Schott, Gaspar
,
Mechanica hydraulico-pneumatica. Pars I. Mechanicae Hydraulico-pnevmaticae Theoriam continet.
,
1657
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Tubum me
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dium & ter
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tium propor
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tionalem in
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venire.</
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Propoſitio V.
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Aliter invenire tertiam proportionalem.
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<
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>QUod fecimus in pręcedenti Propoſitione mediante circulo,
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fieri poteſt faciliùs absque circulo ſic. </
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Lineam ter
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tiam pro
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portionalem
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aliter inve
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nire.
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>Duæ rectæ datæ, AB, & BE, con
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ſtituantur ad angulum rectum ABE,
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ut dictum, & ducatur recta EA. </
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ductâ deinde AB, antecedente ſeu
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primâ duarum datarum, ducatur ex E
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ad AE perpendicularis EC, occur
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rensipſi AB productæ in C; eritque
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BC tertia proportionalis. </
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>Si eſſent propoſitæ duæ rectæ CB,
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BE, deberent ipſæ coniungi ad angu
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lum rectum CBE, & ductâ rectâ CE,
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productaque CB, deberet duci per
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pendicularis AE, ad rectam CE,
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eſſetq́ue
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AB tertia quæſita. </
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Annotatio.
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INventâ alterutro modorum tertiâ continuè proportionali, ſi primam
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omiſeris, & alijs duabus tertiam inveneris; habebis quatuor leneas
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continuè proportionales. </
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>Eodemque modo invenies quintam, ſextam,
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ſeptimam, & quamcunque aliam.
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Propoſitio VI.
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Adhuc aliter invenire tertiam proportionalem.
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<
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>SI difficile tibi videtur ducere tot perpendiculares ad inveni
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endam tertiam proportionalem, uti poteris modo præſcripto
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ab Euclide lib. 6. Propoſit. 11. ſic: </
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Adhuc ali
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ter item pre
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ſtare.
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<
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>Sint duæ rectæ AB, AE. </
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Diſponãtur
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eæita, ut efficiant
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angulum A quemcunque,
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producaturque AB quam vis
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eſſe antecedentem ſeu
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primã
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,
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& capiatur BC æqualis ipſi
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AE, quæ conſequens eſſe </
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