Schott, Gaspar, Mechanica hydraulico-pneumatica. Pars I. Mechanicae Hydraulico-pnevmaticae Theoriam continet. , 1657

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              media proportionalis quæſita. </s>
              <s>Demonſtrationem vide apud
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              Euclidem lib. 6. Propoſit. 13. </s>
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            <p type="margin">
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                <emph type="italics"/>
              Lineam me­
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              diam pro­
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              portionalem
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              inter duas
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              invenire.
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              </s>
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            <p type="main">
              <s>
                <emph type="center"/>
              Propoſitio IV.
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              </s>
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            <p type="main">
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              Datis duabus rectis, invenire tertiam pro­
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              portionalem.
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            </p>
            <p type="margin">
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                <emph type="italics"/>
              Lineam ter­
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              tiam propor­
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              tionalem
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              poſt duas in­
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              venire.
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              </s>
            </p>
            <p type="main">
              <s>SInt datæ duæ rectæ AB, & BE, præcedentis figuræ, ſitque
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              invenienda tertia, ad quam ita ſe habeat ſecunda, ſicut pri­
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              ma ad ſecundam. </s>
              <s>Coniungantur rectæ AB, BE, in puncto B
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              ad angulum rectum, ducaturque recta EA; eáque bifariam di­
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              visâ in F, ducatur recta FD perpendicularis ad AE; & facto
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              centro D, intervallo DA deſcribatur circulus, qui neceſſariò
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              tranſibit per punctum E,
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              per quintam Quarti Euclid.
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              Si iam
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              producatur recta AB
                <expan abbr="uſq;">uſque</expan>
              ad circumferentiam circuli, hoc eſt,
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              uſque ad punctum C; erit BC tertia proportionalis quæſita. </s>
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            <p type="main">
              <s>Sint iterum datæ duæ rectæ BC, & BE, ſitque invenien­
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              da tertia proportionalis. </s>
              <s>Coniungantur, ut antea, rectæ illæ
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              in B, ut efficiantangulum rectum, & ducatur recta EC; at­
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              que ex puncto medio G demittatur perpendicularis GD, &
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              producta recta CB in continuum, deſcribatur centro D, in­
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              tervallo DC, circulus, qui iterum tranſibit per punctum E,
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              & ſecabit rectam CB productam in A; eritque hæc recta BA
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              tertia proportionalis quæſita. </s>
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            <p type="main">
              <s>
                <emph type="center"/>
              Annotatio
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              </s>
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            <p type="main">
              <s>
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              QVod dictum eſt de lineis hîc poſitis, dicendum eſt de quibuscunque </s>
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              line is propoſitis. </s>
              <s>Itaque ſipropoſitis duobus tubis inveniendus ſit
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              vel medius, veltertius proportionalis; coniunge lineas rectas tubis da­
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              tis æquales; & operare ut dictum, & invenies quod quæris. </s>
              <s>Quòd ſi
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              tubi propoſiti, ac lineæ ipſis æquales nimis eſſent longæ, ac proinde minùs
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              commodè circulo includi poſſent; accipe ipſarum ſubmultiplices, v.g.
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              dimidiam, tertiam, quartam, &c. partem, & cum ipſis procede
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              ut dictum; eritque inventa linea æquè ſubmultiplex
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              lineæ aut tubi quæſiti.
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              </s>
            </p>
          </chap>
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