[78] The official minute is: Et ei dicto quod dicat veritatem, alias devenietur ad torturam.
[79] The three days June 21-24 the only ones which Galilei could have spent in an actual prison, and there seems no reason to suppose that they were spent elsewhere than in the comfortable rooms in which it is known that he lived during most of April.
[80] Equivalent to portions of the subject now called dynamics or (more correctly) kinematics and kinetics.
[81] He estimates that a body falls in a second a distance of 4 “bracchia,” equivalent to about 8 feet, the true distance being slightly over 16.
[82] Two New Sciences, translated by Weston, p. 255.
[83] The astronomer appears to have used both spellings of his name almost indifferently. For example, the title-page of his most important book, the Commentaries on the Motions of Mars ([§ 141]), has the form Kepler, while the dedication of the same book is signed Keppler.
[84] The regular solids being taken in the order: cube, tetrahedron, dodecahedron, icosahedron, octohedron, and of such magnitude that a sphere can be circumscribed to each and at the same time inscribed in the preceding solid of the series, then the radii of the six spheres so obtained were shewn by Kepler to be approximately proportional to the distances from the sun of the six planets Saturn, Jupiter, Mars, Earth, Venus, and Mercury.
[85] Two stars 4′ apart only just appear distinct to the naked eye of a person with average keenness of sight.
[86] Commentaries on the Motions of Mars, Part II., end of chapter XIX.
[87] An ellipse is one of several curves, known as conic sections, which can be formed by taking a section of a cone, and may also be defined as a curve the sum of the distances of any point on which from two fixed points inside it, known as the foci, is always the same.