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]

Table of contents

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[2.9.] CAP. IX.
Page: 141 (129)
[2.10.] CAP.X.
Page: 142 (130)
[2.11.] CAP. XI. ALITER IDEM.
Page: 143 (131)
[2.12.] JACOBO SOLDATO MEDIOLANENSI Serenißimi Ducis Sabaudiæ Architecto peritißimo. CAP. VII.
Page: 145 (133)
[2.13.] AD EVNDEM IACOBVM. CAP. XIII.
Page: 149 (137)
[2.14.] CAP. XIIII.
Page: 150 (138)
[2.15.] CAP. XV.
Page: 152 (140)
[3.] DE MECHANICIS.
Page: 153 (141)
[3.1.] De differentia ſitus brachiorum libra. CAP.I.
Page: 153 (141)
[3.2.] De proportione ponderis extremitatis brachij libr & in diuerſo ſitu ab orizontali. CAP. II.
Page: 154 (142)
[3.3.] Quòd quantit as cuiuſlibet ponderis, aut uirtus mouens re-ſpectu alterius quantitatis cognoſcatur beneficio perpendicularium ductarum à centro libr & ad line am inclinationis. CAP. III.
Page: 155 (143)
[3.4.] Quemadmodum exſupradictis cauſis omnes staterarum & uectium cauſæ dependeant. CAP. IIII.
Page: 156 (144)
[3.5.] De quibuſdam rebus animaduerſione dignis. CAP.V.
Page: 157 (145)
[3.6.] De ratione cuiuſdam uis adauctæ. CAP. VI.
Page: 158 (146)
[3.7.] De quibuſdam erroribus Nicolai Tartaleæ circa pondera corporum & eorum motus, quorum aliqui deſumpti fuerunt à fordano ſcriptore quodam antiquo. CAP. VII.
Page: 160 (148)
[3.8.] CAP. VIII.
Page: 161 (149)
[3.9.] Quòdſummaratione ſtateræper æqualia interualla ſint diuiſæ. CAP. IX.
Page: 163 (151)
[3.10.] Quòd line a circularis non habe at concauum cum con-uexo coniunctum, & quod Aristo. cir caproportio nes motuum aberrauerit. CAP.X.
Page: 164 (152)
[3.11.] Quod Aristo. in prima mechanicarum quæstionum eius quod inquir it, uer am cauſam non attulerit. CAP. XI.
Page: 165 (153)
[3.12.] De uer a cauſa ſecundæ, & tertiæ quæstionis mechanicæ ab Ariſtotele nonperſpecta. CAP. XII.
Page: 166 (154)
[3.13.] Quòd Ariſtotelisratio in 6. quæſtione poſit a non ſit admittenda. CAP. XIII.
Page: 167 (155)
[3.14.] Quòdrationes ab Ariſtotele de octaua quæstione confictæ ſufficient es non ſint. CAP. XIIII.
Page: 167 (155)
[3.15.] Quod Aristotelis ratio none queſtionis admittendanon ſit. CAP. XV.
Page: 171 (159)
[3.16.] Quod Aristotelis rationes de decima queſtione ſint reijciende. CAP. XVI.
Page: 171 (159)
[3.17.] De uer a cauſa .12. questionis mechanice. CAP. XVII.
Page: 172 (160)
[3.18.] De decimatertia questione. CAP. XVIII.
Page: 173 (161)
[3.19.] De decimaquart a queſtione. CAP. XIX.
Page: 173 (161)
[3.20.] De uer a r atione .17. queſtionis. CAP. XX.
Page: 174 (162)
[3.21.] De uera & intrinſeca cauſa trocble arum. CAP. XXI.
Page: 175 (163)
[3.22.] Depropria cauſa .24. quæſtionis. CAP. XXII.
Page: 177 (165)
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                <s xml:id="echoid-s521" xml:space="preserve">Hoc vt demonſtremus, primus nu-
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                merus linea
                  <var>.a.b.</var>
                ſignificetur, quam di-
                  <lb/>
                uiſam cogitemus in puncto
                  <var>.c.</var>
                in partes
                  <lb/>
                quæſitas, ex quo præſupponitur duas li-
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                neas
                  <var>.a.c.</var>
                et
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                  <lb/>
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                  <var>.d.</var>
                et
                  <var>.e.</var>
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                productum autem radicum cognitum
                  <var>.
