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
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
60 48
< >
page |< < (111) 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-div7" type="chapter" level="2" n="1">
            <div xml:id="echoid-div293" type="appendix" level="3" n="1">
              <p>
                <s xml:id="echoid-s1407" xml:space="preserve">
                  <pb o="111" rhead="THEOREM. ARIT." n="123" file="0123" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0123"/>
                ſecunda verò eſſet .5. pro additione ad tertiam partem ſimplicium, tertia autem eſ-
                  <lb/>
                ſet .11. pro additione ad quartam partem ſimplicium, quarta demum eſſet .23. pro
                  <lb/>
                additione quintæ partis ſimplicium, quarum partium .2. 5. 11. 23. ſumma eſt .41. vt
                  <lb/>
                diximus. </s>
                <s xml:id="echoid-s1408" xml:space="preserve">Hæc igitur ſumma .41. ſubducenda eſt à numero .100. propoſito, vnde re-
                  <lb/>
                linquetur .59. pro ſumma partium ſimplicium numeri propoſiti, quarum prima erit
                  <lb/>
                2. cum vndecim vigeſimisquartis ex diuiſione huiuſmodi .59. per .24. ſummam par-
                  <lb/>
                tium ſimplicium ex viregulæ de tribus, dicendo ſi .24. prouenit nobis ab .1. prima
                  <lb/>
                partium ſimplicium, à quo proueniet nobis .59? </s>
                <s xml:id="echoid-s1409" xml:space="preserve">vnde proueniet à .2. cum vndecim
                  <lb/>
                vigeſimisquartis pro prima parte quæſita, ſecunda verò iuxta propoſitum, erit .6.
                  <lb/>
                cum .22. vigeſimisquartis, tertia autem .12. cum nouem vigeſimisquartis, quarta po­
                  <lb/>
                ſteà .25. cum .18. vigeſimisquartis, quinta demum erit .52. cum .12. vigeſimisquartis,
                  <lb/>
                quarum omnium ſumma erit .100.</s>
              </p>
              <p>
                <s xml:id="echoid-s1410" xml:space="preserve">STifelius in primo exemplo regulæ falſi, ita inquit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1411" xml:space="preserve">Quæratur numerus, à cuius dimidio ſubtractæ partes tertia, & quarta relin-
                  <lb/>
                quatur .300.</s>
              </p>
              <p>
                <s xml:id="echoid-s1412" xml:space="preserve">Ipſe enim ſupponit .300. pro reſiduo cognito alterius numeri incogniti, deinde
                  <lb/>
                accipit .24. pro prima poſitione numeri cogniti, à cuius medietate abſcindit tertiam
                  <lb/>
                & quartam partem ipſius medietatis, vnde remanet .5. qui quidem numerus .5. ex
                  <num value="22">.
                    <lb/>
                  22.</num>
                quinti vel .15. ſeptimiſe ha-
                  <lb/>
                bebit ad .24. vt .300. ad
                  <reg norm="numerum" type="context">numerũ</reg>
                  <lb/>
                  <figure xlink:label="fig-0123-01" xlink:href="fig-0123-01a" number="168">
                    <image file="0123-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0123-01"/>
                  </figure>
                quæſitum, </s>
                <s xml:id="echoid-s1413" xml:space="preserve">quare cum quis multi
                  <lb/>
                plicauerit .300. per .24. & produ-
                  <lb/>
                ctum diuiſerit per .5. proueniet
                  <num value="1440">.
                    <lb/>
                  1440.</num>
                numerus quæſitus, ex vi
                  <lb/>
                regulæ de tribus.</s>
              </p>
              <p>
                <s xml:id="echoid-s1414" xml:space="preserve">Conſideremus igitur
                  <reg norm="meam" type="context">meã</reg>
                di-
                  <lb/>
                ſpoſitionem numerorum huiuſ-
                  <lb/>
                modi exempli, in figura hic ſup-
                  <lb/>
                poſita
                  <var>.F.</var>
                in qua videre licebit
                  <lb/>
                quo pacto ipſe etiam Stifelius ac
                  <lb/>
                cipiat diuiſorem .5. vt
                  <reg norm="differentiam" type="context">differentiã</reg>
                  <lb/>
                errorum & non ut differentiam
                  <lb/>
                duorum conſequentium .5. et .10
                  <lb/>
                ſicuti eſt re uera, ut diuiſor dico,
                  <lb/>
                ex rationibus à me hic ſupra ad-
                  <lb/>
                ductis, quamuis vna & eadem ſit
                  <lb/>
                quantitas neceſſariò ut patet.</s>
              </p>
              <p>
                <s xml:id="echoid-s1415" xml:space="preserve">ACcipiamus adhuc aliud exemplum à Tartalea propoſitione .9.
                  <reg norm="datum" type="context">datũ</reg>
                , &
                  <reg norm="oppoſitum" type="context">oppoſitũ</reg>
                  <lb/>
                priori; </s>
                <s xml:id="echoid-s1416" xml:space="preserve">nam ſicut in illo numerus ſimplex habebatur per ſubtractionem ſum-
                  <lb/>
                mæ numerorum adijciendorum, in hoc fitèconuerſo, hoc eſt per additionem nu-
                  <lb/>
                merorum ſubtrahendorum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1417" xml:space="preserve">Problema igitur ita ſe habet. </s>
                <s xml:id="echoid-s1418" xml:space="preserve">Fuit quidam mercator qui habebat aliquot au-
                  <lb/>
                reos, cuius quantitas poſteà quærenda erit, hic enim fecit duo itinera, ut aliquod
                  <lb/>
                dictis aureis mediantibus lucrum faceret, in primo autem itinere duplicauit nume-
                  <lb/>
                rum ſuorum aureorum, ex quibus poſteà conſumpſit .4. pro aliquibus expenſis, in </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum