Occultus Thelema: iunie 2013

HERON din Alexandria (10 - 70 AD ) - matematician si inventator grec,care si-a desfasurat intreaga activitate stiintifica in Alexandria. A dat,in operele sale "Pneumatica"si Mecanica o sistematizare a cunostintelor antice in domeniul mecanicii aplicate. I se atribuie inventia unor aparate mecanice,cum ar fi fantana lui Heron, aparat mic in care se obtine un jet de apa cu ajutorul unei compresiuni a apei si aerului si eolipilul ,instrument format dintr-o sfera metalica goala in care erau introduse doua tuburi curbate si care primea o miscare de rotatie in jurul axei cu ajutorul vaporilor de apa incalziti, care produceau o forta de reactie.
Formula lui Heron : formula care permite calculul arieri S a unui triunghi in functie de lature a,b si c

Heron’s Books

· Automata (in Arabic Translation) (Greek: moving itself) (lat. De automatis). A collection of constructions called miracles (thaumata) for temples. Heron describes automatic rotating objectives, noise such as thunder, automatic opening doors. Philon from Byzanz describes the existence of automata in his book Mechaniki syntaxis, that includes pneumatic apparatus and automatic astronomical devices as early as 300 BC.

· Catoptrica geometric linear propagation of light, reflection, use of mirrors. A PDF File in German with reference to the Catoptrica.
· Dioptra (in Arabic Translation) (Greek word for a instrument to see through). A collection of constructions for the determination of lengths from a distance. Heron describes constructions similar to the Theodolit used for measurements of angles and other devices such as the odometer used to measure distances.

John F. BROCK in Pyramids to Pythagoras: Surveying from Egypt to Greece – 3000 B.C. to 100 A.D. gives a description of the content of Heron's Dioptra book:

1) and 2) Introduction to “the science of dioptrics”.
3) and 4) Instructions on how to construct a dioptra instrument.
5) Instructions on how to produce a stave for measurement.
6) To observe the difference in height between two points or if their height is the same.
7) To draw a straight line by dioptra from a given point to another invisible point, whatever the distance between them.
8) To find the horizontal (pros diabeten) interval between two given points, one near us, the other distant, without approachingthe distant one.
9) To find the minimum width of a river while staying on the same bank.
10) To find the horizontal interval between two visible but distant points, and their direction.
11) To find a line at right angles at the end of a given line, without approaching either the line or its end.
12) To find the perpendicular height of a visible point above the horizontal plane drawn through our position, without approaching the point.
13) (a) To find the perpendicular height of one visible point above another, without approaching either point. (b) To find the direction of a line connecting two points, without approaching them.
14) To find the depth of a ditch, that is the perpendicular height from its floor to the horizontal plane either through our position or through any other point.
15) To tunnel through a hill in a straight line, where the mouths of the tunnel are given.
16) To sink shafts for a tunnel under a hill, perpendicular to the tunnel.
17) To lay out a harbour wall on a given segment of a circle between given ends.
18) To mound up the ground in a given segment of a spherical surface.
19) To grade the ground at a given angle, so that on a level site with the shape of an equal-sided parallelogram its gradient slopes to a single point.
20) To find a point on the surface above a tunnel so that a auxiliary shaft can be sunk.
21) To lay out with the dioptra a given distance in a given direction from us.
22) To lay out with the dioptra a given distance from another point, parallel to a given line, without approaching the point having the line on which to lay it out.
23) to 30) The first five chapters refer to the dioptra setting out irregular shaped plots of land, while the remaining three explain how to determine the areas from those figures.
31) To measure the discharge or outflow of a spring.
32) and 33) Describes how to utilize the dioptra in a vertical mode for the purposes of astronomical observations.
34)This chapter informs the reader about the usage of another measuring instrument called the odometer, which has a device fitted to the wheels of a carriage such that the horizontal distance is evaluated in a very similar fashion to which a modern day perambulator gives distance

LEWIS, M.J.T., Surveying Instruments of Greece and Rome, (Cambridge University Press, 2001)

