Valerio, Luca - De centro gravitatis solidorum

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1ad T, ita fiat T ad ZY, cuius Zω, tribus GE, EH, V
ſimul ſit æqualis. Dico ABCD portio
nem ad cylindrum SO eſse vt ωΥ ad ΥZ.
Abſciſsa enim GK ipſi EG æquali, cylin
drus PN circa axim GH, & conus KEN
conſtituantur vt in præcedenti. planum igi
tur abſcindens portionem facit fruſtum coni
KEN, quod ſit KLMN, cuius minor ba
ſis circulus, cui diameter LM; maior autem
cui diameter KN. Et vt eſt GE ad EF, hoc
eſt GK ad SH, ita ſit EF, vel SH, ad I.
vt igitur in præcedenti, oſtenderemus cylin
drum SO ad cylindrum PN eſse vt I ad
GK ſiue ad EG. Quoniam igitur ſunt ter
næ deinceps proportionales GE, EF, I, &
X, T, ZY, eſtque vt FE ad EG ita T ad X;
erit vt I ad EG, hoc eſt vt cylindrus SO ad
PN cylindrum ita ZY ad X. Et quoniam eſt vt
GE ad EH, ita EH ad V: hoc eſt, vt GK ad
LH. ita LH ad V: & ponitur X tripla ipſius

83[Figure 83]
EG, hoc eſt ipſius GK, vt autem eſt triplaipſius GK ad
tres deinceps proportionales GK, LH, V, ita eſt cylin
drus PN ad fruſtum LKNM; erit vt X ad tres GE, EH,
V ſimul hoc eſt ad lineam ωZ, ita cylindrus PN ad fru-

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