Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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Theorema
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20.
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Si conſtet ex retardato & accelerato, vt fit in perpendiculari ſurſum, &
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deorſum motus mixtus, linea per quam fit eſt curua,
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ſit enim retardatus
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per AD, ſit acceleratus per AG, aſſumatur AB cum numero impari, putà
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5.BC.3. CD.1. accipiatur AE.1. EF.3. ducantur parallelæ BK. CL. DI.
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& aliæ EM. FH. GI. & per puncta AM. HI. ducatur linea curua, hæc eſt
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linea motus mixti ex retardato & accelerato; hæc porrò non eſt Parabo
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la, vt conſtat, quia quadratum AE non eſt ad ad quadratum AF, vt qua
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dratum AB, vel EM ad quadratum FH, vel AC. </
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Scholium.
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">Obſeruabis in fine huius motus amplitudinem, ſeu ſinum rectum li
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neæ ſcilicet GI, eſſe æqualem altitudini ſeu ſinui verſo, vel ſagittæ AG; </
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cùm enim motus naturaliter acceleratus in eadem proportione creſcat,
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quod hic ſuppono, in qua retardatus decreſcit; </
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">certè AG quæ eſt linea
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accelerati eſt æqualis GI, quæ eſt linea retardati: non tamen dicendum
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eſt lineam AI eſſe circulum, alioquin GH eſſet æqualis GI, ſed GH eſt, v.
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g. 89. cum GI ſit radix quadr.81. eſt enim 9. licèt GM ſit æqualis GH.
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ſed de his lineis infrà. </
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">Vtrùm verò ſit aliquis motus huiuſmodi, videbi
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mus in ſequentibus Theorematis. </
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Theorema
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21.
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Quando corpus proiicitur per horizontalem in aëre libero, mouetur motu
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mixto
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; </
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">probatur, quia ſunt duo impetus in eo corpore, ſcilicet innatus
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deorſum, & impreſſus per horizontalem, vt patet; igitur vterque aliquid
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præſtat ad illum motum per Ax. 1. igitur eſt motus mixtus per def. </
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<
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Theorema
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22.
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Ille motus non eſt mixtus ex vtroque æquabili.
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ex vtroque æquabili eſt rectus per Th.1.& 4. ſed hic motus proiecti per
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horizontalem non eſt rectus per hyp.1. </
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Theorema
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23.
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Ille motus non eſt mixtus ex naturali æquabili & alio accelerato
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; patet,
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quia nulla eſt cauſa, à qua violentus poſſit accelerari. </
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Theorema
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24.
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Non est mixtus ex naturali æquabili & violento retardato
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<
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">Primò, quia
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cùm pro tata concurrant poſt integrum quadrantem vix ſpatium vnius
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palmi confeciſſet in perpendiculari deorſum per Th.59.l.2.quod tamen
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eſt contra experientiam.Secundò, quia ad aliquod tandem punctum per
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ueniretur, in quo mobile haberet tantùm impetum innatun; igitur nul
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lus eſſet ictus contra experientiam. </
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">Tertiò, quia naturalis impetus in
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tenditur in plano inclinato; </
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">igitur in motu per inclinatam, eſt enim
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motus deorſum; igitur intenditur impetus naturalis, vt patet ex lib. 2.
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igitur non eſt mixtus. </
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