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Updated: May 25, 2025


Euclid, in his elements, considers only the relations of some of these magnitudes to each other, but does not compare them with surfaces and solids bounded by straight lines. Archimedes developed the proportions necessary for effecting this comparison, in his treatises on the sphere and cylinder, the spheroid and conoid, and in his work on the measure of the circle.

But now suppose that instead of such a spheroid, we assume one of, say, twenty or thirty times the mass; what will then happen? Notwithstanding convection-currents, the temperature at the centre must always be higher than elsewhere; and in the process of cooling the "critical point" of temperature will sooner be reached in the outer parts.

"Line up!" came the call, and with the last of the preliminaries the practice balls were called in, and the new, yellow one placed on a little mound of earth in the center of the field. There was that ever-inspiring thrill as the spheroid was booted high into the air. Tom had the luck to grab it and then, with fairly good interference, he dashed down the field. "Stick to him, boys!

If then through the point K one now draws KS parallel to Gg, which will be parallel also to QX, the tangent to the Ellipse QGq at Q; and if one conceives a plane passing through KS and touching the spheroid, the point of contact will necessarily be in the Ellipse QMq, because this plane through KS, as well as the plane which touches the spheroid at the point M, are parallel to QX, the tangent of the spheroid: for this consequence will be demonstrated at the end of this Treatise.

Chauncey Wright, which have been advanced in favour of this view, such as the sudden crystallisation of inorganic substances, or the falling of a facetted spheroid from one facet to another, hardly deserve consideration.

Andrews' results, consider what would probably be the successive changes in a condensing nebulous spheroid. Prof. Andrews has shown that for each kind of gaseous matter there is a temperature above which no amount of pressure can cause liquefaction.

We would thus have a spheroid of water, with granite rocks and islands scattered here and there. But this would not be the world which we inhabit; therefore, the question now is, how such continents, as we actually have upon the globe, could be erected above the level of the sea.

Indignantly he had taken his calculations, his blue prints of the spheroid, along with him. If the flight was a success, well and good; if not, they would not be worth much anyway. In spite of his fever to be off, he carefully locked the controls, sealed the outer air-lock. Hilary Grendon was a methodical man: that was the reason he had survived. Then he struck across country, walking very fast.

On the gunwale of your boat divest it of its slender black spines, and with a knife fairly divide the spheroid body, and a somewhat nauseous-looking meat is disclosed; but no more objectionable in appearance than the substance of a fully ripe passion fruit. The flavour! Ah, the flavour! It surpasseth the delectable oyster. It hath more of the savour and piquancy of the ocean.

At the flat end of the spheroid was a small ring of a pink colour, from which ran lines forming the ribs, which supported the sides of the animal. There were eight of these: they possessed great irritability, and if the animal was at all injured, a rapid and continued motion was propagated all along them.

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