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
30 18
31 19
32 20
33 21
34 22
35 23
36 24
37 25
38 26
39 27
40 28
41 29
42 30
43 31
44 32
45 33
46 34
47 35
48 36
49 37
50 38
51 39
52 40
53 41
54 42
55 43
56 44
57 45
58 46
59 47
< >
page |< < (136) 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-div308" type="chapter" level="2" n="2">
            <div xml:id="echoid-div328" type="section" level="3" n="12">
              <p>
                <s xml:id="echoid-s1641" xml:space="preserve">
                  <pb o="136" rhead="IO. BAPT. BENED." n="148" file="0148" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0148"/>
                cere oportet. </s>
                <s xml:id="echoid-s1642" xml:space="preserve">Ratio verò ab ipſo adducta propter quam
                  <var>.E.</var>
                repreſentatur oculo al-
                  <lb/>
                tius quam
                  <var>.b.</var>
                nempe eo quod
                  <var>.A.</var>
                ſuperſtet ipſi
                  <var>.E.</var>
                nihil valet, quia ſi inferius eſſet,
                  <lb/>
                idem contingeret, ſed hoc euenit eo quod
                  <var>.E.</var>
                altius eſt ipſo
                  <var>.b</var>
                . </s>
                <s xml:id="echoid-s1643" xml:space="preserve">Idem dico de
                  <var>.h.</var>
                  <lb/>
                vbi ſimiliter decipitur. </s>
                <s xml:id="echoid-s1644" xml:space="preserve">Idem etiam in .7. cap. fallitur in ſecundo modo, quem oſten
                  <lb/>
                dit pro ſecundo quadrato aliquo degradato à parallelogrammo degradato magis
                  <lb/>
                longo quàm lato, cum ducat parallelam
                  <var>.l.m.</var>
                ad
                  <var>.b.c.</var>
                à puncto
                  <var>.l.</var>
                interſection is ipſius
                  <var>.
                    <lb/>
                  o.c.</var>
                id, quod non rectè efficitur quemadmodum ex rationibus à me allegatis circa
                  <lb/>
                meas figuras
                  <var>.A.A.</var>
                facilè innoteſcit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1645" xml:space="preserve">Nono deinde cap. contrario planè ordine, quam oporteret proceſsit, quia
                  <reg norm="cum" type="context">cũ</reg>
                  <lb/>
                angulus .2. trianguli perfecti magis diſtet à plano ſuper quod degradari debet
                  <lb/>
                triangulum, quàm latus .1. 3. oppoſitum dicto angulo .2. & per confequens longère
                  <lb/>
                motior ſit ab oculo, ipſe in degradato,
                  <reg norm="eum" type="context">eũ</reg>
                magis propinquum eſſe facit, è con-
                  <lb/>
                tra eap .10. rectè fecit contra id, quod capite .9. tradiderat.</s>
              </p>
              <p>
                <s xml:id="echoid-s1646" xml:space="preserve">Quod autem deinceps in prima parte .11. & vltimi capitis aſſerit eſt,
                  <reg norm="admittendum" type="context">admittendũ</reg>
                .
                  <lb/>
                </s>
                <s xml:id="echoid-s1647" xml:space="preserve">Quod verò in ſecunda parte ab eo traditur, ideſt alius quidam modus quem de
                  <reg norm="tranſ" type="context">trãſ</reg>
                  <lb/>
                ferendis punctis à perfecto in degradato proponit, non eſt modus vniuerſalis; </s>
                <s xml:id="echoid-s1648" xml:space="preserve">quia
                  <lb/>
                ſi altitudo
                  <var>.T.Q.</var>
                oculi à plano orizontali, non eſſet æqualis medietati lateris
                  <var>.B.D.</var>
                  <lb/>
                perfecti, interualla
                  <var>.a.b.c.d.e.</var>
                lateris
                  <var>B.D.</var>
                admittenda non eſſent.</s>
              </p>
              <p>
                <s xml:id="echoid-s1649" xml:space="preserve">Pro cuius rei intelligentia ſit in ſubſcripta hic figura corporea
                  <var>.ω.</var>
                parallelogram-
                  <lb/>
                mum rectangulum
                  <var>A.B.C.D.</var>
                in plano orizontali, & linea
                  <var>.Q.H.</var>
                illud per medium
                  <lb/>
                diuidat, quæ ſit parallela duobus lateribus
                  <var>.A.B.</var>
                et
                  <var>.C.D.</var>
                in cuius quolibet puncto
                  <var>.
