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.
[2.10.] CAP.X.
[2.11.] CAP. XI. ALITER IDEM.
[2.12.] JACOBO SOLDATO MEDIOLANENSI Serenißimi Ducis Sabaudiæ Architecto peritißimo. CAP. VII.
[2.13.] AD EVNDEM IACOBVM. CAP. XIII.
[2.14.] CAP. XIIII.
[2.15.] CAP. XV.
[3.] DE MECHANICIS.
[3.1.] De differentia ſitus brachiorum libra. CAP.I.
[3.2.] De proportione ponderis extremitatis brachij libr & in diuerſo ſitu ab orizontali. CAP. II.
[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.
[3.4.] Quemadmodum exſupradictis cauſis omnes staterarum & uectium cauſæ dependeant. CAP. IIII.
[3.5.] De quibuſdam rebus animaduerſione dignis. CAP.V.
[3.6.] De ratione cuiuſdam uis adauctæ. CAP. VI.
[3.7.] De quibuſdam erroribus Nicolai Tartaleæ circa pondera corporum & eorum motus, quorum aliqui deſumpti fuerunt à fordano ſcriptore quodam antiquo. CAP. VII.
[3.8.] CAP. VIII.
[3.9.] Quòdſummaratione ſtateræper æqualia interualla ſint diuiſæ. CAP. IX.
[3.10.] Quòd line a circularis non habe at concauum cum con-uexo coniunctum, & quod Aristo. cir caproportio nes motuum aberrauerit. CAP.X.
[3.11.] Quod Aristo. in prima mechanicarum quæstionum eius quod inquir it, uer am cauſam non attulerit. CAP. XI.
[3.12.] De uer a cauſa ſecundæ, & tertiæ quæstionis mechanicæ ab Ariſtotele nonperſpecta. CAP. XII.
[3.13.] Quòd Ariſtotelisratio in 6. quæſtione poſit a non ſit admittenda. CAP. XIII.
[3.14.] Quòdrationes ab Ariſtotele de octaua quæstione confictæ ſufficient es non ſint. CAP. XIIII.
[3.15.] Quod Aristotelis ratio none queſtionis admittendanon ſit. CAP. XV.
[3.16.] Quod Aristotelis rationes de decima queſtione ſint reijciende. CAP. XVI.
[3.17.] De uer a cauſa .12. questionis mechanice. CAP. XVII.
[3.18.] De decimatertia questione. CAP. XVIII.
[3.19.] De decimaquart a queſtione. CAP. XIX.
[3.20.] De uer a r atione .17. queſtionis. CAP. XX.
[3.21.] De uera & intrinſeca cauſa trocble arum. CAP. XXI.
[3.22.] Depropria cauſa .24. quæſtionis. CAP. XXII.
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            <div xml:id="echoid-div439" type="section" level="3" n="39">
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          <div xml:id="echoid-div441" type="chapter" level="2" n="5">
            <head xml:id="echoid-head321" xml:space="preserve">IN QVINTVM
              <lb/>
            EVCLIDIS LIBRVM</head>
            <p type="title" style="it">
              <s xml:id="echoid-s2404" xml:space="preserve">QVamuis omnia libri quinti Euclid. uerißima ſint.
                <lb/>
              </s>
              <s xml:id="echoid-s2405" xml:space="preserve">Animaduertimus tamen permultos ſumma
                <reg norm="cum" type="context">cũ</reg>
                <lb/>
              difficultate
                <reg norm="eorum" type="context">eorũ</reg>
              demonstr ationes percipere. </s>
              <s xml:id="echoid-s2406" xml:space="preserve">Prœ
                <unsure/>
              -
                <lb/>
              cipuè ubi quint a, aut ſeptima deffinitiones eiuſ-
                <lb/>
              dem libri neceſſariœ
                <unsure/>
              ſunt. </s>
              <s xml:id="echoid-s2407" xml:space="preserve">Illœ enim adeo obſcurœ
                <lb/>
              uidentur, ut longè facilius admißuri ſint hœc no-
                <lb/>
              ſtra poſtulat at anquam clarior a. </s>
              <s xml:id="echoid-s2408" xml:space="preserve">At que etiam tanquam intellectui
                <lb/>
              commodiora, quam ſit illud quintum
                <reg norm="idemque" type="simple">idemq́ꝫ</reg>
              ultimum postulatum
                <lb/>
              eiuſdem in primo libro poſitum, de line a duas alias ſecante. </s>
              <s xml:id="echoid-s2409" xml:space="preserve">Quan-
                <lb/>
              doquidem
                <reg norm="ijs" type="lig">ijs</reg>
              noſtris postulatis admißis, ſequentia Theoremata per
                <lb/>
              facillima reddentur.</s>
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            <div xml:id="echoid-div441" type="section" level="3" n="1">
              <div xml:id="echoid-div441" type="section" level="4" n="1">
                <head xml:id="echoid-head322" style="it" xml:space="preserve">Horum autem primum est.</head>
                <p>
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                    <emph style="sc">Qvod</emph>
                  tota compoſita ex æquali numero partium æqualium, ſunt inuicem
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                  æqualia.</s>
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                <p>
                  <s xml:id="echoid-s2411" xml:space="preserve">Vtſi quis diceret omnes proportiones quæ
                    <reg norm="compoſitæ" type="context">cõpoſitæ</reg>
                  ſunt ex æquali numero alia-
                    <lb/>
                  rum proportionum inuicem æqualium, ſunt etiam inuicem æquales, quod Eucli-
                    <lb/>
                  des conatur demonſtrare in .22. et .23. quinti libri.</s>
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              <div xml:id="echoid-div442" type="section" level="4" n="2">
                <head xml:id="echoid-head323" xml:space="preserve">SECVNDVM.</head>
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                    <emph style="sc">Qvod</emph>
                  ſi à totis æqualibus detractæ fuerint æquales partes, quæ remanent erunt
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                  partes inuicem æquales.</s>
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                <p>
                  <s xml:id="echoid-s2413" xml:space="preserve">Et è conuerſo ſi æqualibus æqualia addas compoſita erunt inuicem æqualia.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2414" xml:space="preserve">Quod in ipſis proportionibus hoc loco ſemper intelligendum eſt.</s>
                </p>
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              <div xml:id="echoid-div443" type="section" level="4" n="3">
                <head xml:id="echoid-head324" xml:space="preserve">TERTIVM.</head>
                <head xml:id="echoid-head325" style="it" xml:space="preserve">Quę est εuclidis ſeptima propoſitio.</head>
                <p>
                  <s xml:id="echoid-s2415" xml:space="preserve">
                    <emph style="sc">Qvod</emph>
                  ſi fuerint plures termini æquales inuicem, ratio ſeu proportio vnius ip-
                    <lb/>
                  ſorum ad alium tertium terminum maiorem, minoremúe, ſed eiuſdem generis, erit
                    <lb/>
                  cadem quæ cuiuſuis alterius termini ad eundem tertium. </s>
                  <s xml:id="echoid-s2416" xml:space="preserve">Et è conuerſo, quæ fuerit
                    <lb/>
                  proportio tertij termini ad vnum prædictorum æqualium, eadem erit, ſpecie, cum
                    <lb/>
                  alio eorundem terminorum.</s>
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