                    <lb/>
                  f.</var>
                quandoquidem datum eſt, cuius qua-
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                dratum æquale erit producto quadra-
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                torum
                  <var>.d.e.</var>
                adinuicem, nempe
                  <var>.b.c.</var>
                in
                  <var>.a.c.</var>
                ex .19. theoremate huius. </s>
                <s xml:id="echoid-s522" xml:space="preserve">Quod verbi
                  <lb/>
                gratia ſit
                  <var>.x.</var>
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                cognitum, quo facto, doctrinam .45. theorematis libri huius ſecuti,
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                propoſitum conſequemur.</s>
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            <div xml:id="echoid-div122" type="math:theorem" level="3" n="60">
              <head xml:id="echoid-head76" xml:space="preserve">THEOREMA
                <num value="60">LX</num>
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              <p>
                <s xml:id="echoid-s523" xml:space="preserve">CVR productum differentiæ duarum radicum in ſummam ipſarum, ſemper
                  <lb/>
                differentia ſit quadratorum ipſarum radicum.</s>
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              <p>
                <s xml:id="echoid-s524" xml:space="preserve">
                  <reg norm="Exempli" type="context">Exẽpli</reg>
                gratia, quoslibet duos numeros pro radicibus ſumpſerimus, vt potè .3. et
                  <num value="5">.
                    <lb/>
                  5.</num>
                quorum differentia eſt .2. certè ſi differentiam hanc per ſummam radicum ſcili-
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                cet .8. multiplicauerimus, dabitur numerus .16. quod productum differentia eſt
                  <lb/>
                ſuorum quadratorum, nempeinter .9. et .25.</s>
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              <p>
                <s xml:id="echoid-s525" xml:space="preserve">Hoc vt ſpeculemur, duæ radices in linea
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                ſignificentur, quarum vna ſit
                  <var>.n.c.</var>
                &
                  <lb/>
                altera
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                ipſarum autem differentia
                  <var>.n.t.</var>
                ex quo
                  <var>.t.
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                  c.</var>
                æqualis erit
                  <var>.c.i</var>
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                <s xml:id="echoid-s526" xml:space="preserve">Tum cogitato toto quadrato
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                    <image file="0050-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0050-02"/>
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                cum diametro
                  <var>.d.i.</var>
                  <reg norm="ductaque" type="simple">ductaq́</reg>
                parallela lateri
                  <var>.n.d.</var>
                à
                  <lb/>
                puncto
                  <var>.c.</var>
                & altera à puncto
                  <var>.t.</var>
                & à puncto
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                tertia
                  <lb/>
                ipſi
                  <var>.n.i.</var>
                & à puncto
                  <var>.a.</var>
                quarta
                  <var>.x.a.e.</var>
                parallela ipſi
                  <var>.
                    <lb/>
                  o.</var>
                inueniemus
                  <var>.b.n.</var>
                productum eſſe differentiæ
                  <var>.n.
                    <lb/>
                  t.</var>
                in ſumma radicum
                  <var>.n.i.</var>
                & cum
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                et
                  <var>.a.o.</var>
                ſint
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                quadrata radicum prædictarum: </s>
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                  <var>.
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                ex quo gnomon
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                æqualis erit producto
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                quod ſcire cupiebamus.</s>
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            <div xml:id="echoid-div124" type="math:theorem" level="3" n="61">
              <head xml:id="echoid-head77" xml:space="preserve">THEOREMA
                <num value="61">LXI</num>
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              <p>
                <s xml:id="echoid-s528" xml:space="preserve">CVR propoſitum aliquem numerum diuiſuri in duas eiuſmodi partes, vt diffe-
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                rentia radicum quadratarum æqualis ſit alteri numero propoſito, cuius ta-
                  <lb/>
                men quadratum dimidij primi quadratum non excedat. </s>
                <s xml:id="echoid-s529" xml:space="preserve">Rectè ſecundum numerum
                  <lb/>
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                  <reg norm="rurſusque" type="simple">rurſusq́;</reg>
                di
                  <lb/>
                midium reſidui quadrant, & quadratum hoc ex quadrato dimidij primi ſubtrahunt,
                  <lb/>
                atque ita radice quadrata reſidui, dimidio primi coniuncta, pars maior datur, qua
                  <lb/>
                ex ipſo dimidio detracta, pars minor relinquitur.</s>
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                pe vt differentia radicum quadratarum dictarum partium æqualis ſit binario, bina-
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                rium hocin ſeipſum multiplicabimus, cuius quadratum .4. è primo numero .20. de­ </s>
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