Square Quotes (5 quotes)

Circles to square and cubes to double

Would give a man excessive trouble.

The longitude uncertain roams,

In spite of Whiston and his bombs.

Would give a man excessive trouble.

The longitude uncertain roams,

In spite of Whiston and his bombs.

He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side.

— Plato

In 1684 Dr Halley came to visit him at Cambridge, after they had been some time together, the Dr asked him what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it. Sr Isaac replied immediately that it would be an Ellipsis, the Doctor struck with joy & amazement asked him how he knew it, why saith he I have calculated it, whereupon Dr Halley asked him for his calculation without any farther delay. Sr Isaac looked among his papers but could not find it, but he promised him to renew it, & then to send it him.

*[Recollecting Newton's account of the meeting after which Halley prompted Newton to write*The Principia*. When asking Newton this question, Halley was aware, without revealing it to Newton that Robert Hooke had made this hypothesis of plantary motion a decade earlier.]*
The Hypotenuse has a square on,

which is equal Pythagoras instructed,

to the sum of the squares on the other two sides

If a triangle is cleverly constructed.

which is equal Pythagoras instructed,

to the sum of the squares on the other two sides

If a triangle is cleverly constructed.

The mathematics of cooperation of men and tools is interesting. Separated men trying their individual experiments contribute in proportion to their numbers and their work may be called mathematically additive. The effect of a single piece of apparatus given to one man is also additive only, but when a group of men are cooperating, as distinct from merely operating, their work raises with some higher power of the number than the first power. It approaches the square for two men and the cube for three. Two men cooperating with two different pieces of apparatus, say a special furnace and a pyrometer or a hydraulic press and new chemical substances, are more powerful than their arithmetical sum. These facts doubtless assist as assets of a research laboratory.