Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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que diſtat extremitate; ſimiliter quemadmodum iactus æqualiter à me
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dio iactu 45. diſtantes æqualem amplitudinem acquirunt in horizontali
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BG, ita qui æqualiter diſtant à medio iactu 90.vel horizontali BG æqua
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lem amplitudinem acquirunt in aliquo plano horizontali, ſcilicet in eo
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vnde vterque iactus deſinit in perpendicularem deorſum. </
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<
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id
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">Obſeruabis ſecundo, omnes perpendiculares deorſum perinde accipi,
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atque ſi eſſent parallelæ propter inſenſibilem differentium; </
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<
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ab omnibus admittitur; quomodo verò per diuerſa plana deorſum cor
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pus tendere poſſit, vſque ad centrum terræ, Libro ſequenti explica
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bimus. </
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Theorema
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67.
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In iactu per inclinatam deorſum dato tempore minùs detrahitur de impetu
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violento, quàm in iactu per inclinatam ſurſum
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ſit enim circulus centro A
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ſemidiametro AG; </
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">ſitque AG horizontalis, & AO perpendiculatis deor
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ſum; </
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<
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">ſit iactus per inclinatam ſurſum AD, ſitque impetus violentus vt A
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D, & naturalis deorſum vt DE; </
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<
s
id
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">linea motus erit DAE; </
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<
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">igitur aſſumatur A
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E in AC, & DE in CB, ex impetu AD detrahitur DB, vt conſtat ex dictis
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quia totius ille fruſtrà eſt; </
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<
s
id
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">ſit autem inclinata deorſum cum impetu vio
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lento æquali AI æqualis AD, ſitque naturalis deorſum acceleratus pro
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rata plani inclinati vt IL, linea motus erit AL; </
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<
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">aſſumatur AK, vt AL, &
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KH vt IL, detrahitur tantùm IH, ſed IH eſt minor DB; igitur tempore
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ſequenti æquali impetus violentus inclinatæ ſurſum erit vt EF æqualis
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AB inclinatæ deorſum, vt LM, quæ maior eſt EF, quia eſt æqua
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lis AH. </
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<
s
id
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">Ratio à priori eſt, quia cum inclinata deorſum faciat acutum angu
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lum cum perpendiculari deorſum, cum quo obtuſum facit inclinata ſur
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ſum, maior eſt in illa linea motus; </
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<
s
id
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">eſt enim maior diagonalis, in hac ve
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rò minor, igitur in illa minùs impetus eſt fruſtrà, in iſta verò plùs, igitur
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minùs impetus in illa deſtruitur, plùs in iſta; quæ omnia conſtant ex
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Th. 110. & 139. & 140. l.1. habes etiam in qua proportione decreſcat
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impetus. </
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Theorema
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68.
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Hinc in iactu qui fit per inclinatam deorſum minùs detrahitur,
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& in eo
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qui fit per inclinationem ſurſum plùs detrahitur, in perpendiculari deor
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ſum nihil detrahitur, in perpendiculari ſurſum totus detrahitur qui po
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teſt extrahi, id eſt ex collectione vtriuſque naturalis, & violenti dupli
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naturalis in prima linea motus; hæc omnia ſequuntur ex dictis. </
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<
s
id
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">Obiici poteſt vnum ſatis difficile; quia ſi in perpendiculari deorſum
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purà in AP nihil detrahitur impetus violenti, igitur creſcit ſemper vis
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ictus, quod videtur eſſe contra experientiam. </
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<
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id
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">Reſp. me aliquando fuiſſe in ea ſententiâ, vt reuerâ exiſtimarem de
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creſcere impetum violentum in iactu perpendiculari deorſum; </
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<
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id
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">cum
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etiam exiſtimarem decreſcere vim ictus; </
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<
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">ſed re melius conſiderata, cum
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nunquam id experiri potuerim; </
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<
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">nam ſemper ſentio vim ictus maiorem, </
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