Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Table of figures

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            <p type="main">
              <s id="s.002780">
                <pb pagenum="163" xlink:href="009/01/163.jpg"/>
              ditur,
                <expan abbr="locumq́">locumque</expan>
              ; ſcalmi, ſuper quo circulari motu remus vertitur, in medio
                <lb/>
              ipſius remi poſitum eſſe, vt ſcilicet tantum diſtet à manubrio, quantum à
                <lb/>
              palmula. </s>
              <s id="s.002781">Duæ
                <expan abbr="itaq;">itaque</expan>
              rectæ lineæ ponantur æquales A B, & D E, quæ quidem
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              in C, puncto medio ſe inuicem ſecent, & connectantur A B, & D E: remus
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              autem in initio vnius remigationis poſitionem habeat rectam lineam A B,
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                <expan abbr="ſitq́">ſitque</expan>
              ; A, manubrium; B, palmula; C, verò ſcalmus. </s>
              <s id="s.002782">Cum igitur A, remi ca­
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              put in fine ipſius remigationis eò tranſlatum fuerit D, non erit B, vbi E; ſi
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                <figure id="id.009.01.163.1.jpg" place="text" xlink:href="009/01/163/1.jpg" number="91"/>
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              enim ibi fuerit; remus igitur poſitionem
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              habebit rectam lineam D E; & quoniam
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              contrapoſiti anguli, qui ad C, æquales ſunt,
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              & duo latera A C, & D C, trianguli A D C,
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              duobus lateribus B C, & C E, trianguli B­
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              E C, æqualia etiam ſunt: reliqui igitur an­
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              guli,
                <expan abbr="atq;">atque</expan>
              baſes ipſorum
                <expan abbr="triãgulorum">triangulorum</expan>
              æqua­
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              les erunt per 4. propoſitionem primi libri
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              Euclidis, & propterea tantum ſpatium per­
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              curret B, quantum A: ſcalmus verò C, im­
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              motus omninò erit: & nauigium idcircò, in
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              quo ipſe ſcalmus, immotum etiam erit con­
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              tra hypotheſim. </s>
              <s id="s.002783">ſupponitur enim in queſtio­
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              ne, quod nauigium illa remigatione in anteriora moueatur, remi verò pal­
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              mula retrocedat. </s>
              <s id="s.002784">Scalmus porrò quamquam circularis remi motus expers
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              ſit; motu tamen nauigij commouetur. </s>
              <s id="s.002785">Remus igitur poſitionem habeat in
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              fine ipſius remigationis rectam lineam D Z, quæ quidem rectam A B, ſecet
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              in T, inter B, & C; rectam verò B E, in Z. </s>
              <s id="s.002786">Et quoniam duo coalterni anguli
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              C A D, & C B E, æquales
                <expan abbr="oſtẽſi">oſtenſi</expan>
              ſunt, & angulus A T D, contrapoſito B T Z,
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              æqualis eſt: duo igitur triangula A T D, & B Z T, æquiangula erunt per 32.
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              primi, & communem ſententiam. </s>
              <s id="s.002787">Similia
                <expan abbr="itaq;">itaque</expan>
              erunt ipſa triangula,
                <expan abbr="late-raq́">late­
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                raque</expan>
              ; habebunt proportionalia per 4. 6. ſicut A T, ad B T, ita D A, ad B Z.
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              </s>
              <s id="s.002788">Maior eſt autem A T, quàm B T: maior igitur D A, quàm B Z, quod etiam
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              per
                <expan abbr="cõmunem">communem</expan>
                <expan abbr="ſentẽtiam">ſententiam</expan>
              neglecta
                <expan abbr="triangulorũ">triangulorum</expan>
              ſimilitudine concludi poteſt.</s>
            </p>
            <p type="main">
              <s id="s.002789">Maius
                <expan abbr="itaq;">itaque</expan>
              ſpatium decurrit manubrium, quàm remi palmula,
                <expan abbr="atq;">atque</expan>
              illuc
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              tranſuehetur nauigium, quò remi capulus deportatus fuerit: nauigium igi­
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              tur in diuerſa procedens, plus ſpatij, quàm remi palmula tranſmittet. </s>
              <s id="s.002790">Vti­
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              mur aurem tralatione,
                <expan abbr="atq;">atque</expan>
              demonſtrationis figura Victoris Fauſti. </s>
              <s id="s.002791">Aduer­
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              tendum eſt tamen, quod cum remus poſitionem habuerit D Z, remi palmu­
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              la erit infra Z. </s>
              <s id="s.002792">Nam quoniam
                <expan abbr="triãguli">trianguli</expan>
              A D C, duo latera A C, & D C, æqua­
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              lia poſita ſunt: duo igitur anguli, qui ad D, & A, æquales erunt: angulus
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              igitur A D T, angulo D A T, maior erit: & idcircò latus A T, trianguli A­
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              T D, latere D T, maius erit per 19. primi. </s>
              <s id="s.002793">Aæqualis porrò oſtenſus eſt an­
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              guius B Z T, angulo A D T, præterea angulus D A T; angulo T B Z, æqua­
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              lis: angulus igitur B Z T, angulo T B Z, maior erit, & propterea latus B T,
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              trianguli B T Z, latere T Z, maius erit: tota igitur recta linea A B, tota
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              D Z, maior erit: & idcircò cum remus poſitionem habuerit rectam lineam
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              D Z palmula erit vltra Z. </s>
              <s id="s.002794">Eſto igitur in K, & connectantur rectæ lineæ B D,
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              & B K: ſpatium igitur decurſum ab ipſa palmula non erit B Z, ſed B K: quod </s>
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