Euclid

Euclid Police shot and wounded one man following a traffic stop for a suspected stolen vehicle and another male who fled the scene and was considered armed and dangerous turned himself in a few hours later. According to a department news release, at 12:30 p.m. on June 7 officers located and stopped a suspected stolen Hyundai Sonata on Fox Avenue at East 222nd Street. The traffic stop led to a Euclid officer shooting and wounding a 19-year-old male. According to the release, that male has been transported to an area hospital with a single non-life threatening gunshot wound to his leg. For the sake of fairness and transparency, Ohio’s Bureau of Criminal Investigation has been called in to investigate the shooting. According to the release, during the traffic stop, a Euclid detective received a non-gunshot-related injury to his leg and was transported to a local hospital for treatment. A 14-year-old male passenger was taken into custody without incident, according to the department. According to the release, another male fled the scene on foot. He was observed brandishing a handgun at a resident on Heartland Avenue. According to an updated release, at 4:35 p.m. on June 7, the suspect-at-large, a 16-year old Cleveland resident, turned himself in peacefully at the Euclid Police Department. He was escorted by an adult family member. There are no other suspects at large. The department expressed appreciation for the assistance of the public in bringing the search to a peaceful co...

Euclid biography Euclid (c. 325 BC – 265 BC) – Greek Mathematician considered the “Father of Geometry”. His textbook ‘Elements’ remained a highly influential mathematics teaching book until the late 19th Century and is one of the most widely published books in the world. It has had a lasting influence on the sciences -, especially in mathematics. In a list by Michael H. Hast – Euclid is considered to be 14th most Euclid was born in the mid 4th Century BC and lived in Alexandria; he was mostly active during the reign of Ptolemy I (323-283BC) His name Euclid means “renowned, glorious” – he is also referred to as Euclid of Alexandria. Details about Euclid’s life are sparse – the main biographical information was not written until many centuries later, e.g. Proclus c. 450 AD. Proclus writes about Euclid: “Not much younger than these [pupils of Plato] is Euclid, who put together the “Elements”, arranging in order many of Eudoxus’s theorems, perfecting many of Theaetetus’s, and also bringing to irrefutable demonstration the things which had been only loosely proved by his predecessors. This man lived in the time of the first Ptolemy; for It is likely Euclid worked with a team of mathematics in Alexandria and he received a degree of help in his mathematical works. Some historians feel the works of Euclid may have been the result of several authors, but most agree that one person – Euclid – was the principal author. It is likely that Euclid would have studied at Another later hist...

In Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios (flourished c. 440 bce), not to be confused with the physician Hippocrates of Cos (c. 460–375 bce). The latest compiler before Euclid was Theudius, whose textbook… • algorithms • In …infinite classes of questions; Euclid’s Elements, published about 300 bce, contained one for finding the greatest common divisor of two natural numbers. Every elementary-school student is drilled in long division, which is an algorithm for the question “Upon dividing a natural number a by another natural number b, what are… • foundations of mathematics • In Euclid’s Elements ( c. 300 bce), which presented a set of formal logical arguments based on a few basic terms and axioms, provided a systematic method of rational exploration that guided mathematicians, philosophers, and scientists well into the 19th century. Even serious objections to the lack of… • influence on Hobbes • In …of demonstrating theorems in the Elements. According to a contemporary biographer, he came upon a volume of Euclid in a gentleman’s study and fell in love with geometry. Later, perhaps in the mid-1630s, he had gained enough sophistication to pursue independent research in optics, a subject he later claimed to… SIDEBAR • Teaching the “Elements” • In With the European recovery and translation of Greek mathematical texts during the 12th century—the first Latin translation of Euclid’s Elements, by Adelard of Bath, wa...

Statue of Euclid in Oxford (Public Domain) Euclid gathered up all of the knowledge developed in Greek mathematics at that time and created his great work, a book called 'The Elements' (c300 BCE). This treatise is unequaled in the history of science and could safely lay claim to being the most influential non-religious book of all time. Euclid probably attended Plato's academy in Athens before moving to Alexandria, in Egypt. At this time, the city had a huge library and the ready availability of papyrus made it the center for books, the major reasons why great minds such as Euclid's Elements Euclid's Elements Title Page (Public Domain) Euclid's great work consisted of thirteen books covering a vast body of mathematical knowledge, spanning arithmetic, geometry and number theory. The books are organized by subjects, covering every area of mathematics developed by the Greeks: • Books I - IV, and Book VI: Plane Geometry • Books XI - XIII: Solid Geometry • Books V and X: Magnitudes and Ratios • Books VII - IX: Whole Numbers The basic structure of the elements begins with Euclid establishing axioms, the starting point from which he developed 465 propositions, progressing from his first established principles to the unknown in a series of steps, a process that he called the 'Synthetic Approach.' He looked at mathematics as a whole, but was concentrated on geometry and that particular discipline formed the basis of his work. Euclid's Axioms Euclid based his approach upon 10 axioms,...

