The theorem on the sum of the three angles of a triangle, presumably known to Thales, was proved by the Pythagoreans after the manner of Euclid. They demonstrated also that the plane about a point is completely filled by six equilateral triangles, four squares, or three regular hexagons, so that it is possible to divide up a plane into figures of either kind.
A child of eight is many-sided. By eighteen most of his auspicious angles have been polished away; he is(George) Norman Douglas
The Eudemian Summary ascribes to Thales the invention of the theorems on the equality of vertical angles, the equality of the angles at the base of an isosceles triangle, the bisection of a circle by any diameter, and the congruence of two triangles having a side and the two adjacent angles equal respectively. The last theorem he applied to the measurement of the distances of ships from the shore. Thus Thales was the first to apply theoretical geometry to practical uses.
All humanity inspires me. Every passer-by is my unconscious sitter; and as strange as it may seem, I really draw folk as I see them. Surely it is not my fault that they fall into certain lines and angles.aubrey beardsley
I think you need inspiration, motivation from different angles to keep you going, because it isn’t that simple just to wake up every morning and go for another travel around the world, another practice, all these other things; another fitness workout, another stretch. It’s always nice, but you need to have some success and you need to have the right reasons why you’re doing it. I think I’ve always been able to do that and I really enjoy myself out on the court.roger federer
Computer programming is like the ability or skill to see what Picasso saw from all the different angles at once. If it is an art, the crucial element of art is to look at things from an angle that produces new insight or at least has that potential.erik naggum
Time, so to say, runs at right angles to the page at each point on the curve.joan robinson
I well remember when this realization first came on me with full force. The EDSAC was on the top floor of the building and the tape-punching and editing equipment one floor below. [...] It was on one of my journeys between the EDSAC room and the punching equipment that "hesitating at the angles of stairs" the realization came over me with full force that a good part of the remainder of my life was going to be spent in finding errors in my own programs.maurice wilkes
Though we cannot SEE angles, we can INFER them, and this with great precision. Our sense of touch, stimulated by necessity, and developed by long training, enables us to distinguish angles far more accurately than your sense of sight, when unaided by a rule or measure of angles.edwin abbot
Assuming her most gracious manner, my Wife advanced towards the Stranger, "Permit me, Madam, to feel and be felt by " then, suddenly recoiling, "Oh! it is not a Woman, and there are no angles either, not a trace of one. Can it be that I have so misbehaved to a perfect Circle?" "I am indeed, in a certain sense a Circle," replied the Voice, "and a more perfect Circle than any in Flatland; but to speak more accurately, I am many Circles in one."edwin abbot
Wow, look at all the places you can park,” he said, as if for all these years he had been cruising endlessly, unable to terminate a journey. For about a year the most dangerous place to drive in Des Moines was the parking lot of Merle Hay Mall because of all the cars speeding at joyous random angles across its boundless blacktop without reflecting that other happy souls might be doing likewise.Bill Bryson
The towers themselves must be either round or polygonal. Square towers are sooner shattered by military engines, for the battering rams pound their angles to pieces but in the case of round towers they can do no harm being engaged as it were in driving wedges to their center.vitruvius
Space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to these planes, each at right angle to the others. But some philosophical people have been asking why three dimensions particularly why not another direction at right angles to the other three? and have even tried to construct a Four Dimensional geometry.
There are many modes of thinking about the world around us and our place in it. I like to consider all the angles from which we might gain perspective on our amazing universe and the nature of existence.john archibald wheeler
The consideration of lines, angles and figures is of the greatest utility since it is impossible for natural philosophy to be known without them... All causes of natural effects have to be given through lines, angles and figures, for otherwise it is impossible for the reason why ( propter quid ) to be known in them.
There has been much controversy among ancient and modern critics on the postulates and axioms. An immense preponderance of manuscripts and the testimony of Proclus place the 'axioms' about right angles and parallels (Axioms 11 and 12) among the postulates . This is indeed their proper place, for they are really assumptions , and not common notions or axioms.
( Ptolemy ) left in his Optics , the earliest surviving table of angles of refraction from air to water. ...This table, quoted and requoted until modern times, has been admired... A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order... As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience.
The towers themselves must be either round or polygonal. Square towers are sooner shattered by military engines, for the battering rams pound their angles to pieces but in the case of round towers they can do no harm being engaged as it were in driving wedges to their center.
Two signs of learned person are: acceptance of other people's criticism, and being knowledgeable about the angles and dimensions of rhetoric and debate.
Non Angli, sed angeli. Not angles, but angels. 372Pope Gregory I
Non Angli sed Angeli (Not angles but Angels).
Architecture is an art which is basically geometrical. The cube is the basis of architecture because the right angle is necessarythe steps of a staircase consist of vertical and horizontal planes and the corners of rooms are nearly always right angles.We need right angles. 542