Arabic Measures-3 (original) (raw)
Related papers
Earth Measurement in the Classical World
This paper is Chapter 4 of Measurements of the Gods with a little added to the text. The chapter describes the knowledge regarding Earth dimensions in classical times. In so doing great doubt is cast upon the concept of the variations in degree length around the meridian of Earth and the polar flattening being understood in that era or earlier. Given that the meridian circumference and the diameter derived from that were known and the ancient measures relate to these it is accepted that these were the only two measures relating to the dimensions of Earth that were understood and therefore the equatorial values also were not known. Earth was accepted to be a globe
2024
This paper presents a hypothesis on the advanced metrological skills of the Ancient Egyptians and/or Britons, evidenced by their precise estimation of the Earth's quadrature with an error margin below 0.005%, as detailed in the "Giza-Stonehenge Connection Paper." Their use of a base-10 system and emphasis on geometric principles led to the division of the Earth's circumference into four parts, each subdivided into 10,000,000 units, prefiguring the metric system's development. The term "Met-hah-ua," meaning "one of ten-million," is proposed for this ancient unit, correlating with the modern meter. Utilizing the sacred ratio of √5, this measurement was subdivided to establish the Royal Cubit, with the perimeter of a specific triangle divided into segments measuring 0.523606797 meters each. This detail introduces an educational scenario: calculating the height of a triangle with a perimeter of 10 Royal Cubits, revealing it to be 1 Met- hah-ua. Further analysis refines Glen Dash's reported Great Pyramid base length to a more precise range between 230.35 and 230.40 meters. With the pyramid presumed to be designed at 440 cubits, the Royal Cubit measures between 0.52352 and 0.52363 meters, fitting neatly with the proposed 0.523606 meters and linking to the significant √5. The analysis ends with a brief illustration of the ability of this formulation to predict pi, to a value within 0.0015% This hypothesis underscores the Ancient Egyptians' integration of mathematical precision into their spiritual and architectural endeavors, highlighting their deep understanding of geometry and metrology reflected in their monumental constructions.
ORIGINS OF METROLOGY: AN INTERPRETATION OF THE 360-DEGREE CIRCLE AND THE ROYAL CUBIT
Origins of Metrology - An Interpretation of the circle and the Royal Cubit, 2024
laboratories investigate the options discussed in my work. The archaeological evidence has been available to society for a long time, but it just has not been interpreted correctly yet. And, difficult as it might seem to believe, there are many scholars, me included, who believe that the change to a metric measurement system following the French Revolution was a great mistake for science. The original metrological systems in-place at the time were the result of sophisticated methods and scientific capabilities that were not given the credit deserved and were allowed to fall away. Yet the ancient designs carry a (partially hidden) wealth of information that should be studied in more detail with modern scientific attitudes and capabilities. This is simply what I have done. I hope you find the content of the article stimulating, and feel free to contact me at my email address if you wish to discuss anything, or to provide a better explanation for the origin of the 360-degree circle.
2024
This study explores and builds on my hypothesis that ancient civilizations, particularly the Egyptians and the builders of Stonehenge, might have had an advanced understanding of celestial mechanics and Earth's dimensions, predating known measurement units like the royal cubit and megalithic yard with a measure akin to the modern meter. Through monumental constructions and precise astronomical observations, these ancients may have discerned the Earth's circumference, embedding this knowledge in structures like the Great Pyramid and Stonehenge. The text suggests these insights align with modern scientific understanding, highlighting Euclid's geometric construction of the dodecahedron from a cube via the golden ratio as a significant legacy of ancient knowledge. This geometric symbol, representing the Earth and the cosmos, was deeply infused with mathematical and metaphysical meaning, suggesting a sophisticated blend of science, philosophy, and spirituality in ancient metrological systems. The discussion extends to the Duat in Egyptian texts, portrayed through symbols like the encircled pentagon, reflecting a complex cosmology that integrates celestial and terrestrial realms. This exploration posits that ancient and contemporary measurement systems might share a profound connection, inviting a reevaluation of ancient societies' engagement with the universe through architectural and metrological strategies. This inquiry connects past architectural achievements and celestial engagements with current scientific discoveries, underlining humanity's enduring quest to understand the cosmic order.
