Concavity

Definition and stakes

Portrait of Albrecht Dürer Albrecht Dürer,  Of the Just Shaping of Letters

“ Afterwards you shall add the extension, which you shall make this way: take before f. in the line e. f., a point g. no farther distant from f. than the breadth of the narrower limb; on this point set one leg of your compass, & let the other be extended to the angle d., from which let it be guided back along the broad but invisible blind limb: thence will result the lower convexity of the tail you seek; but its upper concavity look for in this way: divide f. d. in its middle point h.; on this set one leg of your compass, and with the other describe an arc passing through d. ”
Source: Gutenberg

A. M. Worthington,  A Study of Splashes

“ If the surface is flat, like the surface of still liquid in a bowl, this surface-tension has only the effect of exerting a small inward pull on the walls of the bowl. But if the surface is curved, with a convexity outwards, then the surface layers, on account of their tension, press the interior liquid back, and thus tend to check the growth of any protuberance; while, on the other [pg 33] hand, if the surface is concave outwards, then the surface-tension tends to pull the interior liquid forward, and so to diminish the concavity. ”
Source: Gutenberg

Alexander Campbell Fraser,  Thomas Reid — Chapter V (1898)

“ Has reason got anything to show in justification of this preliminary sacrifice of a conviction on which men have to act, whatever their theories may be? Must I surrender the conviction, that when I am seeing or touching I am actually having revealed to me something that is extended and solid, and that, as such, must be more and other than the private sensations and ideas of the person that is seeing and touching? Must this conviction, and others like it, on which human experience practically depends, be all sacrificed on the altar of authority and conjecture? ”
Source: Wikisource

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