Geometrical Solutions Derived from Mechanics

 Table of Contents

 Introduction

 Geometrical Solutions Derived from Mechanics.

 Proposition I

 Proposition II

 Proposition III

 Proposition IV

 Proposition V

 Proposition VI

 Proposition VII

 Proposition VIIa

 Proposition VIII

 Proposition IX

 Proposition X

 Proposition XI

 Proposition XII

 Proposition XIII

 Proposition XIV

Proposition IX

In a similar way it can also be perceived that the center of gravity of any segment of an ellipsoid lies on the straight line which is the axis of the segment so divided that the portion at the vertex of the segment bears the same ratio to the remaining portion as the axis of the segment + 4 times the axis of the opposite segment bears to the axis of the segment + twice the axis of the opposite segment.