Geometrical teaching conducts the mind to the same order of contemplations; leading it away from variable particulars to unchangeable universal Essence. Some persons extol Geometry chiefly on the ground of its usefulness in applications to practice. But this is a mistake: its real value is in conducing to knowledge, and to elevated contemplations of the mind. It does, however, like Arithmetic, yield useful results in practice: and both of them are farther valuable as auxiliaries to other studies.[231] [Footnote 231: Plato, Republic, vii. pp. 526-527.] [Side-note: Astronomy--how useful--not useful as now taught--must be studied by ideal figures, not by observation.] After Geometry--the measurement of lines and superficial areas--the proper immediate sequel is Stereometry, the measurement of solids. But this latter is nowhere properly honoured and cultivated: though from its intrinsic excellence, it forces its way partially even against public neglect and discouragement.[232] Most persons omit it, and treat Astronomy as if it were the immediate sequel to Geometry: which is a mistake, for Astronomy relates to solid bodies in a state of rotatory movement, and ought to be preceded by the treatment of solid bodies generally.[233] Assuming Stereometry, therefore, as if it existed, we proceed to Astronomy. [Footnote 232: Plato, Republic, vii. p. 528 A-C.] [Footnote 233: Plato, Republic, vii. p. 528 A-B. [Greek: e)n periphora=| o)\n ê)/dê stereo\n labo/ntes, pri\n au)to\ kath' au(to\ labei=n.] Also 528 E.]