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
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
91 79
92 80
93 81
94 82
95 89
96 84
97 85
98 96
99 87
100 88
< >
page |< < (106) 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">
              <pb o="106" rhead="IO. BAPT. BENED." n="118" file="0118" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0118"/>
              <p>
                <s xml:id="echoid-s1364" xml:space="preserve">SEDijdem errores proueniunt exſummis partium ſimplicium.</s>
              </p>
              <p>
                <s xml:id="echoid-s1365" xml:space="preserve">Vtexempli gratia, in figura
                  <var>.B.</var>
                ſumma propoſita partium ſimplicium eſt .39.
                  <lb/>
                vt diximus, eo quòd ab ipſo .50. detraxerimus .11. ſumma ſcilicet numerorum adij
                  <lb/>
                ciendorum ad efficiendas partes compofitas, ſumma poſteà fimplicium partium
                  <lb/>
                primæ poſitionis, erit .60. eo quòd prima pars erat .10. ſecunda autem ſimplex 20.
                  <lb/>
                tertia verò fimplex .30. iuxta ordinem propoſiti. </s>
                <s xml:id="echoid-s1366" xml:space="preserve">Summa deinde ſimplicium
                  <reg norm="partium" type="context">partiũ</reg>
                  <lb/>
                fecundæ poſitionis effet .48. quia prima eius pars erat .8. ſecunda verò ſimplex .16.
                  <lb/>
                tertia autem ſimplex .24. vnde prima ſumma excederet datam .39. per .21. differen-
                  <lb/>
                tiæ, ſecunda verò per .9. vt ſupra vidimus de ſummis compoſitis à dato .50. compo-
                  <lb/>
                fito, & hoc quidem mirandum non eft, quod ſcilicet tres ſummæ fimplicium par-
                  <lb/>
                tium ſintinuicem inæqua-
                  <lb/>
                les, ijſdem differentijs me-
                  <lb/>
                  <figure xlink:label="fig-0118-01" xlink:href="fig-0118-01a" number="162">
                    <image file="0118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0118-01"/>
                    <caption xml:id="echoid-caption2" xml:space="preserve">Simpricium</caption>
                  </figure>
                diantibus, quibus
                  <reg norm="differunt" type="context">differũt</reg>
                  <lb/>
                dictæ tres ſummæ compofi
                  <lb/>
                tæ, cum ab vnaquaque
                  <reg norm="con" type="context">cõ</reg>
                  <lb/>
                  <reg norm="poſitarum" type="context">poſitarũ</reg>
                ablatus fit nume-
                  <lb/>
                rus .11. æqualiter, vnde ex
                  <lb/>
                neceſſitate, permutando,
                  <lb/>
                  <reg norm="earum" type="context">earũ</reg>
                differentiæ
                  <reg norm="relinquem" type="context">relinquẽ</reg>
                  <lb/>
                dæ erant æquales inuicem
                  <lb/>
                ex
                  <ref id="ref-0017">.78. theoremate hu-
                    <lb/>
                  ius noſtri lib.</ref>
                ſummæ enim
                  <lb/>
                compofitæ erant .71. 59. et
                  <lb/>
                50. fimplices verò .60. 48.
                  <lb/>
                et .39. differentes à primis
                  <lb/>
                per .11. vt dictum eft, qua
                  <lb/>
                re veritas ita manabit à compofitis, quemadmodum à fimplicibus, ſed à fimplici-
                  <lb/>
                bus per ſe, & a compofitis per accidens vtiam iam videbimus.</s>
              </p>
              <p>
                <s xml:id="echoid-s1367" xml:space="preserve">ANtiquorumigitur primus m odus vtitur regula detribus, hocordine, multi-
                  <lb/>
                plicando ſcilicet ſecundum errorem, qui eft .9. cum differentia primarum par
                  <lb/>
                tium pofitarum, quæ eft .2. & productum diuidendo per differentiam errorum, quæ
                  <lb/>
                eft .12. proueniens poftea quod eft .1. cum dimidio additur hoc loco primæ parti ſe-
                  <lb/>
                cundæ poſitionis.
                  <reg norm="&c." type="unresolved">&c.</reg>
                quòd benè ſe habet. </s>
                <s xml:id="echoid-s1368" xml:space="preserve">Vbi animaduertendum eſt, quod ille
                  <lb/>
                numerus .12. non eft accipiendus per ſe vt differentia errorum hoc eft .21. et .9. nifi
                  <lb/>
                peràccidens, fed benè perfe, vt
                  <reg norm="differentia" type="context">differẽtia</reg>
                inter .60. er .48. ſimplices ſummas, quem
                  <lb/>
                admodum .9. in hoc propoſito eft differentia per ſe inter .48. et .39 per accidens ve-
                  <lb/>
                ro inter .59. et .50.</s>
              </p>
              <p>
                <s xml:id="echoid-s1369" xml:space="preserve">Cognoſcendum igitur eft mediante .24. quinti Eucli. quod eadem proportio
                  <lb/>
                eft primæ ſummæ (ſimplicium dico) ad ſuam primam partem, quæ ſecundæ ſum-
                  <lb/>
                mæ ad ſuam, & tertiæ ſummæ ad fuam fimiliter (vbi rectè etiam feciffent hoc in lo-
                  <lb/>
                co antiqui ſi multiplicauiffent tertiam ſummam fim plicem cum prima parte prioris
                  <lb/>
                fummæ fimplicis, & productum diuififfent per primam ſummam, vnde prima pars
                  <lb/>
                quæſita tertiæ ſummæ orta fuiffet, abſque ullo negotio ipfius plus velminus) </s>
                <s xml:id="echoid-s1370" xml:space="preserve">Quare
                  <lb/>
                habebimus tres terminos antecedentes ab vna parte, & tres terminos conſequen-
                  <lb/>
                tesab alia parte continentes vnam
                  <reg norm="eandemque" type="simple">eandemq́;</reg>
                proportionem, vnde ex .19. quinti,
                  <lb/>
                vel .12. ſeptimi eorum differentiæ proportionales erunt, hoc eft,
                  <reg norm="quod" type="simple">ꝙ</reg>
                eadem propor­ </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum