< >
page |< < (365) 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-div708" type="section" level="3" n="36">
              <div xml:id="echoid-div708" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s4356" xml:space="preserve">
                    <pb o="365" rhead="EPISTOL AE." n="377" file="0377" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0377"/>
                  ſit angulo
                    <var>.a.h.b.</var>
                  propter æquidiſtantiam dictam, æqualis etiam erit angulo
                    <var>.d.</var>
                  & ar-
                    <lb/>
                  cus
                    <var>.a.x.</var>
                  æqualis arcui
                    <var>.a.g.</var>
                  vnde angulus
                    <var>.a.i.x.</var>
                  æqualis erit
                    <var>.d.</var>
                  ſed angulus
                    <var>.i.a.d.</var>
                  com-
                    <lb/>
                  munis eſt triangulis
                    <var>.c.a.d.</var>
                  et
                    <var>.i.a.t</var>
                  . </s>
                  <s xml:id="echoid-s4357" xml:space="preserve">quare angulus
                    <var>.a.t.i.</var>
                  rectus erit, vt
                    <var>.c.</var>
                  hoc eſt
                    <var>.i.x.</var>
                  per
                    <lb/>
                  pendicularis erit ipſi
                    <var>.a.d</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4358" xml:space="preserve">Sed vbitibi ſcripſi circa finem illius epiſtolæ, Tartaleam erraſſe in quinta propo-
                    <lb/>
                  ſitione primi lib. ſuæ nouæ ſcientiæ, non ſine ratione illud ſcripſi. </s>
                  <s xml:id="echoid-s4359" xml:space="preserve">Nam, inquit ipſe,
                    <lb/>
                  nullum corpus æquè graue poteſt in aliquo temporis ſpatio moueri motu naturali,
                    <lb/>
                    <reg norm="violentoque" type="simple">violentoq́;</reg>
                  ſimul miſtis. </s>
                  <s xml:id="echoid-s4360" xml:space="preserve">Vbi decipitur, eo quod non animaduertit incrementum ve
                    <lb/>
                  locitatis vnius motus, ſimul eſſe cum decremento velocitatis alterius,
                    <reg norm="eodemque" type="simple">eodemq́;</reg>
                  tem
                    <lb/>
                  pore, vt manifeſtè patet in itinere corporis, ab ipſo pro exemplo aſſumpto, hoc eſt
                    <lb/>
                  quod velocitas motus in ſpatio
                    <var>.c.d.</var>
                  creſcit vt naturalis, & decreſcit vt violenta. </s>
                  <s xml:id="echoid-s4361" xml:space="preserve">
                    <reg norm="nam" type="context">nã</reg>
                    <lb/>
                  creſcit orizontem verſus & decreſcit in remotione à linea
                    <var>.a.b.</var>
                  ſed ſi à puncto
                    <var>.c.</var>
                  ad
                    <lb/>
                  punctum
                    <var>.d.</var>
                  motus eſſet purè violentus, vt putat Tartalea, corpus illud minimè de-
                    <lb/>
                  ſcenderet, eo quod uirtus mouens, in
                    <var>.a.</var>
                  poſita, nullo pacto poteſt talem effectum ef-
                    <lb/>
                  ficere, vnde ab ipſa natura prouenit deſcenſio illius corporis propter
                    <reg norm="grauitatem" type="context">grauitatẽ</reg>
                  ,
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  dictum corpus habet in tali medio, aeris ſcilicet, & non ex violentia aliqua. </s>
                  <s xml:id="echoid-s4362" xml:space="preserve">Sed ſi
                    <lb/>
                  dixiſſet ipſe, illum motum eſſe purum naturalem, hoc eſſet falſum, eo quod purus
                    <lb/>
                  naturalis motus alicuius corporis non impediti, extra locum ſuum, ſit per lineam re
                    <lb/>
                  ctam, & non per curuam, vt videre eſt inter
                    <var>.c.</var>
                  et
                    <var>.d</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4363" xml:space="preserve">In vltima propoſitione deinde eiuſdem lib. quæ .6. eſt decipitur ſimiliter, & hæc
