Water, Air and Fire at Work in Hero's Machines
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The Evolution of Diesel Engines
GENERAL ARTICLE The Evolution of Diesel Engines U Shrinivasa Rudolf Diesel thought of an engine which is inherently more efficient than the steam engines of the end-nineteenth century, for providing motive power in a distributed way. His intense perseverance, spread over a decade, led to the engines of today which bear his name. U Shrinivasa teaches Steam Engines: History vibrations and dynamics of machinery at the Department The origin of diesel engines is intimately related to the history of of Mechanical Engineering, steam engines. The Greeks and the Romans knew that steam IISc. His other interests include the use of straight could somehow be harnessed to do useful work. The device vegetable oils in diesel aeolipile (Figure 1) known to Hero of Alexandria was a primitive engines for sustainable reaction turbine apparently used to open temple doors! However development and working this aspect of obtaining power from steam was soon forgotten and with CAE applications in the industries. millennia later when there was a requirement for lifting water from coal mines, steam was introduced into a large vessel and quenched to create a low pressure for sucking the water to be pumped. Newcomen in 1710 introduced a cylinder piston ar- rangement and a hinged beam (Figure 2) such that water could be pumped from greater depths. The condensing steam in the cylin- der pulled the piston down to create the pumping action. Another half a century later, in 1765, James Watt avoided the cooling of the hot chamber containing steam by adding a separate condensing chamber (Figure 3). This successful steam engine pump found investors to manufacture it but the coal mines already had horses to lift the water to be pumped. -
The History of Egypt Under the Ptolemies
UC-NRLF $C lb EbE THE HISTORY OF EGYPT THE PTOLEMIES. BY SAMUEL SHARPE. LONDON: EDWARD MOXON, DOVER STREET. 1838. 65 Printed by Arthur Taylor, Coleman Street. TO THE READER. The Author has given neither the arguments nor the whole of the authorities on which the sketch of the earlier history in the Introduction rests, as it would have had too much of the dryness of an antiquarian enquiry, and as he has already published them in his Early History of Egypt. In the rest of the book he has in every case pointed out in the margin the sources from which he has drawn his information. » Canonbury, 12th November, 1838. Works published by the same Author. The EARLY HISTORY of EGYPT, from the Old Testament, Herodotus, Manetho, and the Hieroglyphieal Inscriptions. EGYPTIAN INSCRIPTIONS, from the British Museum and other sources. Sixty Plates in folio. Rudiments of a VOCABULARY of EGYPTIAN HIEROGLYPHICS. M451 42 ERRATA. Page 103, line 23, for Syria read Macedonia. Page 104, line 4, for Syrians read Macedonians. CONTENTS. Introduction. Abraham : shepherd kings : Joseph : kings of Thebes : era ofMenophres, exodus of the Jews, Rameses the Great, buildings, conquests, popu- lation, mines: Shishank, B.C. 970: Solomon: kings of Tanis : Bocchoris of Sais : kings of Ethiopia, B. c. 730 .- kings ofSais : Africa is sailed round, Greek mercenaries and settlers, Solon and Pythagoras : Persian conquest, B.C. 525 .- Inarus rebels : Herodotus and Hellanicus : Amyrtaus, Nectanebo : Eudoxus, Chrysippus, and Plato : Alexander the Great : oasis of Ammon, native judges, -
Greeks Doing Algebra
Greeks Doing Algebra There is a long-standing consensus in the history of mathematics that geometry came from ancient Greece, algebra came from medieval Persia, and the two sciences did not meet until seventeenth-century France (e.g. Bell 1945). Scholars agree that the Greek mathematicians had no methods comparable to algebra before Diophantus (3rd c. CE) or, many hold, even after him (e.g. Szabó 1969, Unguru and Rowe 1981, Grattan-Guinness 1996, Vitrac 2005. For a survey of arguments see Blåsjö 2016). The problems that we would solve with algebra, the Greeks, especially the authors of the canonical and most often studied works (such as Euclid and Apollonius of Perga), approached with spatial geometry or not at all. This paper argues, however, that the methods which uniquely characterize algebra, such as information compression, quantitative abstraction, and the use of unknowns, do in fact feature in Greek mathematical works prior to Diophantus. We simply have to look beyond the looming figures of Hellenistic geometry. In this paper, we shall examine three instructive cases of algebraic problem-solving methods in Greek mathematical works before Diophantus: The Sand-reckoner of Archimedes, the Metrica of Hero of Alexandria, and the Almagest of Ptolemy. In the Sand-reckoner, Archimedes develops a system for expressing extremely large numbers, in which the base unit is a myriad myriad. His process is indefinitely repeatable, and theoretically scalable to express a number of any size. Simple though it sounds to us, this bit of information compression, by which a cumbersome quantity is set to one in order to simplify notation and computation, is a common feature of modern mathematics but was almost alien to the Greeks. -
