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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                eſſe gnomoni
                  <var>.e.c.u.</var>
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                gnomonem
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                æqualem gnomoni
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                mon
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                ex præſuppoſito, maior eſt gnomone
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                duabus vnitatibus
                  <var>.b.</var>
                et
                  <var>.d.</var>
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                Itaque etiam gnomon
                  <var>.b.f.d.</var>
                duabus vnitatibus gnomonem
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                ſuperabit. </s>
                <s xml:id="echoid-s777" xml:space="preserve">Qua-
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                re
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                quadratum ſubſequens componet. </s>
                <s xml:id="echoid-s778" xml:space="preserve">Eadem ratione probabitur de quadrato
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                ſe
                  <lb/>
                quenti
                  <var>.o.f.</var>
                & gnomone
                  <var>.i.n.a.</var>
                cum hic ordo ſpeculationis ſit vniuerſalis. </s>
                <s xml:id="echoid-s779" xml:space="preserve">In
                  <lb/>
                quo cernitur quemlibet gnomonem ſibi
                  <reg norm="contiguum" type="context">contiguũ</reg>
                inferiorem ſemper duabus vni-
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                tat ibus excedere, cumque quadrata non niſi gnomonibus ſibi inuicem ſuccedant.
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                <s xml:id="echoid-s780" xml:space="preserve">Sed
                  <reg norm="cum" type="context">cũ</reg>
                primus
                  <var>.e.c.u.</var>
                diſpar fuerit,
                  <reg norm="proculdubio" type="simple">ꝓculdubio</reg>
                  <reg norm="etiam" type="context">etiã</reg>
                  <reg norm="neceſſarioque" type="simple">neceſſarioq́;</reg>
                cæteri diſpares
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                .
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                <s xml:id="echoid-s781" xml:space="preserve">Ex qua ſpeculatione, oritur regula ab antiquis tradita
                  <lb/>
                inueniendi vltimi numeri diſparis
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                ad
                  <reg norm="compo­ ſitionem" type="context">cõpo­
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                  ſitionem</reg>
                alicuius quadrati. </s>
                <s xml:id="echoid-s782" xml:space="preserve">Vt ſi quis ſeire deſideret nu-
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                merum vltimum diſparem, quo mediante quadratum
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                  o.n.</var>
                conſtitutum fuit, quod aliud non eſt quam ſcire
                  <lb/>
                quantus ſit numerus vltimi gnomonis
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                æqualis gno
                  <lb/>
                moni
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                . </s>
                <s xml:id="echoid-s783" xml:space="preserve">Itaque vt ſciamus hunc gnomonem
                  <var>.i.o.a.</var>
                  <lb/>
                patet duplicandam eſſe radicem
                  <var>.o.e.b.i.</var>
                  <reg norm="dabiturque" type="simple punctuation">dabiturq́,</reg>
                  <var>.o.e.
                    <lb/>
                  b.i.</var>
                et
                  <var>.o.u.d.a.</var>
                vbi bis reperitur
                  <var>.o.</var>
                nos autem tantummo
                  <lb/>
                do quærimus ſcire gnomonem .i.b.e.o.u.d.a. </s>
                <s xml:id="echoid-s784" xml:space="preserve">Itaque
                  <lb/>
                minor eſt vnitate duplo radicis, cum unitas
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                bis repe-
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                tatur, quæ tamen in gnomone ſemel tantum ſumebatur.</s>
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              <head xml:id="echoid-head108" xml:space="preserve">THEOREMA
                <num value="91">XCI</num>
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                <s xml:id="echoid-s785" xml:space="preserve">CVR ſumma quadratorum, quorum radices ſunt in proportione ſeſquitertia
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                nempe .4. ad .3. quadrata ſit.</s>
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              <p>
                <s xml:id="echoid-s786" xml:space="preserve">Exempli gratia, ſumemus quadratum .3. ſcilicet 9. quod in ſummam cum qua-
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                drato .4. colligemus, nempè .16.
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                quadratum .25. & ita quadratum .6. hoc eſt
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                  36.</num>
                collectum cum quadrato .8. nempè .64. efficiet quadratum .100. ita etiam qua-
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                dratum .9. hoceſt .81. coniunctum quadrato .12. nempè .144. producet quadra-
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                tum .225.</s>
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              <p>
                <s xml:id="echoid-s787" xml:space="preserve">In cuius gratiam ſint duo quadrata ſubſcripta
                  <var>.q.o.</var>
                et
                  <var>.q.a.</var>
                quorum radices ſint
                  <var>.q.</var>
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                g. et
                  <var>.q.p.</var>
                hoc eſt
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                quatuor vnitatum, et
                  <var>.q.
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                  p.</var>
                trium, ex quo
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                erit .16. vnitatum et
                  <var>.q.o.</var>
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                nouem. </s>
                <s xml:id="echoid-s788" xml:space="preserve">Ad hæc cogitemus applicari quadra-
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                to
                  <var>.q.a.</var>
                gnomonem
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                tam amplum ſiue la-
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                tum
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                gnomon
                  <var>.b.a.g.</var>
                nempè vt
                  <var>.h.</var>
                ſit æqua
                  <lb/>
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                  <var>.q.g.</var>
                maior eſt
                  <var>.
                    <lb/>
                  q.p.</var>
                  <reg norm="huncque" type="simple">huncq́;</reg>
                gnomonem
                  <var>.f.s.h.</var>
                dico ęqualem eſ
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                ſe quadrato
                  <var>.q.o.</var>
                nam ex preſuppoſito
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                terra
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                dicem
                  <var>.q.p.</var>
                ingreditur, & quater
                  <var>.q.g.</var>
                ex quo,
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                tres partes
                  <var>.q.k.p.</var>
                inter ſe æquales ſunt vnde
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                etiam quadratum
                  <var>.q.o.</var>
                nouem partibus ſuper-
                  <lb/>
                ficialibus quadratis conſtabit, quarum ſingula
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                rum radix æqualis erit
                  <var>.g.</var>
                cumque præcedenti
                  <lb/>
                theoremate didicerimus quemlibet gnomo-
                  <lb/>
                nem quadrati immediatè ſequentis æquę amplitudinis cum gnomone præcedentis, </s>
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