Chapter VII: ARITHMETIC. Having built your house, young people, and

understanding the light of heaven, and the measures of earth, you may marry--and can't do better. And here is now your conclusive science, which you will have to apply, all your days, to all your affairs.

The Science of Number. Infinite in solemnity of use in Italy at this time; including, of course, whatever was known of the higher abstract mathematics and mysteries of numbers, but reverenced especially in its vital necessity to the prosperity of families and kingdoms, and first fully so understood here in commercial Florence.

Her hand lifted, with two fingers bent, two straight, solemnly enforcing on your attention her primal law--Two and two are--four, you observe,--not five, as those accursed usurers think.

Under her, Pythagoras.

Above, medallion of king, with sceptre and globe, counting money. Have you ever chanced to read carefully Carlyle's account of the foundation of the existing Prussian empire, in economy?

You can, at all events, consider with yourself a little, what empire this queen of the terrestrial sciences must hold over the rest, if they are to be put to good use; or what depth and breadth of application there is in the brief parables of the counted cost of Power, and number of Armies.

To give a very minor, but characteristic, instance. I have always felt that with my intense love of the Alps, I ought to have been able to make a drawing of Chamouni, or the vale of Cluse, which should give people more pleasure than a photograph; but I always wanted to do it as I saw it, and engrave pine for pine, and crag for crag, like Albert Dürer. I broke my strength down for many a year, always tiring of my work, or finding the leaves drop off, or the snow come on, before I had well begun what I meant to do. If I had only _counted_ my pines first, and calculated the number of hours necessary to do them in the manner of Dürer, I should have saved the available drawing time of some five years, spent in vain effort.

But Turner counted his pines, and did all that could be done for them, and rested content with that.

So in all the affairs of life, the arithmetical part of the business is the dominant one. How many and how much have we? How many and how much do we want? How constantly does noble Arithmetic of the finite lose itself in base Avarice of the Infinite, and in blind imagination of it! In counting of minutes, is our arithmetic ever solicitous enough? In counting our days, is she ever severe enough? How we shrink from putting, in their decades, the diminished store of them! And if we ever pray the solemn prayer that we may be taught to number them, do we even try to do it after praying?

_Technical Points_.--The Pythagoras almost entirely genuine. The upper figures, from this inclusive to the outer wall, I have not been able to examine thoroughly, my scaffolding not extending beyond the Geometry.

Here then we have the sum of sciences,--seven, according to the Florentine mind--necessary to the secular education of man and woman. Of these the modern average respectable English gentleman and gentlewoman know usually only a little of the last, and entirely hate the prudent applications of that: being unacquainted, except as they chance here and there to pick up a broken piece of information, with either grammar, rhetoric, music, [Footnote: Being able to play the piano and admire Mendelssohn is not knowing music.] astronomy, or geometry; and are not only unacquainted with logic, or the use of reason, themselves, but instinctively antagonistic to its use by anybody else.

We are now to read the series of the Divine sciences, beginning at the opposite side, next the window.