Champ Math Study Guide Indesign
Champions of Mathematics — Study Guide — Questions and Activities Page 1 Copyright © 2001 by Master Books, Inc. All rights reserved. This publication may be reproduced for educational purposes only. BY JOHN HUDSON TINER To get the most out of this book, the following is recommended: Each chapter has questions, discussion ideas, research topics, and suggestions for further reading to improve students’ reading, writing, and thinking skills. The study guide shows the relationship of events in Champions of Mathematics to other fields of learning. The book becomes a springboard for exploration in other fields. Students who enjoy literature, history, art, or other subjects will find interesting activities in their fields of interest. Parents will find that the questions and activities enhance their investments in the Champion books because children of different age levels can use them. The questions with answers are designed for younger readers. Questions are objective and depend solely on the text of the book itself. The questions are arranged in the same order as the content of each chapter. A student can enjoy the book and quickly check his or her understanding and comprehension by the challenge of answering the questions. The activities are designed to serve as supplemental material for older students. The activities require greater knowledge and research skills. An older student (or the same student three or four years later) can read the book and do the activities in depth. CHAPTER 1 QUESTIONS 1. A B C D — Pythagoras was born on an island in the (A. Aegean Sea B. Atlantic Ocean C. Caribbean Sea D. -
15 Famous Greek Mathematicians and Their Contributions 1. Euclid
15 Famous Greek Mathematicians and Their Contributions 1. Euclid He was also known as Euclid of Alexandria and referred as the father of geometry deduced the Euclidean geometry. The name has it all, which in Greek means “renowned, glorious”. He worked his entire life in the field of mathematics and made revolutionary contributions to geometry. 2. Pythagoras The famous ‘Pythagoras theorem’, yes the same one we have struggled through in our childhood during our challenging math classes. This genius achieved in his contributions in mathematics and become the father of the theorem of Pythagoras. Born is Samos, Greece and fled off to Egypt and maybe India. This great mathematician is most prominently known for, what else but, for his Pythagoras theorem. 3. Archimedes Archimedes is yet another great talent from the land of the Greek. He thrived for gaining knowledge in mathematical education and made various contributions. He is best known for antiquity and the invention of compound pulleys and screw pump. 4. Thales of Miletus He was the first individual to whom a mathematical discovery was attributed. He’s best known for his work in calculating the heights of pyramids and the distance of the ships from the shore using geometry. 5. Aristotle Aristotle had a diverse knowledge over various areas including mathematics, geology, physics, metaphysics, biology, medicine and psychology. He was a pupil of Plato therefore it’s not a surprise that he had a vast knowledge and made contributions towards Platonism. Tutored Alexander the Great and established a library which aided in the production of hundreds of books. -
Hero's Engine Build Instructions
OMAHA MAKER GROUP Explore Technology, Science, & Art 8410 K Street, #5 – Omaha, NE 68127 [email protected] www.omahamakergroup.org How to Make a Hero’s Steam Engine Description: An easy steam engine (Hero's engine) is constructed from a soda can, some thread, and a heat source. Burning fuel heats the engine to produce steam. The chemical energy in the fuel is converted to a rotation of the can, illustrating the conversion of chemical energy to thermal energy to mechanical energy. Materials: Unopened soda can, thread, a small nail or pin, thread, something to hang the can over the fuel, candle or “Sterno” fuel, lighter, gloves Step 1 Do this outside or over a sink. Use a pin or small nail to make a hole in the side of a soda can. The can must still be unopened. When you pull the pin out there will likely be some spray. Step 2 Empty the can through the pinhole. Depending on the soda in the can, shaking it will increase the pressure in the can causing the soda to come out faster. Don't worry if there's a little soda left when you're done. Step 3 Make another hole in the other side of the can. Step 4 Put the pin back in one of the holes and pull it down as shown in the photos below. This modifies the hole enough for the steam to later come out at an angle with respect to the can. Step 5 Do the same for the other hole, pulling the pin in the same direction with respect to the can. -
The Mechanical Problems in the Corpus of Aristotle