The Structure and Function of Ancient Metrology
Wonders Lost and Found: A celebration of the archaeological work of Professor Michael Vickers, 2020
The evidence for the structure of ancient metrology strongly suggests that all the measurement systems in use throughout the ancient world formed part of a unified system. This may at first sight appear to be a bold claim but it is justified since their similarities far outweigh any differences. These similarities are clear when considered in the light of variations in individual modules. It is acknowledged that variations in the same module exist, but this is largely attributed to errors of copyists when making new rulers. This is, however, inherently unlikely since canonical rulers were presumably issued by the custodians of the temples where prototypes were maintained. If these were lost then the known dimensions of the temple itself would guarantee a faithful copy. Furthermore, the variations in the modules were universal and occurred in every ancient standard of mensuration. The eminent Egyptologist W. Flinders Petrie was aware of such variations and observed two that occurred repeatedly that were variations of the 450 th and 170 th part. 1 Subsequent research has enabled these variations to be more exactly expressed as the 440 th and the 175 th part. The reasons for their existence lies in the need to maintain integers in both diameters and perimeters of circular designs, wheels, rotundas, storage vessels and surveying at geographic scales etc. Ancient sources, from cuneiform texts to Vitruvius state that if the diameter of a circle is a multiple of four units then 3.125 (25/8) is the ratio used for pi and the difference between this and the universally used 22/7 is the unit fraction 175 to 176. This means that an integer is maintained by using a module the 175 th part longer on the perimeter. In all other cases seven is the number that defines the radius of a circle and the design module is found by dividing the radius by seven. When archaeologists today analyse ancient measures, they tend to create averages of the variations as the definition of the units, but this destroys the integrity of the system to which they belong and obscures the fact that the variations in question were both practical and deliberate. Both fractions are most easily demonstrable in the structure of metrology with commonly known measures such as Greek and Roman that are universally acknowledged to be linked by the unit fraction 25 to 24. If we consider the variant of the "Roman" foot given by Petrie at Stonehenge 2 it perfectly illustrates both the precision and permanence with which standards could be maintained in a structure, and the international nature of the modules. We now know that the absolute value of the "Roman" foot that he deduced from the inner diameter of the sarsen circle was .9732096ft and Petrie measured the whole 100 Roman feet to within one twentieth of an inch of this value. He termed it a Pelasgo Roman foot and later termed the same value as Etrurian, the implication being that he had found evidence of the same foot length being used at these locations. Livio measured this value to within a millimetre overall as the length of the naos or cella of the Parthenon. The same foot value is given with extreme accuracy as the measured length of the running track of the Nemea
2024
The Metrological Relief at the Ashmolean Museum, likely originating from the island of Samos during the 5th century BCE, represents a fascinating intersection of ancient metrology, trade, and intellectual exchange. Believed to have adorned the doorway of a building of weights and measures, the relief features a man with outstretched arms and an impressed foot, symbolizing standard units of measurement such as the fathom and foot. This artifact offers insight into ancient systems of measurement, suggesting a link between Samos, Egypt, and broader Mediterranean civilizations. This study investigates whether ancient systems of measurement were influenced by a prototypical "mètre de archive," possibly derived from the estimated circumference of the Earth, a concept tied to the Silver Ratio Cubit (SRC). Analysis of the relief's dimensions reveals an arm span of approximately 2073.4 millimeters, recalibrated from Adolf Michaelis's original 1883 measurements, and a foot length of 287.98 millimeters. These measurements correspond remarkably well with Herodotus's reported base of the Great Pyramid, measured as 800 feet, implying either direct use of the same standard or knowledge of a tradition linking the Samian foot to 1/800th of the Great Pyramid's base. Further examination reveals that the arm span on the relief is not tied to the commonly assumed Greek fathom of 7 feet but rather a ratio of 7.2 feet, aligning it with Alexander Thom's hypothesized Megalithic Rod. Comparative analysis of related units-including the Egyptian Royal Cubit, Egyptian Remen, Albion Megalithic Rod, Samian Fathom, Roman Pace, and others-demonstrates a striking convergence of these measures at 103.672 meters, equivalent to 198 Egyptian Royal Cubits. This study posits that such alignment is not coincidental but could reflect an underlying metrological framework rooted in the SRC, developed around 2600 BCE by the Ancient Egyptians based on their estimation of the Earth's circumference. The Great Pyramid and Stonehenge may have served as immovable "mètres de archive," eternal benchmarks linking these systems of measurement. This hypothesis underscores the interconnectedness of ancient metrological traditions, cross-pollinated through trade routes and intellectual exchange, with Egypt playing a pivotal role in disseminating this knowledge across the ancient world.
