285183MATHEMATICA. Lib. I. Cap. XXVII.
Dum elaſteria actionibus æqualibus in ſe mutuo premunt, utrumque agit
quaſi obſtaculo immobili inſiſteret; & integram ſuam vim in partem oppoſitam
exerit ; id eſt elaſteria agunt in corpora A & C ita, ut ſingulis, præter 11561. moratas vires, communicent vim C ff; quare vis corpori A communicata va-
let B ff + 2C ff, & C movetur vi A ff + B ff + Cff, dum B ad par-
tem Cpellitur actione quæ valet A ff-C ff.
quaſi obſtaculo immobili inſiſteret; & integram ſuam vim in partem oppoſitam
exerit ; id eſt elaſteria agunt in corpora A & C ita, ut ſingulis, præter 11561. moratas vires, communicent vim C ff; quare vis corpori A communicata va-
let B ff + 2C ff, & C movetur vi A ff + B ff + Cff, dum B ad par-
tem Cpellitur actione quæ valet A ff-C ff.
Sed B non poteſt moveri, quin eâdem velocitate propellatur elaſterium
inter B & C, & ab elaſterio ita agitato accipit corpus C vim ftatim memo-
ratam eodem modo ac in nave, in qua elaſterium obſtaculo cede-
re neſcio inſiſteret, actione elaſterii moveretur; id eſt velocitas qua
corpus C a B recedit, aut B celerius movetur, illa eſt quæ competit impreſſio-
ni ſtatim memoratæ, quæ velocitas eſt f {√A + B + C\x{0020}/C} . Si corporis B 22470. locitas dicatur x, erit x + f {√A + B + C\x{0020}/C} velocitas corporis C. Summa viri-
um horum corporum eſt A ff + B ff + C ff & præterea A ff-C ff, ideſt
valet ſumma hæc 2 A ff + B ff; Unde deducimus {B xx + C xx +
2fx √AC + BC + CC\x{0020} + A ff + B ff + C ff = 2Aff + Bff ; 33479. aut {x x + 2f x √AC + BC + CC\x{0020}/B + C = Aff-Cff/B + C}; &
{x = f√AB + 2AC\x{0020}-f√AC + BC + CC\x{0020}/B + C}: additâ velocitate
f√A + B + C\x{0020}/C} qua C recedit à B habemus ipſius C velocitatem
{fC √AB + 2AC\x{0020} + fB √AC + BC + CC\x{0020}/BC + CC}
inter B & C, & ab elaſterio ita agitato accipit corpus C vim ftatim memo-
ratam eodem modo ac in nave, in qua elaſterium obſtaculo cede-
re neſcio inſiſteret, actione elaſterii moveretur; id eſt velocitas qua
corpus C a B recedit, aut B celerius movetur, illa eſt quæ competit impreſſio-
ni ſtatim memoratæ, quæ velocitas eſt f {√A + B + C\x{0020}/C} . Si corporis B 22470. locitas dicatur x, erit x + f {√A + B + C\x{0020}/C} velocitas corporis C. Summa viri-
um horum corporum eſt A ff + B ff + C ff & præterea A ff-C ff, ideſt
valet ſumma hæc 2 A ff + B ff; Unde deducimus {B xx + C xx +
2fx √AC + BC + CC\x{0020} + A ff + B ff + C ff = 2Aff + Bff ; 33479. aut {x x + 2f x √AC + BC + CC\x{0020}/B + C = Aff-Cff/B + C}; &
{x = f√AB + 2AC\x{0020}-f√AC + BC + CC\x{0020}/B + C}: additâ velocitate
f√A + B + C\x{0020}/C} qua C recedit à B habemus ipſius C velocitatem
{fC √AB + 2AC\x{0020} + fB √AC + BC + CC\x{0020}/BC + CC}
Corporis autem A velocitas ex ipſius vi ante determinata detegitur eſtque
velocitas hæc {f√AB + 2AC\x{0020}/A}.
velocitas hæc {f√AB + 2AC\x{0020}/A}.
Velocitates hæ ex velocitate v ſunt ſubtrahendæ, aut ipſi ſunt addendæ,
44647. pro ut cum motu navis conſpirant aut contrariæ agunt.
44647. pro ut cum motu navis conſpirant aut contrariæ agunt.
Si in primo motu A celerius B feratur, id eſt m ſuperet n, velocitas cor-
poris A poſt ictum erit {v-f√AB + 2AC\x{0020}/A}; reliquæ velocitates detectæ
corporum B & C ipſi v addendæ ſunt.
poris A poſt ictum erit {v-f√AB + 2AC\x{0020}/A}; reliquæ velocitates detectæ
corporum B & C ipſi v addendæ ſunt.
In ſcholio 2.
Capitis ſequentis demonſtrabimus ſummam virium poſt ictum
55648. æqualem eſſe A mm + B nn + C pp; quod cum ante demonſtratis congruit .
66558.55648. æqualem eſſe A mm + B nn + C pp; quod cum ante demonſtratis congruit .
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