The New Thoughts of Galileo

Natural and forced, or violent, movements, in order to contemplate their properties and effects. And if these five Books do not contain all his discourses word for word, they give at the very least their entire substance, if one excepts the addition he makes regarding centers of gravity; but I shall put here several particular remarks to compensate for the treatise he makes on it, which have been made by an excellent Geometer: and then I shall finish this Preface with the contemplation of numbers, of which the aliquot parts are multiples, in order to supply what is missing in the 13th Observation placed at the end of the Harmonie universelle Universal Harmony.

Now, many have found the center of gravity of some bodies, for example, that of the conoid; which, having a circle as its base, is described by a parabola that rotates around its axis, which is divided by said center into three equal parts, such that the distance from this center to the summit of this conoid is double that which is from this same center to the base. Galileo gives a small Treatise on centers