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 X

It can also be seen by this method that [a segment of a hyperboloid] bears the same ratio to a cone having the same base and axis as the segment, that the axis of the segment + 3 times the addition to the axis bears to the axis of the segment of the hyperboloid + twice its addition [De Conoid. 25]; and that the center of gravity of the hyperboloid so divides the axis that the part at the vertex bears the same ratio to the rest that three times the axis + eight times the addition to the axis bears to the axis of the hyperboloid + 4 times the addition to the axis, and many other points which I will leave aside since the method has been made clear by the examples already given and only the demonstrations of the above given theorems remain to be stated.