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Page:Carroll - Notes by an Oxford Chiel.djvu/134

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three Means treated of in Mathematics. For there is the Arithmetic Mean, the Geometric, and the Harmonic. And note further, that a Mean is that which falleth between two magnitudes. Thus it is, that the entrance you here behold falleth between the magnitudes of the doorways and the gateways, and is in truth the Non-harmonic Mean, the Mean Absolute. But that the Mean, or Middle, is ever the safer course, we have a notable ensample in Egyptian history, in which land (as travellers tell us) the Ibis standeth ever in the midst of the river Nile, so best to avoid the onslaught of the ravenous alligators, which infest the banks on either side: from which habit of that wise bird is derived the ancient maxim 'Medio tutissimus Ibis.'

Ven. But wherefore be they two? Surely one arch were at once more comely and more convenient?

Tutor. Sir, so long as public approval be won, what matter for the arch? But that they are two, take this as sufficient explication——that they are too tall for doorways, too narrow for gateways; too light without, too dark within; too plain to be ornamental, and