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]

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                  <pb o="115" rhead="THEOREM. ARIT." n="127" file="0127" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0127"/>
                ſed exceſſus quartæ ſupra tertiam eſt .10. vnde ſupra ſecundam erit .18. & ſupra pri-
                  <lb/>
                mam erit .24. quæ omnia ſimul addita erunt .44. & in qualibet harum trium remane-
                  <lb/>
                bit una pars æqualis primæ quantitati, </s>
                <s xml:id="echoid-s1457" xml:space="preserve">quare ſi ex .96. detractus fuerit numerus .44.
                  <lb/>
                reliquus 52. erit quadruplus primæ, </s>
                <s xml:id="echoid-s1458" xml:space="preserve">quare prima pars valebit .13. ſecunda .19. ter-
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                tia .27. & quarta .37. quarum omnium ſumma eſt .96.</s>
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                <s xml:id="echoid-s1459" xml:space="preserve">EX poſitionibus autem Tartaleæ in noſtra figura
                  <var>.K.</var>
                digeſtis, videre poſſumus
                  <lb/>
                quo pacto
                  <reg norm="colligantur" type="context">colligãtur</reg>
                huiuſ
                  <lb/>
                modi
                  <reg norm="conſequentes" type="context">conſequẽtes</reg>
                numeri ſimpli-
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                ces .36. et .52. more figuræ
                  <var>.E.</var>
                quia
                  <lb/>
                  <figure xlink:label="fig-0127-01" xlink:href="fig-0127-01a" number="172">
                    <image file="0127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0127-01"/>
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                colliguntur primò partes compoſi
                  <lb/>
                tæ .9. 15. 23. 33. ex quarum ſumma
                  <lb/>
                80. ſubtrahitur .36. ſumma ſim-
                  <lb/>
                plex ex ſimplicibus partibus .9. 9.
                  <lb/>
                9. 9. &
                  <reg norm="reſiduum" type="context">reſiduũ</reg>
                quod eſt .44. ſubdu
                  <lb/>
                citur ex .96. ſumma compoſita &
                  <lb/>
                propoſita, vnde remanet .52. pro
                  <lb/>
                ſumma ſimplici, ex numero dato,
                  <lb/>
                cuius proportio ad .13. eadem eſt
                  <lb/>
                quæ .36 ad .9. & proptereà ſuper-
                  <lb/>
                flua eſt ſecunda poſitio,
                  <reg norm="quando" type="context">quãdo</reg>
                ſci
                  <lb/>
                mus inuenire tales duos numeros
                  <lb/>
                conſequentes, vt in hoc exemplo
                  <lb/>
                ſunt .36. et .52. quia ex regula de
                  <lb/>
                tribus poſteà elicitur veritas quæ-
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                ſita. </s>
                <s xml:id="echoid-s1460" xml:space="preserve">
                  <reg norm="Idem" type="context">Idẽ</reg>
                dico de 33. problemate.</s>
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                <s xml:id="echoid-s1461" xml:space="preserve">PRO quo .33. problemate acci
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                piantur poſitiones primi
                  <reg norm="exem" type="context">exẽ</reg>
                  <lb/>
                pli Tonſtalli hoc eſt .33. et .31. vt in figuris hic ſubiectis
                  <var>.P.Q.</var>
                facile quis poteſt vi-
                  <lb/>
                dere, vbi in figura P. videbit nume-
                  <lb/>
                ros compoſitos, in figura verò
                  <var>.Q.</var>
                cer
                  <lb/>
                  <figure xlink:label="fig-0127-02" xlink:href="fig-0127-02a" number="173">
                    <image file="0127-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0127-02"/>
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                net numeros ſimplices, à quibus pro
                  <lb/>
                ueniunt rationes per ſe huiaſmodi
                  <lb/>
                operationis, in figura autem
                  <var>.R.</var>
                vide
                  <lb/>
                bitur meus ordo, & iſtæ tres figuræ ſi
                  <lb/>
                miles
                  <reg norm="erunt" type="context">erũt</reg>
                tribus illis primis
                  <var>.A.B.C.</var>
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                ita quòd cum quis illas intellexerit, il
                  <lb/>
                lico etiam iſtas cognoſcet, vbi
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                videbit quam confusè
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                ij
                  <lb/>
                qui ignorant hunc meum ordinem
                  <lb/>
                ſimplicium
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                , à quibus fluit
                  <lb/>
                tota ratio (vt ſupra dixi) huiuſcemo
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                di operationis.</s>
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