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Faculty Publications, Classics and Religious Studies Department Classics and Religious Studies July 2007 The Mechanical Problems in the Corpus of Aristotle Thomas Nelson Winter University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/classicsfacpub Part of the Classics Commons Winter, Thomas Nelson, "The Mechanical Problems in the Corpus of Aristotle" (2007). Faculty Publications, Classics and Religious Studies Department. 68. https://digitalcommons.unl.edu/classicsfacpub/68 This Article is brought to you for free and open access by the Classics and Religious Studies at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications, Classics and Religious Studies Department by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Th e Mechanical Problems in the Corpus of Aristotle Th omas N. Winter Lincoln, Nebraska • 2007 Translator’s Preface. Who Wrote the Mechanical Problems in the Aristotelian Corpus? When I was translating the Mechanical Problems, which I did from the TLG Greek text, I was still in the fundamentalist authorship mode: that it survives in the corpus of Aristotle was then for me prima facie Th is paper will: evidence that Aristotle was the author. And at many places I found in- 1) off er the plainest evidence yet that it is not Aristotle, and — 1 dications that the date of the work was apt for Aristotle. But eventually, 2) name an author. I saw a join in Vitruvius, as in the brief summary below, “Who Wrote Th at it is not Aristotle does not, so far, rest on evidence. -
The Ptolemies: an Unloved and Unknown Dynasty. Contributions to a Different Perspective and Approach
THE PTOLEMIES: AN UNLOVED AND UNKNOWN DYNASTY. CONTRIBUTIONS TO A DIFFERENT PERSPECTIVE AND APPROACH JOSÉ DAS CANDEIAS SALES Universidade Aberta. Centro de História (University of Lisbon). Abstract: The fifteen Ptolemies that sat on the throne of Egypt between 305 B.C. (the date of assumption of basileia by Ptolemy I) and 30 B.C. (death of Cleopatra VII) are in most cases little known and, even in its most recognised bibliography, their work has been somewhat overlooked, unappreciated. Although boisterous and sometimes unloved, with the tumultuous and dissolute lives, their unbridled and unrepressed ambitions, the intrigues, the betrayals, the fratricides and the crimes that the members of this dynasty encouraged and practiced, the Ptolemies changed the Egyptian life in some aspects and were responsible for the last Pharaonic monuments which were left us, some of them still considered true masterpieces of Egyptian greatness. The Ptolemaic Period was indeed a paradoxical moment in the History of ancient Egypt, as it was with a genetically foreign dynasty (traditions, language, religion and culture) that the country, with its capital in Alexandria, met a considerable economic prosperity, a significant political and military power and an intense intellectual activity, and finally became part of the world and Mediterranean culture. The fifteen Ptolemies that succeeded to the throne of Egypt between 305 B.C. (date of assumption of basileia by Ptolemy I) and 30 B.C. (death of Cleopatra VII), after Alexander’s death and the division of his empire, are, in most cases, very poorly understood by the public and even in the literature on the topic. -
From Ancient Greece to Byzantium
Proceedings of the European Control Conference 2007 TuA07.4 Kos, Greece, July 2-5, 2007 Technology and Autonomous Mechanisms in the Mediterranean: From Ancient Greece to Byzantium K. P. Valavanis, G. J. Vachtsevanos, P. J. Antsaklis Abstract – The paper aims at presenting each period are then provided followed by technology and automation advances in the accomplishments in automatic control and the ancient Greek World, offering evidence that transition from the ancient Greek world to the Greco- feedback control as a discipline dates back more Roman era and the Byzantium. than twenty five centuries. II. CHRONOLOGICAL MAP OF SCIENCE & TECHNOLOGY I. INTRODUCTION It is worth noting that there was an initial phase of The paper objective is to present historical evidence imported influences in the development of ancient of achievements in science, technology and the Greek technology that reached the Greek states from making of automation in the ancient Greek world until the East (Persia, Babylon and Mesopotamia) and th the era of Byzantium and that the main driving force practiced by the Greeks up until the 6 century B.C. It behind Greek science [16] - [18] has been curiosity and was at the time of Thales of Miletus (circa 585 B.C.), desire for knowledge followed by the study of nature. when a very significant change occurred. A new and When focusing on the discipline of feedback control, exclusively Greek activity began to dominate any James Watt’s Flyball Governor (1769) may be inherited technology, called science. In subsequent considered as one of the earliest feedback control centuries, technology itself became more productive, devices of the modern era. -
Bridges Conference Paper
