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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
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De
15 Feb. 1643
Comentis subfinem de quadramus speciatibusnma
Lalu
AB x BC 9. Momentum figurae ex altitudine
sit Trilineum ABC. id posit quaeritur
ejus momentum ex axe ABCCi es librationis AB. circa
quem quiescentem figura librari potest.
Momentum
Filinei componitur ex omnibus momentis omnium rectansuloum
componentium ut 1B2BDIC. Ha sit AB X. BC y.
et 1B. d differentia duarum X indifinite differentium dicatur
dx. et Drc dicatur dys. rectangulum componens rempe
1B2BD. C  erit ydx. Ejus centrigravitatis E distantim
ab axe AB est =y. haec ducra in rectangulum dat
rectanguli momentum, est ergo 1yy ax momentum rectanguli
 lorum summa :(yyax est momentum totius Trilnci
C ex axe A) Et vicitria eodem modo : xxdys est momentum
trliner AFC ex AF
At momentum hilinei ABC ex AF seu ex vertice
est factum siomma ex factis triangulorum ut 1B2BD.C in distantias
ab vr AB. erit ergo momentuntr
o trilinei ABC ex AF.
PX yd
momentum
Jam Momentum ips silinei ABC ex AF una cum momento
trilinei AFC ex AF facit momentum rectanguli.  ABCF exAF
Et hoc momentum est XXy ergo erit: Lxxy aequ  Sxxdy + sxydx
quae aequatio ex calculo differentiali statim demonstratur
e
ut per proinde non fuerit opus aecursu ad figuram: necurpe
d = XXy _ est LXXdy +1y. 2X du seu Lxxdy + yxdx
Momentum Trilinei ABC ex BC est cylinder AB ex ABC in X
demto momento ipsius ABC ex AF. Ergo Momentum Trilinei
ABC ex BC est X sydx = sxydx. Sed xsydx. Txyax est
idem quod
Sylxdx. Nam calculo differentiali instituto
fiet d x sydx = (xy x aeqo (X ydx) + sydx ax (=  xydx)
Ergo
sydx de est nomentum trilinei ABC ex BC
ubi si
aciaus dx esse constantem seu unitatem, fiet Momentum Trlinei
Bc ex basi BC erit summa summarum, ex ordinatis, seu sy
ita calculo invenimus, quod vix alii mulla meditatione ex ebulem
platione figurarum. In schemale serici adjectae, patlet summ
summarum esse momentum ordinatarum ex basi, continet enim ordinatas per distantias
mndiltiplicatas nemipe sugunqus sumontarum olienium a b. cide continet e sml,
et dbis, et eter et bquater, etc.
5
a bas