                    <lb/>
                  deceptio oritur ab ignoratione quintæ, & à putando motum naturalem non eſſe cau
                    <lb/>
                  ſam ipſius deſcenſus per ſpatium
                    <var>.c.d</var>
                  . </s>
                  <s xml:id="echoid-s4364" xml:space="preserve">Sed quia tibi ſignificaui expeditiorem viam
                    <lb/>
                  repeririad
                    <reg norm="cognoſcendam" type="context">cognoſcendã</reg>
                  proportionem inter
                    <var>.a.h.</var>
                  et
                    <var>.a.e.</var>
                  in vltima propoſitione ſe-
                    <lb/>
                  cundi lib. ipſius Tartaleæ, ipſam nunc tibi ſcribo. </s>
                  <s xml:id="echoid-s4365" xml:space="preserve">
                    <reg norm="Nam" type="context">Nã</reg>
                  iam ſcis angulum
                    <var>.h.l.i.</var>
                  diui-
                    <lb/>
                  ſum eſſe per æqualia ab
                    <var>.P.l.</var>
                  & quod
                    <var>.a.h.</var>
                  et
                    <var>.h.p.</var>
                  ęquales inuicem ſunt ex .6. primi Eu-
                    <lb/>
                  cli. </s>
                  <s xml:id="echoid-s4366" xml:space="preserve">vnde
                    <var>.p.i.</var>
                  et
                    <var>.a.h.</var>
                  æquales erunt inuicem ſimiliter, ſed ex .3. ſexti ita eſt ipſius
                    <var>.a.l.</var>
                    <lb/>
                  ad
                    <var>.l.i.</var>
                  vt ipſius
                    <var>.a.p.</var>
                  ad
                    <var>.p.i.</var>
                  & coniunctim ita erit
                    <var>.a.l.i.</var>
                  ad
                    <var>.l.i.</var>
                  vt
                    <var>.a.i.</var>
                  ad
                    <var>.p.i.</var>
                  ſed
                    <var>.a.l.</var>
                  cogni
                    <lb/>
                  ta eſt ex eius quadrato, et
                    <var>.l.i.</var>
                  etiam, cum æqualis ſit ipſi
                    <var>.a.i.</var>
                  vnde ex regula de tribus
                    <lb/>
                  notam habebimus
                    <var>.p.i.</var>
                  reſpectu
                    <var>.a.i.</var>
                  & ita reſpectu
                    <var>.a.e.</var>
                  ſi hypotheſes ipſius Tartaleæ
                    <lb/>
                  veræ ſunt.</s>
                </p>
              </div>
              <div xml:id="echoid-div710" type="letter" level="4" n="2">
                <head xml:id="echoid-head538" style="it" xml:space="preserve">Alia demonstratio impoßibilitatis diuidendi per æqualia
                  <lb/>
                proportionem ſuperparticularem in
                  <lb/>
                diſcretis.</head>
                <head xml:id="echoid-head539" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4367" xml:space="preserve">QVod à me poſtulas, hoc eſt ſcientiam impoſſibilitatis diuidendi per æqualia
                    <lb/>
                  proportionem ſuperparticularem in numeris ſatis à Campano in .8. octaui
                    <lb/>
                  potes habere, Iacobus Faber Stapulenſis etiam idem tractat
                    <unsure/>
                  in libello ſuę muſicæ
                    <lb/>
                  demonſtratæ. </s>
                  <s xml:id="echoid-s4368" xml:space="preserve">Sed ſi etiam alia via idem deſideras, quamuis longiori, nih
                    <unsure/>
                  ilomi-
                    <lb/>
                  nus vniuerſaliori, conſidera duos numeros
                    <var>.g.</var>
                  et
                    <var>.h.</var>
                  inuicem relatos ſecundum pro-
                    <lb/>
                  portionem ſuperparcicularem, quam volueris. </s>
                  <s xml:id="echoid-s4369" xml:space="preserve">Tunc dico impoſſibile eſle, vt per
                    <lb/>
                  æqualia diuidatur, quod ſi dixeris poſſibile eſſe, ſit per te
                    <var>.K.</var>
                  medius numerus </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum