611594INTRODUCTIO AD COHÆRENTIAM
xx - ax = 0 hinc additis utrimque, ut radix extrahi
- {12px/cr} poſſit, {1/4} aa + {6ap/cr} + {36pp/ccrr}.
fit xx - ax + {1/4} aa = {1/4} aa. Radice ex his extracta.
- {12px/cr} + {6ap/cr} + {6ap/cr}
+ {36pp/ccrr} + {36pp/ccrr}
fit x = {1/2}a + {6p/cr} + {aa/4} + {6ap/cr} + {36pp/ccrr}.
- {12px/cr} poſſit, {1/4} aa + {6ap/cr} + {36pp/ccrr}.
fit xx - ax + {1/4} aa = {1/4} aa. Radice ex his extracta.
- {12px/cr} + {6ap/cr} + {6ap/cr}
+ {36pp/ccrr} + {36pp/ccrr}
fit x = {1/2}a + {6p/cr} + {aa/4} + {6ap/cr} + {36pp/ccrr}.
PROPOSITIO LXIX.
Tab.
XXVI.
fig.
I.
In Parabolâ Cubica A B C, &
cjus ſeg-
mento D B E, momenta ex gravitate propria oriunda ſunt inter
ſe, uti radii A F, D G, elevati ad octavam potentiam.
mento D B E, momenta ex gravitate propria oriunda ſunt inter
ſe, uti radii A F, D G, elevati ad octavam potentiam.
Vocetur radius C F, r.
circumferentia circuli baſeos, c.
longi-
tudo B F, a. radius ſegmenti E G, d. erit hujus baſeos circumferen-
tia = {dc/r}. & longitudo B G = {ad3/r3}. Soliditas autem Parabolæ Cu-
bicæ eſt = {3/10} acr, diſtatque ejus centrum gravitatis a puncto F, {3/8}a.
unde momentum hujus erit = {9/86} aacr. Eſt ſoliditas ſegmenti
D B E = {3acd5/10r4}. ejuſque momentum {9a acd8/80r7}. ſed eſt {9/80} aacr, ad
{9aacd8/80r7}: : r8, ad d8. quare momenta integræ Parabolæ Cubicæ
& ſegmenti ſunt inter ſe, uti radii baſium elevati ad octavam po-
tentiam.
tudo B F, a. radius ſegmenti E G, d. erit hujus baſeos circumferen-
tia = {dc/r}. & longitudo B G = {ad3/r3}. Soliditas autem Parabolæ Cu-
bicæ eſt = {3/10} acr, diſtatque ejus centrum gravitatis a puncto F, {3/8}a.
unde momentum hujus erit = {9/86} aacr. Eſt ſoliditas ſegmenti
D B E = {3acd5/10r4}. ejuſque momentum {9a acd8/80r7}. ſed eſt {9/80} aacr, ad
{9aacd8/80r7}: : r8, ad d8. quare momenta integræ Parabolæ Cubicæ
& ſegmenti ſunt inter ſe, uti radii baſium elevati ad octavam po-
tentiam.
PROPOSITIO LXX.
Tab.
XXVI.
fig.
I.
Si conſideretur Parabola Cubica A B C, abs-
que graritate, at que e vertice B pendeat pondus P, id babebit ad
Cobærentiam baſeos eandem proportionem, quamcunque longitudi.
nem babuerit Parabola.
que graritate, at que e vertice B pendeat pondus P, id babebit ad
Cobærentiam baſeos eandem proportionem, quamcunque longitudi.
nem babuerit Parabola.
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