Isaac Newton

Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of …

The Simplicity of Figures depend upon the Simplicity of their Genesis and Ideas, and an Æquation is nothing else than a Description (either Geometrical or Mechanical) by which a Figure is generated and rendered more easy to the Conception.

the reasoning from the Simplicity of the Æquation will not hold. The modern Geometers are too fond of the Speculation of Æquations.

In my Judgment no Lines ought to be admitted into plain Geometry besides the right Line and the Circle.

Useful Things, though Mechanical, are justly preferable to useless Speculations in Geometry, as we learn from Pappus.

Geometrical Speculations have just as much Elegancy as Simplicity, and deserve just so much praise as they can promise Use.

Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation.

In Constructions that are equally Geometrical, the most simple are always to be preferr'd. This Law is so universal as to be without Exception. But Algebraick Expressions add nothing to the Simplicity of the Construction

The Circle is a Geometrical Line, not because it may be express'd by an Æquation, but because its Description is a Postulate. It is not the Simplicity of the Æquation, but the Easiness of the Description, which is to determine the Choice …

But it is not the Æquation, but the Description that makes the Curve to be a Geometrical one.

But the Moderns advancing yet much farther, have receiv'd into Geometry all Lines that can be express'd by Æquations, and have distinguish'd, according to the Dimensions of the Æquations, those Lines into Kinds; and have made it a Law, …

distinguish'd Problems into three Kinds

After the same Manner in Geometry, if a Line drawn any certain Way be reckon'd for Affirmative, then a Line drawn the contrary Way may be taken for Negative: As if AB be drawn to the right, and BC to the left; and AB be reckon'd …

Whereas in Arithmetick Questions are only resolv'd by proceeding from given Quantities to the Quantities sought, Algebra proceeds in a retrograde Order, from the Quantities sought as if they were given, to the Quantities given as if they …

A good watch may serve to keep a recconing at Sea for some days and to know the time of a Celestial Observ[at]ion: and for this end a good Jewel watch may suffice till a better sort of Watch can be found out. But when the Longitude at sea …

One [method] is by a Watch to keep time exactly. But, by reason of the motion of the Ship, the Variation of Heat and Cold, Wet and Dry, and the Difference of Gravity in different Latitudes, such a watch hath not yet been made.

much after the manner, that in the sense of hearing, nature makes use of aereal vibrations of several bignesses to generate sounds of divers tones; for the analogy of nature is to be observed.

as bodies excite sounds of various tones and consequently vibrations, in the air of various bignesses, so when rays of light by impinging on the stiff refracting superficies excite vibrations in the ether, these rays excite vibrations of …

And now to explain colours.

go through and are refracted.

at other times, when it is

too dense and stiff to let the ray through, and so reflects it; but

continually expanded and compressed by turns, if a ray of light impinge on it when it is much compressed

always kept in a vibrating motion