                    <lb/>
                  Q.</var>
                ſit infimus terminus altitudinis oculi, & in
                  <var>.
                    <lb/>
                    <figure xlink:label="fig-0148-01" xlink:href="fig-0148-01a" number="202">
                      <image file="0148-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0148-01"/>
                    </figure>
                  T.</var>
                ad perpendiculum ipſius
                  <var>.Q.</var>
                ſit verus ſitus
                  <lb/>
                eiuſdem, tantum eleuatus à
                  <var>.Q.</var>
                quanta eſt
                  <lb/>
                medietas ipſius
                  <var>.D.B.</var>
                ſitq́ue figura corpo-
                  <lb/>
                rea finita ſimilis meæ
                  <var>.A.</var>
                vnde
                  <var>.Q.T.</var>
                æqualis
                  <lb/>
                erit ipſi
                  <var>.Q.æ.</var>
                & planum perpendiculare
                  <reg norm="orizon- ti" type="context">orizõ-
                    <lb/>
                  ti</reg>
                , ſuper quod punctum
                  <var>.k.</var>
                perfecti duci debet
                  <lb/>
                ſit
                  <var>.R.D.B.</var>
                ſintq́ue ductæ per imaginationem
                  <lb/>
                lineæ
                  <var>.T.K</var>
                :
                  <var>Q.K.</var>
                et ſit
                  <var>.K.N.</var>
                perpendicularis la-
                  <lb/>
                teri
                  <var>.C.D.</var>
                à quo puncto
                  <var>.N.</var>
                imaginatione ſit
                  <reg norm="con" type="context">cõ</reg>
                  <lb/>
                præhenſa linea
                  <var>.N.Q.</var>
                at que hæ tres lineæ ſectæ
                  <lb/>
                ſint à plano in punctis
                  <var>.c.i.</var>
                et .2. quorum
                  <reg norm="punctum" type="context">punctũ</reg>
                .
                  <lb/>
                2. erit quæſitum plani. </s>
                <s xml:id="echoid-s1650" xml:space="preserve">Imaginemur nunc duos
                  <lb/>
                triangulos
                  <var>.K.T.Q.</var>
                et
                  <var>.N.Q.æ.</var>
                qui ſecti
                  <reg norm="erunt" type="context">erũt</reg>
                  <lb/>
                à plano
                  <var>.R.B.D.</var>
                quorum communes ſectiones
                  <lb/>
                erunt .1. 2. et
                  <var>.D.c.</var>
                & quia
                  <var>.N.K.D.i.</var>
                et
                  <var>.æ.Q.</var>
                  <lb/>
                inuicem ſunt parallelæ, ſequitur eandem pro-
                  <lb/>
                portionem futuram ipſius
                  <var>.Q.K.</var>
                ad
                  <var>.K.i.</var>
                quæ eſt
                  <lb/>
                ipſius
                  <var>.æ.N.</var>
                ad
                  <var>.N.D.</var>
                imaginatione concipien
                  <lb/>
                do a puncto
                  <var>.K.</var>
                vſque ad
                  <var>.æ.Q.</var>
                quandam paral-
                  <lb/>
                lelam ipſi
                  <var>.N.æ.</var>
                quemadmo dum ex te ipſo intel
                  <lb/>
                ligere potes. </s>
                <s xml:id="echoid-s1651" xml:space="preserve">Sed ratione ſimilitudinis trian-
                  <lb/>
                gulorum ita ſe res habet de
                  <var>.æ.Q.</var>
                ad
                  <var>.D.c.</var>
                vt de
                  <var>.
                    <lb/>
                  æ.N.</var>
                ad
                  <var>.N.D.</var>
                vt quoque de
                  <var>.T.Q.</var>
                ad .2. 1. quemadmodum ipſius
                  <var>.Q.K.</var>
                ad
                  <var>.K.i.</var>
                vn-
                  <lb/>
                de ex .11. quinti, idem erit de
                  <var>.Q.T.</var>
                ad .1. 2. quod de
                  <var>.Q.æ.</var>
                ad
                  <var>.c.D.</var>
                & ex .16. eiuſdem
                  <lb/>
                de
                  <var>.Q.T.</var>
                ad
                  <var>.Q.æ.</var>
                quod de .1. 2. ad
                  <var>.c.D.</var>
                & exiſtente
                  <var>.æ.Q.</var>
                ex ſuppoſito æquali ipſi.</s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>