Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N15AC3">
            <p id="N176A1" type="main">
              <s id="N17713">
                <pb pagenum="106" xlink:href="026/01/138.jpg"/>
              4.progreſſio longiùs diſcedet à vera; </s>
              <s id="N1771E">vt ſuprà iam totius repetitum fuit: </s>
              <s id="N17722">
                <lb/>
              quippe hæc progreſſio in puris inſtantibus fieri tantùm poteſt, cum ſin­
                <lb/>
              gulis inſtantibus noua fiat acceſſio velocitatis, in hoc enim eſt error,
                <lb/>
              quòd in tota parte temporis AC ponatur æquabilis velocitas, eiuſque
                <lb/>
              principium A, ſit æquale fini C; </s>
              <s id="N1772D">nam AB, & GH ſunt æquales; </s>
              <s id="N17731">cùm ta­
                <lb/>
              men ſit minor velocitas in A, quàm in C, niſi AC ſit tantùm
                <expan abbr="inſtãs">inſtans</expan>
              ; </s>
              <s id="N1773B">vnde
                <lb/>
              tota velocitas in hypotheſi Galilei acquiſita in 4.partibus temporis aſ­
                <lb/>
              ſumptis eſt, vt triangulum AFN; </s>
              <s id="N17743">acquiſita verò in noſtra hypotheſi eſt vt
                <lb/>
              ſumma rectangulorum CB, CI, EK, EN, quæ ſumma eſt ad triangulum
                <lb/>
              AFN, vt 10, ad 8. vel vt 5.ad 4. igitur maior 1/4; nam prima pars tempo­
                <lb/>
              ris addit triangulum ABG, ſecunda GHI. &c. </s>
            </p>
            <p id="N1774D" type="main">
              <s id="N1774F">Si tamen diuidantur iſtæ partes temporis in minores v. g. in 8. tunc
                <lb/>
              ſumma rectangulorum erit tantùm maior 1/8; </s>
              <s id="N17759">ſi in 16. (1/16) ſi in 32. (1/32); </s>
              <s id="N1775D">ſi in
                <lb/>
              64.(11/64), cuius ſehema hîc habes; ſint enim 3.partes temporis ſenſibiles A
                <lb/>
              CDFE, & ſpatium vt triangulum AFN, ſpatia verò acquiſita in ſingulis
                <lb/>
              partibus, vt portiones trianguli prædicti, quæ ipſis reſpondent v. g. ac­
                <lb/>
              quiſitum in prima parte ad acquiſitum in ſecunda tantùm, vt triangu­
                <lb/>
              lum ACG ad trapezum GCDI &c. </s>
              <s id="N1776F">denique acquiſitum in temporibus
                <lb/>
              inæqualibus, vt quadrata temporum v. g. acquiſitum in prima parte ad
                <lb/>
              acquiſitum in duabus, vt triangulum ACG ad triangulum ADI; </s>
              <s id="N1777B">id eſt
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              quadratum CA ad quadratum DA; </s>
              <s id="N17781">in noſtra verò hypotheſi, ſi velocitas
                <lb/>
              in tota prima parte AC ponatur vt CG æquabiliter; </s>
              <s id="N17787">haud dubiè ſpatium
                <lb/>
              acquiſitum in prædictis 4. temporibus erit, vt ſumma rectangulorum C
                <lb/>
              B, CI, EK, EN, quæ maior eſt toto triangulo, AFN, 4. triangulis ABG,
                <lb/>
              GHI, IKL, LMN, ie eſt 1/4 totius trianguli AFN; atque ita ſumma re­
                <lb/>
              ctangulorum continet 10. quadrata æqualia quadrato CB, & triangu­
                <lb/>
              lum AFN, continet. </s>
              <s id="N17795">tantùm 8. </s>
            </p>
            <p id="N17798" type="main">
              <s id="N1779A">Iam verò diuidantur 4. partes temporis AF, in 8. æquales; </s>
              <s id="N1779E">in ſenten­
                <lb/>
              tia Galilei totum ſpatium erit ſemper triangulum AFN, id eſt vt ſubdu­
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              plum quadrati ſub AF; </s>
              <s id="N177A6">quæ cùm ſit 8. quadratum erit 64.& ſubduplum
                <lb/>
              quadrati 32. at verò ſumma rectangulorum eſt 36. id eſt continet 36.
                <lb/>
              quadrata æqualia quadrato XA; cùm tamen triangulum AFN, conti­
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              neat tantùm 32. igitur ſumma prædicta eſt ad triangulum AFN, vt 36.
                <lb/>
              ad 32. id eſt vt 9.ad 8. igitur ſumma eſt maior triangulo 1/8, quæ omnia
                <lb/>
              conſtant. </s>
            </p>
            <p id="N177B4" type="main">
              <s id="N177B6">Præterea diuidatur vlteriùs tempus AF in 16. æquales partes; </s>
              <s id="N177BA">qua­
                <lb/>
              dratum 16. cum ſit 256. accipiatur ſubduplum id eſt 128. & erit trian­
                <lb/>
              gulum AFN, cui ſemper reſpondet totum ſpatium acquiſitum in ſenten­
                <lb/>
              tia Galilei; </s>
              <s id="N177C4">at verò ſumma rectangulorum erit 136. igitur ſumma eſt ad
                <lb/>
              ſummam vt 136.ad 128.id eſt vt 17.ad 16. igitur eſt maior ſumma trian­
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              gulo (1/16) atque ita deinceps; </s>
              <s id="N177CC">ſi vlteriùs diuidas prædictum tempus in par­
                <lb/>
              tes minores: quot porrò erunt, antequam fiat tota reſolutio in inſtan­
                <lb/>
              tia, ſint enim v. g. in tempore AF inſtantia 1000000. ſumma quæ reſ­
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              pondet noſtræ progreſſioni, erit maior altera, quæ reſpondet progreſſio­
                <lb/>
              ni Galilei (1/1000000) quis hoc percipiat? </s>
            </p>
          </chap>
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    </archimedes>
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