Schott, Gaspar
,
Mechanica hydraulico-pneumatica. Pars I. Mechanicae Hydraulico-pnevmaticae Theoriam continet.
,
1657
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media proportionalis quæſita. </
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>Demonſtrationem vide apud
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Euclidem lib. 6. Propoſit. 13. </
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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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Propoſitio IV.
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Datis duabus rectis, invenire tertiam pro
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portionalem.
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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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<
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>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. </
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<
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>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
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ad circumferentiam circuli, hoc eſt,
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uſque ad punctum C; erit BC tertia proportionalis quæſita. </
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<
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>Sint iterum datæ duæ rectæ BC, & BE, ſitque invenien
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da tertia proportionalis. </
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<
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>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. </
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Annotatio
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QVod dictum eſt de lineis hîc poſitis, dicendum eſt de quibuscunque </
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line is propoſitis. </
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>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. </
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<
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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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