· Metrica (in Arabic Translation) A collection of 3 books for the determination of areas and volume of objectives. Part 1 considers the area of triangles and other polygons with 4-12 sides, Surfaces of pyramids, cylinders, spheres etc. Part 2 considers the volume of sphere, cylinder, prisms, pyramids etc. Part 3 considers the division of areas and volumes in parts. He gives a method fort he determination of the cubit root and calculates the cubic root of 100.
· Pneumatica (Spiritalia) Two books, A collection of around 80 mechanical apparatus, that work with air, steam or hydraulic pressure. This includes a fire extinction apparatus, automata that provide water if a coin is inserted and the first steam engine (Aeolipile). The Heronball, Thermoscope, Syphon, Fontain, and Aeolipile. 1899 Edition in Greek
· Belopoeica A Collection of war machines. The original manuscript did nor survive but medieval handwritten copies exist.1918 Version in Greek
· Mechanica 3 Books of how to move heavy objects. Part 1 provides the basis of statics and dynamics. Part 2 shows 5 simple machines. Part 3 describes lifting machines and pressures. Mechanica 1999 Edition

Other books possible also from Heron are

· Geometrica A collection of equations and exercises based on the first chapter of Metrica.
· Stereometrica. Examples of three dimensional objectives based on the second Metrica Chapter.
· Mensurae. Objects that can be used for measuring based on Stereometrica and Metrica.
· Cheirobalistra. (xeiroballistrwn kataskeuh kai summetria.) A Part of a lexicon about Catapults.

Inventions[edit]

Heron's Aeolipile

Hero described^[8] the construction of the aeolipile (a version of which is known as Hero's engine) which was a rocket-like reaction engine and the first-recorded steam engine (although Vitruvius mentioned the aeolipile in De Architectura some 100 years earlier than Hero). It was created almost two millennia before the industrial revolution. Another engine used air from a closed chamber heated by an altar fire to displace water from a sealed vessel; the water was collected and its weight, pulling on a rope, opened temple doors.^[9]Some historians have conflated the two inventions to assert that the aeolipile was capable of useful work.^[10]

Hero's wind-powered organ(reconstruction)

The first vending machine was also one of his constructions, when a coin was introduced via a slot on the top of the machine, a set amount of holy water was dispensed. This was included in his list of inventions in his book, "Mechanics and Optics". When the coin was deposited, it fell upon a pan attached to a lever. The lever opened up a valve which let some water flow out. The pan continued to tilt with the weight of the coin until it fell off, at which point a counter-weight would snap the lever back up and turn off the valve.^[11]

A windwheel operating an organ, marking the first instance of wind powering a machine in history.^[5]^[6]

Hero also invented many mechanisms for the Greek theater, including an entirely mechanical play almost ten minutes in length, powered by a binary-like system of ropes, knots, and simple machines operated by a rotating cylindrical cogwheel. The sound of thunder was produced by the mechanically-timed dropping of metal balls onto a hidden drum.

Hero's fire-engine

The force pump was widely used in the Roman world, and one application was in a fire-engine.

A syringe-like device was described by Heron to control the delivery of air or liquids.^[12]

The syringe

In optics, Hero formulated the Principle of the Shortest Path of Light: If a ray of light propagates from point A to point B within the same medium, the path-length followed is the shortest possible. It was nearly 1000 years later that Alhacen expanded the principle to both reflection and refraction, and the principle was later stated in this form by Pierre de Fermat in 1662; the most modern form is that the path is at an extremum.

A standalone fountain that operates under self-contained hydrostatic energy. (Heron's fountain)

A programmable cart that was powered by a falling weight. The "program" consisted of strings wrapped around the drive axle.^[13]

Mathematics[edit]

Heron described a method of iteratively computing the square root.^[14] Today, though, his name is most closely associated with Heron's Formula for finding the area of a triangle from its side lengths.

The imaginary number, or imaginary unit, is also noted to have been first observed by Hero while calculating the volume of a pyramidal frustum.^[15]