A New Perspective on Eratosthenes' Measurement of the Earth
The Physics Teacher, 2011
Around 240 B.C., Eratosthenes made what is considered to be the most famous and accurate of the ancient measurements of the circumference of the Earth.1 It was accomplished by making presumably simultaneous measurements of the angles of the shadows cast by a vertical stick at Syene (today known as Aswan) and another at Alexandria, at noon on the day of the summer solstice (about June 21 every year). From these measurements, and knowing the distance from Syene to Alexandria along the assumed same meridian of longitude, Eratosthenes was able to provide a remarkably accurate estimate of the radius of the Earth.
Historical Metrology-Measurements of the Gods.
This work relates the basic metrological structures and related individual measures in use in the ancient and not so ancient worlds. The narrative commences with the onset of metrication in Britain and the loss of an ages old system that was a part of the ancient methodology. The journey is eventually completed at what is almost certainly the source of the ancient system and along the way various examples and situations are covered, some that will surprise many readers. This is a surprisingly interesting subject area with a commencement much further back in time than most would imagine but the evidence is clear and points to a specific location. This is the one subject that should be a part of any archaeology qualification but unfortunately is not.
Biruni's measurement of the Earth
The peak from which Biruni measured the Earth is pinpointed; his measurements are shown to tally with the geographical features of the landscape around the peak. Mathematics shows what measurements he is likely to have taken, and his famous formula is fully derived. Besides, an appendix is given for those who want to try measuring mountains by themselves and follow in Biruni’s footsteps.
commentary on How to Measure the Earth' Circumference.pdf
2018
In 'How to Measure the Earth's circumference' Michael Baizerman mentions the modern equatorial measure in conjunction with the meridian degree length. Confusing. The Greek methodologies invariably were conducted in a north/south direction. They were attempting to measures a distance along a meridian. This distance was then expanded to a count of diverse stade values applied to the meridian circumference. At no time was an equatorial circumference given in the ancient world. What emerges from an assessment of these values when evaluated with knowledge of the measures of the ancient world is that these diverse stadia values all ultimately gave the same dimension for the circumference of Earth in a meridian direction. It was John Michell who extending and adapting the works of previous scholars including Berryman, Stechini and Petrie to name but three, revealed the ancient measuring system. While I disagree with some of his conclusions, his measures were correct. Michell claimed that various differences in values were due to the difference in degree lengths around the meridian quadrant whereas I argue that the same values can be found via counts of time such as days of the month in its various formats. In fact the measures applied greatly predate the interpretation of the Earth's shape from a pure globe to a flattened version. It was not until well into the Christian era that reasonably accurate knowledge of this flattening became available. The unit measures, whether cubits, reeds or stadia, among other denominations are related to the meridian circumference of Earth as accepted before the French determinations for the metric system. Some of these divide accurately into that meridian while others work via specific factors. The Earth's diameter was also derived from this via a pi value of 3.1418181818. This diameter of course was 7920 miles. The circumference measure can be seen as 24883.2 British miles. It was Michell who calculated this value and it and its component parts are verified via ancient cubit rods, measures of buildings etc. Here is an extract from my work Measurements of the Gods showing the values applied by Michell, the French calculation for the metric values and NASA [early 1990s] :