Bridges 2018 Conference Proceedings Landmarks in Algebra Quilt Elaine Krajenke Ellison Sarasota, Florida, USA; [email protected]; www.mathematicalquilts.com Abstract The Landmarks in Algebra quilt was an effort to include as many cultures that contributed significantly to the development of algebra as we know it today. Each section of the quilt illustrates a culture or a mathematician that made important advances in the development of algebra. Space did not allow more than four cultures, even though other nationalities made contributions. Babylonian mathematicians, Greek mathematicians, Indian mathematicians, and Persian mathematicians are highlighted for their important work. Figure 1: The Landmarks in Algebra quilt, 82 inches by 40 inches. First Panel: Plimpton 322 The first panel of the quilt illustrates the Plimpton 322 tablet. The Plimpton 322 tablet inspired me to design a quilt based on algebra. Recent historical research by Eleanor Robson, an Oriental Scholar at the University of Oxford, has shed new light on the ancient work of algebra [8]. The 4,000 year old Babylonian cuneiform tablet of Pythagorean Triples was purchased by George Arthur Plimpton in 1923 from Edgar J. Banks. Banks said the tablet came from a location near the ancient city of Larsa in Iraq [4]. Our first knowledge of mankind’s use of mathematics comes from the Egyptians and the Babylonians [1]. The Babylonian “texts” come to us in the form of clay tablets, usually about the size of a hand. The tablets were inscribed in cuneiform, a wedge-shaped writing owing its appearance to the stylus that was used to make it. Two types of mathematical tablets are generally found, table-texts and problem-texts [1]. -
Far-Reaching Hellenistic Geographical Knowledge Hidden in Ptolemy’S Data
NISSUNA UMANA INVESTIGAZIONE SI PUO DIMANDARE VERA SCIENZIA S’ESSA NON PASSA PER LE MATEMATICHE DIMOSTRAZIONI LEONARDO DA VINCI vol. 6 no. 3 2018 Mathematics and Mechanics of Complex Systems LUCIO RUSSO FAR-REACHING HELLENISTIC GEOGRAPHICAL KNOWLEDGE HIDDEN IN PTOLEMY’S DATA msp MATHEMATICS AND MECHANICS OF COMPLEX SYSTEMS Vol. 6, No. 3, 2018 dx.doi.org/10.2140/memocs.2018.6.181 ∩ MM FAR-REACHING HELLENISTIC GEOGRAPHICAL KNOWLEDGE HIDDEN IN PTOLEMY’S DATA LUCIO RUSSO The paper summarizes and discusses the main theses exposed in a previous book (L’America dimenticata, Mondadori Università, 2013; in Italian) in light of more recent results. Specifically, the work addresses the problem of explaining the origin of the systematic error on longitudes in Ptolemy’s Geographia and its logical relation with the reduced estimate for the dimension of the Earth given there. The thesis is sustained that, contrary to a frequently advanced conjecture, the shrinking of the dimension of the Earth is a consequence of a scale error in longitudes, which, in turn, was originated by a misidentification of the Islands of the Blessed. The location of the Islands of the Blessed according to the source of Ptolemy is identified in the Caribbean. The analysis of a passage of Pliny provides an independent and quantitative confirmation of the proposed identifi- cation, which sheds new light on possible contact among civilizations. 1. The shrinking of the Earth and the dilation of longitudes in Ptolemy’s Geographia It is well known that Eratosthenes, in the 3rd century BC, measured the circum- ference of the Earth, obtaining the value of 252,000 stadia (corresponding to 700 stadia per degree). -
Table of Contents More Information
Cambridge University Press 978-0-521-76376-9 - The Mechanical Hypothesis in Ancient Greek Natural Philosophy Sylvia Berryman Table of Contents More information Contents List of illustrations page vii Acknowledgements viii Introduction 1 1 Mechanics and the mechanical: some problems of terminology 9 The critics of prevailing usage 11 Some candidate definitions of the ‘mechanistic’ 15 2 ‘Mechanistic’ thought before mechanics? 21 Divine versus human technology 24 Working artifacts before the fourth century 29 Ancient atomism and the machine analogy 34 The ‘shortfalls’ of ancient technology 39 The ‘exclusion’ of ancient mechanics 43 3 Mechanics in the fourth century 54 The scope of ancient Greek mechanics 55 Archytas and the foundation of mechanics 87 Aristotle’s ‘mechanics’ of motion 97 Conclusion 104 4 The theory and practice of ancient Greek mechanics 105 The Aristotelian Mechanica 106 Ctesibius 115 Archimedes 117 Philo of Byzantium 123 v © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-76376-9 - The Mechanical Hypothesis in Ancient Greek Natural Philosophy Sylvia Berryman Table of Contents More information vi Contents Vitruvius 130 Hero of Alexandria 134 Pappus of Alexandria 143 Models of the heavens 146 5 Ancient Greek mechanics continued: the case of pneumatics 155 Pneumatic technology in the post-classical period 157 Ancient Greek pneumatic theory 165 The status of mechanics revisited: natural or artificial? 170 6 The philosophical reception of mechanics in antiquity 177 Mechanical theory in natural philosophy 179 The theory of pneumatics in natural philosophy 191 Pneumatics and medical theory 197 Working artifacts and the notion of a self-mover 201 Mechanical analogies for the functioning of organisms 205 Working artifacts in astronomy 216 Mechanical analogies in cosmology 220 Conclusion 231 Appendix: Ancient mechanics and the mechanical in the seventeenth century 236 Bibliography 250 Index of passages 274 General index 282 © Cambridge University Press www.cambridge.org.