The true Mathematical and Mechanical Form of all manner of Arches for building with the true butment necessary to each of them, a Problem which no Ar… - Robert Hooke

Having now retrieved a little more of leasure, both for Delineation and Description, for a further elucidation of what I have said, I shall make it my third Attempt, to explain;
First, A Helioscope to look upon the body of the Sun, without any offence to the Observers eye.
Secondly, A way of shortening reflective and refractive Telescopes.
Thirdly, A way of using a Glass of any length, without moving the Tube.
Fourthly, An Instrument for taking the Diameters of the Sun, Moon and Planets, or for taking any other Distances, to five or ten Degrees, to the certainty of a Second. ...
Fifthly, An Instrument for describing all manner of Dials, by the tangent projection.
Sixthly, The uses thereof;
1. For adjusting the Hand of a Clock, so as to make it move in the shadow of a Dial, whose style is parallel to the Axis: Or,
2. In the Azimuth of any Celestial Body, that is, in the shadow of the upright, or any other way inclining Style, upon any plain.
3. For making a Hand move according to the true æquation of Time.
4. For making all manner of Elliptical Dials, in Mr. Foster's way, &c.
5. For communicating a circular motion in a Curve Line, without any shaking: And for divers other excellent purposes.

About this time, 1655, having an opportunity of acquainting myself with astronomy by the kindness of Dr. Ward, I apply'd myself to the improving of the pendulum for such observations, and in the year 1656, or 1657, I contriv'd a way to continue the motion of the pendulum, so much commended by Ricciolus in his Almagestum which Dr. Ward had recommended to me to peruse. I made some trials to this end, which I found to succeed to my wish. The success of these made me further think of improving it for finding the longitude; and the method I had made for myself for mechanick inventions, quickly led me to the use of springs, instead of gravity, for the making a body vibrate in any posture. Whereupon I did first in great, and afterwards in smaller modules, satisfy myself of the practicableness of such an invention; and hoping to have made great advantage thereby, I acquainted divers of my freinds, and particularly Mr. Boyle, that I was possessed of such an invention, and crav'd their assistance for improving the use of it to my advantage. Immediately after his majesty's restoration Mr. Boyle was pleased to acquaint the lord Brouncher and Sir with it, who advis'd me to get a patent for the invention, and propounded very probable ways of making considerable advantage by it. To induce them to a belief of my performance, I shewed a pocket watch, accommodated with a spring, apply'd to the arbor of the ballance, to regulate the motion thereof, concealing the way I had for finding the longitude. This was so well approv'd of, that Sir Robert Moray drew me up the form of a patent, the principal part whereof, viz. the description of the watch so regulated, is his own hand writing, which I have yet by me. The discouragement I met with in the management of this affair, made me desist for that time.

Some other Course therefore must be taken to promote the Search of Knowledge. Some other kind of Art for Inquiry than what hath been hitherto made use of, must be discovered; the Intellect is not to he suffer'd to act without its Helps, but is continually to be assisted by some Method or Engine, which shall be as a Guide to regulate its Actions, so as that it shall not be able to act amiss: Of this Engine, no Man except the incomparable Verulam hath had any Thoughts, and he indeed hath promoted it to a very good pitch; but there is yet somewhat more to be added, which he seem'd to want time to compleat. By this, as by that Art of Algebra in Geometry, 'twill be very easy to proceed in any Natural Inquiry, regularly and certainly: And indeed it may not improperly be call'd a Philosophical Algebra, or an Art of directing the Mind in the search after Philosophical Truths, for as 'tis very hard for the most acute Wit to find out any difficult Problem in Geometry. without the help of Algebra to direct and regulate the Acts of the Reason in the Process from the question to the quœsitum, and altogether as easy for the meanest Capacity acting by that Method to compleat and perfect it, so will it be in the inquiry after Natural Knowledge.