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

Seite: 96
DOI Seite: 10.11588/diglit.29349#0104
Zitierlink: i
http://digi.ub.uni-heidelberg.de/diglit/agricola1773/0104
Lizenz: Creative Commons - Namensnennung - Weitergabe unter gleichen Bedingungen
0.5
1 cm
facsimile
$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\js 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-
loading ...