Agricola, Joseph; Molitor, Ludwig: Theoria Motus In Conflictu Corporum Physice Et Algebraice Exposita ([Heidelberg], 1773) [VD18 14363399]

$6

Celeritas massae M.
^MC^mC : M + m. §. $.theor. j. cap.z.p.z.
Ejusdem celeritatis quadratum
= MC — mC.MC— mC : (M + m) z
=M2C2~ MmC2 —MmC2 + m2C2 : (M+m)2
=M2C2 — 2MmC2 + m2C2 : M2 + Mm+Mm+m2
~M2C2 _2MmC2 + m2C2 : M2 +zMm+m2

Fa&um cx massa in quadratum celeritatis
M2C2-2MmC2 + m2C2
— i, mvmm, ( j\j[ 1
^ M2 + 2 M m + m2
^ M3 C2 + 2M 2mC 2 + Mm 2C 2 : M2 + 2Mm + m2
.
Celeritas massae m.
=! 2MC : M + m
Celeritas ejus quadrata

— 2MC . 2MC : M+m . M + m
=3 4M^Ca : M2 + zMm + ma
Jadtum ex masTa in quadratum celeritatis
_ 4MaCa
' !•*»****'**„ *» 1-1 ' ~JU*r~ s'j J
M*+2Mm+m*'
=J4MamC2 : M2 +2Mm + ma

Summa fadtorum
M3C2 —1 2M2mCa +Mm2C2+ 4MamCa
t- _ _| i,, m m |---- —
M2 + 2Mm + m2
- M3C2 + 2MamC2 + Mm2 _ m2> ^
M2 + 2Mm + m^
Id ipsum eodem modo reperics in aliis casibus.
Scholion I. Theorema hoc a cl. H u G E N i o
inventum ess+ cujus similem nostrae demonstratio-
nem vide inP. B o s c o v i c h thcor.p. II. n. 27$.
SCHO-