One important definition is the fourth: " Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal.

He quickly eliminated the possibility that the fourth angle is obtuse, as had Saccheri and Khayyam, and then proceeded to prove many theorems under the assumption of an acute angle.

:"... the moment of the torque is, for wires of the same metal, proportional to the torsional angle, the fourth power of the diameter and the inverse of the length of the wire ..."

" Even if a guitar is built so that there are no " fret or neck angle errors, inharmonicity can make the simple approach of tuning open strings to notes stopped on the fifth or fourth frets " unreliable.

The dihedral angle varies only the distance between the first and fourth atoms ; the other interatomic distances are constrained by the chemical bond lengths and bond angles.

When the fourth atom eclipses the first atom, the dihedral angle is zero ; when the atoms are exactly opposite ( as in Figure 2 ), the dihedral angle is 180 °.

This problem may be overcome by use of a fourth gimbal, intelligently driven by a motor so as to maintain a large angle between roll and yaw gimbal axes.

It is situated at the medial and lower angle of the carpus, with its base downward, resting on the fourth and fifth metacarpal bones, and its apex directed upward and lateralward.

Innovations such as the Aliquot string, a fourth string that vibrated sympathetically and that is tuned in unison as well as the cylindrical soundboard and angle cut hammers, created a unique voice for the Blüthner instrument.

The processor locates the three distinctive squares at the corners of the image, and uses a smaller square near the fourth corner to normalize the image for size, orientation, and angle of viewing.

Above each tablet is a dial, exhibiting the hour to each of the three principal streets ; the fourth being excluded from this advantage by standing at an angle.

The fourth thoracic vertebra, together with the fifth, is at the same level as the sternal angle.

The fifth thoracic vertebra, together with the fourth, is at the same level as the sternal angle.

Here, the light falloff is proportional to the fourth power of the cosine of the angle at which the light impinges on the film or sensor array.

The two other openings of the fourth ventricle are lateral apertures ( foramina of Luschka ), one on the left and one on the right, which drain cerebrospinal fluid into the cerebellopontine angle cistern.

This flow angle is a solution to a Legendre polynomial of the second order which was presented in a scientific paper by Dr. Ahmed at the fourth National Congress of Applied Mechanics at Harvard University, Cambridge, Massachusetts, USA, in 1972.

Vampiro was involved in a what MTV claimed was a controversial angle which led to MTV canceling the fourth WSX show, due to air on Tuesday February 20.

The energy stored in the bending strain of the fluoride ion is proportional to the fourth power of the displacement angle, unlike most other materials where it is proportional to the square of the displacement.

A draw at home to Cardiff at the end of January would see Saints ' home form start to turn around while they continued to take points on the road, with welcomed draws against promotion pushing Birmingham and West Ham, a 3 – 0 win, and Lambert's third hat-trick of the campaign at Watford, and an emphatic 3 – 2 victory at The New Den, where Saints had trailed 2 – 1 to Millwall until 2 Lambert penalties in the last 5 minutes saw Lambert secure his fourth hat-trick and another key 3 points for what seemed like Southampton's inevitable promotion, as they were 2 points clear at the top of the table and 5 points clear of the 3rd spot.

A member of the fourth generation, William E. Doolittle studied with Billie Lee Turner II, earned the Ph. D. in 1979, became a professor in the Department of Geography and the Environment at University of Texas at Austin, and has extended the school into the fifth generation: Dean P. Lambert ( 1992 ), Andrew Sluyter ( 1995 ), Emily H. Young ( 1995 ), Eric P. Perramond ( 1999 ), Phil L. Crossley ( 1999 ), Jerry O.

The anterior surface, of smaller size, but also irregularly triangular, is divided by a vertical ridge into two facets, forming the fourth and fifth tarsometatarsal joints: the medial facet, quadrilateral in form, articulates with the fourth metatarsal ; the lateral, larger and more triangular, articulates with the fifth.

CG, FG and DG are joined forming cyclic quadrilateral DFCG in which three sides belong to the regular decagon ( length c ) and the fourth DG is of length z. Diagonals DC and FG are both of length a ( side of the pentagon ) Then:

A fourth view is the transformation of emotion, as in Housman's fine phrase on the arts: they `` transform and beautify our inner nature ''.

That is, we must find Saxons in East Anglia, Kent, Sussex and Hampshire in the last half of the fourth century.

Milton's name being fourth is neither too high nor too low to be assigned to the arbitrary action of vice-chancellor, proctor, master, or other mighty hand.

If you were required to file a declaration of estimated tax for the calendar year 1961, it is not necessary to pay the fourth installment otherwise due on January 15, 1962, if you file your income tax return Form 1040, and pay your tax in full for the calendar year 1961 by January 31, 1962.

This work is progressing on schedule and we expect to make initial shipments in the fourth quarter of this year.

There is a break in continuity just before the fourth variation in the `` Forellen '' movement, and I suspect that this is due to imperfect splicing between sides of the original Aj.

The radiation loss from the anode surface was computed according to Af where Af is the mean of the fourth powers of the temperatures Af and Af calculated analogously to equation ( 1 ).

To practice new procedures under guided supervision and with constant feedback is the fourth step.

In the third column is given the optimal policy for stage R, and in the fourth, the resulting state of the stream when this policy is used.

The type of presentation of results used in the deterministic process may be used here, except that now the fourth column is redundant.

A `` mental image '' subconsciously impressing us from beneath its language symbols in wakeful thought, or consciously in light sleep, is actually not an image at all but is comprised of realities, viewed not in the concurrent sensory stream, but within the depths of the fourth dimension.

If the fourth dimension is a physical concept and not purely metaphysical, through what medium does it extend??

The technique of reality confusion -- the use of paradox and riddles to shake the mind's grip on reality -- originated with fourth and third century B.C. Chinese Quietism: the koan is not basically a new device.

A weekly showcase for contemporary music, from the austere archaism of Stravinsky to the bleeps and bloops of electronic music, is celebrating its fourth anniversary this month.

There is one volume of Aristotle's concerning logic not found in the Organon, namely the fourth book of Metaphysics.

The first three of these prizes are awarded for eminence in physical science, in chemistry and in medical science or physiology ; the fourth is for literary work " in an ideal direction " and the fifth prize is to be given to the person or society that renders the greatest service to the cause of international fraternity, in the suppression or reduction of standing armies, or in the establishment or furtherance of peace congresses.

Although it is the third element in the transuranic series, it was discovered fourth, after the heavier curium.

April is the fourth month of the year in the Julian and Gregorian calendars, and one of four months with a length of 30 days.

* Earliest day on which National Heroes ' Day can fall, while August 28 is the latest ; celebrated on the fourth Monday in August.

The full version of the song from Melbourne Punch, the fourth verse of which is pasted onto the urn

This is the fourth verse of a song-lyric published in Melbourne Punch on 1 February 1883: