''Mathematical Magick'' (complete title: ''Mathematical Magick, or, The wonders that may by performed by mechanical geometry''.) is a

treatise A treatise is a Formality, formal and systematic written discourse on some subject concerned with investigating or exposing the main principles of the subject and its conclusions."mwod:treatise, Treatise." Merriam-Webster Online Dictionary. Acc ...

by the English clergyman,

natural philosopher Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics, that is, nature and the physical universe, while ignoring any supernatural influence. It was dominant before the developme ...

polymath A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, ...

and author

John Wilkins John Wilkins (14 February 1614 – 19 November 1672) was an English Anglican ministry, Anglican clergyman, Natural philosophy, natural philosopher, and author, and was one of the founders of the Royal Society. He was Bishop of Chester from 1 ...

(1614 – 1672). It was first published in 1648 in London, another edition was printed in 1680 and further editions were published in 1691 and 1707.

Abstract

Wilkins dedicated his work to ''His Highness the Prince Elector Palatine'' ( Charles I Louis) who was in London at the time. It is divided into two books, one headed ''Archimedes'', ''because he was the chiefest in discovering of Mechanical powers'', the other was called ''Daedalus'' because he ''was one of the first and most famous amongst the Ancients for his skill in making Automata.'' Wilkins sets out and explains the principles of mechanics in the first book and gives an outlook in the second book on future technical developments like flying which he anticipates as certain if only sufficient exercise, research and development would be directed to these topics. The treatise is an example of his general intention to disseminate scientific knowledge and method and of his attempts to persuade his readers to pursue further scientific studies.

First book

In the 20 chapters of the first book, traditional mechanical devices are discussed such as the

balance Balance may refer to: Common meanings * Balance (ability) in biomechanics * Balance (accounting) * Balance or weighing scale * Balance, as in equality (mathematics) or equilibrium Arts and entertainment Film * Balance (1983 film), ''Balance'' ( ...

, the

lever A lever is a simple machine consisting of a beam (structure), beam or rigid rod pivoted at a fixed hinge, or '':wikt:fulcrum, fulcrum''. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, l ...

, the

wheel A wheel is a rotating component (typically circular in shape) that is intended to turn on an axle Bearing (mechanical), bearing. The wheel is one of the key components of the wheel and axle which is one of the Simple machine, six simple machin ...

pulley Sheave without a rope A pulley is a wheel on an axle or shaft enabling a taut cable or belt passing over the wheel to move and change direction, or transfer power between itself and a shaft. A pulley may have a groove or grooves between flan ...

and the

block and tackle A block and tackle or only tackle is a system of two or more pulleys with a rope or cable threaded between them, used to provide tension and lift heavy loads. The pulleys are assembled to form blocks and then blocks are paired so that one is ...

, the

wedge A wedge is a triangle, triangular shaped tool, a portable inclined plane, and one of the six simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by conver ...

, and the

screw A screw is an externally helical threaded fastener capable of being tightened or released by a twisting force (torque) to the screw head, head. The most common uses of screws are to hold objects together and there are many forms for a variety ...

. The powers acting on them are compared to those acting in the human body. The book deals with the phrase attributed to

Archimedes Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...

saying ''that if he did but know where to stand and fasten his instrument, he could move the world'' and shows the effect of a series of gear transmissions one linked to the other. It shows the importance of various speeds and the theoretical possibility to increase speed beyond the speed of the earth at the

equator The equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...

. Finally,

siege engines A siege engine is a device that is designed to break or circumvent heavy castle doors, thick city walls and other fortifications in siege warfare. Some are immobile, constructed in place to attack enemy fortifications from a distance, while othe ...

catapult A catapult is a ballistics, ballistic device used to launch a projectile at a great distance without the aid of gunpowder or other propellants – particularly various types of ancient and medieval siege engines. A catapult uses the sudden rel ...

s are compared with the cost and effect of then-modern guns.

Second book

Various devices

In the 15 chapters of the second book, various devices are examined which move independently of human interference like clocks and watches, water mills and wind mills. Wilkins explains devices being driven by the motion of air in a chimney or by pressurized air. A land yacht is proposed driven by two sails on two masts, and a wagon powered by a vertical axis wind turbine. A number of independently moving small artificial figures representing men and animals are described. The possibilities are considered to improve the type of

submarine A submarine (often shortened to sub) is a watercraft capable of independent operation underwater. (It differs from a submersible, which has more limited underwater capability.) The term "submarine" is also sometimes used historically or infor ...

designed and built by

Cornelis Drebbel Cornelis Jacobszoon Drebbel (; 1572 – 7 November 1633) was a Dutch engineer and inventor. He was the builder of the first operational submarine in 1620 and an innovator who contributed to the development of measurement and control systems, opti ...

. The tales about various flying devices are related and doubts as to their truth are dissipated. Wilkins explains that it should be possible for a man, too, to fly by himself if a frame were built where the person could sit and if this frame was sufficiently pushed in the air.

Art of flying

In chapter VII, Wilkins discusses various methods how a man could fly, namely by the help of spirits and good or evil angels (as related on various occasions in the Bible), by the help of fowls, by wings fastened immediately to the body or by a flying chariot. The whole of this chapter (and of the following one) concern the possibilities of flying. In a single preliminary phrase, he refers to previous reports of flight attempts: He writes that sufficient practise should enable a man to fly, most probably by "a flying chariot, which may be so contrived as to carry a man within it"''Mathematical Magick'', p. 209 and equipped with a sort of engine, or else big enough to carry several people, each successively working to fly it. He used the next chapter to dissipate any doubts there may be as to the possibility of such a flying chariot, should a number of particular items be developed and tested.

Perpetual motion and perpetual lamps

In Chapters IX to XV, extensive discussions and deliberations are set out why a

perpetual motion Perpetual motion is the motion of bodies that continues forever in an unperturbed system. A perpetual motion machine is a hypothetical machine that can do work indefinitely without an external energy source. This kind of machine is impossible ...

should be feasible, why the stories about lamps burning for hundreds of years were true and how such lamps could be made and perpetual motions created.

External links

Copy of the 1691 original
on

Internet Archive The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ...

References

{{reflist 1648 books Applied mathematics Mechanical engineering