Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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AKC acquiritur æqualis acquiſitæ in AC; </
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<
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acquiritur
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æqualis; </
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<
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C; Item in tribus acquiritur æqualis ac
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quiſitæ in duabus, atque ita deinceps. </
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">Præterea velocitas acquiſita in chordis mediis.v.g. </
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<
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æqualis acquiſitæ in LZ, vel RT, vel in ſinu toto AB, minùs ſinu verſo
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arcus LA, & ſinu recto arcus IC; ſed hæc ſunt ſatis facilia. </
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">Idem dico de chordis arcus quadrantis funependuli AEB figura Lem
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ma.4. v. g. de chorda IB, in qua velocitas acquiſita eſt æqualis acqui
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ſitæ in RB, vel in duabus ILB, vel in tribus 4. 5. atque ita deinceps:
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hinc etiam vides in quadrante EB acquiri æqualem velocitatem, ſiue
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EA ſit perpendicularis deorſum, ſiue AB. </
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Lemma
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14.
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Citiùs deſcendet corpus per duas EIB, quàm per IB
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; </
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<
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">quia deſcenſus eſt
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æquè diuturnus per EB, & IB; ſed citiùs deſcendit per EIB, quàm per
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EB, vt iam ſuprà dictum eſt in Lem. 8. igitur citiùs per EIB, quàm
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per IB. </
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Lemma
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15.
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Citiùs deſcendet per
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duas chordas BHF, quàm per duas BGF, à quiete
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B; </
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<
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">ſint enim duæ BHF, ſitque BH. v.g. chorda arcus 30.grad.ſc.5 1764.
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earum partium, quarum ſinus totus eſt 100000. ſit Tangens BE; </
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perpendicularis in BH, & HT in BD; </
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<
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nalis inter DT, & TB; </
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<
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">eſtque differentia ſinus totius, & ſinus OH 60.
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grad. eſt autem OH 86603. igitur HT 13397. quadretur HT, produ
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ctum diuidatur per BT 50000. quotiens dabit TD 3589. quæ ſi adda
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tur BT, habebitur tota BD 53589. quadretur BD; </
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<
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quadrati, ex quo extrahatur radix; </
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<
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">habebitur KD, vel BK 37893. ſit
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autem LF 200000. ad 141422. æqualem BF, ita BF ad LH 100000.
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certè tempus per LH eſt ad tempus per BH, vt LH ad BH; </
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<
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id
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">ſed tempus
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per LH eſt ad tempus per LF, vt LH ad 141422.igitur tempus per BH
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eſt ad tempus per HF facto initio motus ex L, vt BH 51764. ad 41422.
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igitur ad tempus per BHF, vt 51764.ad 93186. porrò BH & BK æqua
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li tempore percurruntur; </
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<
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">igitur tempus per BK eſt BH, id eſt 51764.
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cùm autem ſpatia in eadem linea ſint in ratione duplicata temporum;
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certè ſpatium BK acquiſitum tempore 51764.eſt ad ſpatium acquiſitum
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in BF tempore 93186. vt quadratum 51764. ad quadratum 93186.id eſt,
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vt 2679511696.ad 8676630576.vnde factâ regulâ trium habeo ſpatium
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decurſum in BF 122702. tempore 93186. ſed tota BF eſt 141422. igitur
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citiùs percurruntur duæ BHF, quàm BF. </
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">Præterea ſint duæ BGF, BG eſt 100000.ſit perpendicularis G 4 cùm
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angulus GB 4.ſit grad.30. erit vt 5 G ad GB, ita BG ad B 4. igitur B 4.
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erit 115469. ſit 4.3.perpendicularis in BF, quadratum B 4. eſt duplum
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quadrati B 3.igitur B 3. erit 81655. iam verò FN eſt ſecans grad.75. ſci
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licet 386370.igitur GN eſt 334606. detracta ſcilicet FG æquali BH; </
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<
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autem NG ad 359557. vt hæc ad NF; </
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