Hutton, Charles A Mathematical and Philosphical Dictionary

 ACUTE
ACUTE

, or sharp; a term opposed to obtuse. Thus, Acute Angle, in Geometry, is that which is less than a right angle; and is measured by less than 90°, or by less than a quadrant of a circle. As the angle ABC.

Acute angled Triangle, is that whose three angles are all acute; and is otherwise called an oxygenous triangle. As the triangle DEF.

Acute-angled Cone, is that whose opposite sides make an acute angle at the vertex, or whose axis, in a right cone, makes less than half a right angle with the side As the cone GHI.

Pappus, in his Mathematical Collections, says, this name was given to such a cone by Euclid and the ancients, before the time of Apollonius. And they called an

Acute-angled Section of a Cone, an Ellipsis, which was made by a plane cutting both sides of an acuteangled cone: not knowing that such a section could be generated from any cone whatever, till it was shewn by Apollonius.

Acute, in Music

, is understood of a tone, or sound, which is high, sharp, or shrill, in respect of some other: in which sense the word stands opposed to grave. And both these sounds are independent of loudness or force: so that the tone may be acute or high, without being loud; and loud without being high or acute. For both the affections of acute and grave, depend intirely on the quickness or slowness of the vibrations by which they are produced.

Sounds considered as grave and acute, that is, in the relation of gravity and acuteness, constitute what is called tune, the soundation of all harmony.