Euclid was from Euclid, Greek Eukleides, (flourished c. 300 bce, Alexandria, Egypt), the most prominent mathematician of Greco-Roman antiquity, best known for his Elements. Life Of Euclid’s life nothing is known except what the Greek philosopher ce) reports in his “summary” of famous Greek mathematicians. According to him, Euclid taught at bce. Elements, and Euclid replied that there was no royal road to geometry.” Today few historians challenge the bce). Sources and contents of the Euclid compiled his Elements from a number of works of earlier men. Among these are bce), not to be confused with the physician bce). The latest compiler before Euclid was Theudius, whose textbook was used in the bce). The older elements were at once superseded by Euclid’s and then forgotten. For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own, A brief survey of the Elements belies a common belief that it concerns only See the table of Euclid’s 10 initial assumptions.) Book I then proves elementary theorems about see Euclid's axioms 1 Given two points there is one straight line that joins them. 2 A straight line segment can be prolonged indefinitely. 3 A circle can be constructed when a point for its centre and a distance for its radius are given. 4 All right angles are equal. 5 If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight ...

Euclid, often called the father of geometry, changed the way we learn about shapes with his 13-book series, Euclid's Elements. He used basic ideas called axioms or postulates to create solid proofs and figure out new ideas called theorems and propositions. Studying Euclidean geometry helps us think better and solve problems more effectively. Created by Sal Khan. There are other branches of mathematics that do not use Euclid's axioms as their basis, such as spherical geometry and many others. These geometries reject Euclid's axioms and substitute others, and thus the properties of lines and shapes and other things are different from those in Euclid. But that doesn't mean Euclid is wrong. Euclidean geometry is consistent within itself, meaning the axioms all agree with each other and with all the properties derived from them. That's all you can ask from a branch of mathematics--internal consistency. There is no one universal geometry that satisfies all situations and which contains all possible true statements. So we have to start by defining our terms (axioms), and Euclid was the first one to do that. There was a big debate for hundreds of years about whether you really needed all 5 of Euclid's basic postulates. Mathematicians kept trying to prove that the 5th postulate (commonly known as the parallel postulate) could be proved from the first four postulates and thus was unnecessary. Some really great proofs were created by mathematicians trying to prove the parallel postul...

Euclidean geometry, the study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician bce). In its rough outline, Euclidean geometry is the plane and solid geometry commonly taught in secondary schools. Indeed, until the second half of the 19th century, when geometry meant Euclidean geometry. It is the most typical expression of general mathematical thinking. Rather than the memorization of simple In its rigorous deductive organization, the Elements remained the very model of scientific exposition until the end of the 19th century, when the German mathematician Foundations of Geometry (1899). The modern version of Euclidean geometry is the theory of Euclidean (coordinate) spaces of multiple See Fundamentals Elements with some undefined terms, such as “a point is that which has no part” and “a As a basis for further logical

Statue of Euclid in Oxford (Public Domain) Euclid gathered up all of the knowledge developed in Greek mathematics at that time and created his great work, a book called 'The Elements' (c300 BCE). This treatise is unequaled in the history of science and could safely lay claim to being the most influential non-religious book of all time. Euclid probably attended Plato's academy in Athens before moving to Alexandria, in Egypt. At this time, the city had a huge library and the ready availability of papyrus made it the center for books, the major reasons why great minds such as Euclid's Elements Euclid's Elements Title Page (Public Domain) Euclid's great work consisted of thirteen books covering a vast body of mathematical knowledge, spanning arithmetic, geometry and number theory. The books are organized by subjects, covering every area of mathematics developed by the Greeks: • Books I - IV, and Book VI: Plane Geometry • Books XI - XIII: Solid Geometry • Books V and X: Magnitudes and Ratios • Books VII - IX: Whole Numbers The basic structure of the elements begins with Euclid establishing axioms, the starting point from which he developed 465 propositions, progressing from his first established principles to the unknown in a series of steps, a process that he called the 'Synthetic Approach.' He looked at mathematics as a whole, but was concentrated on geometry and that particular discipline formed the basis of his work. Euclid's Axioms Euclid based his approach upon 10 axioms,...

Euclid, often called the father of geometry, changed the way we learn about shapes with his 13-book series, Euclid's Elements. He used basic ideas called axioms or postulates to create solid proofs and figure out new ideas called theorems and propositions. Studying Euclidean geometry helps us think better and solve problems more effectively. Created by Sal Khan. There are other branches of mathematics that do not use Euclid's axioms as their basis, such as spherical geometry and many others. These geometries reject Euclid's axioms and substitute others, and thus the properties of lines and shapes and other things are different from those in Euclid. But that doesn't mean Euclid is wrong. Euclidean geometry is consistent within itself, meaning the axioms all agree with each other and with all the properties derived from them. That's all you can ask from a branch of mathematics--internal consistency. There is no one universal geometry that satisfies all situations and which contains all possible true statements. So we have to start by defining our terms (axioms), and Euclid was the first one to do that. There was a big debate for hundreds of years about whether you really needed all 5 of Euclid's basic postulates. Mathematicians kept trying to prove that the 5th postulate (commonly known as the parallel postulate) could be proved from the first four postulates and thus was unnecessary. Some really great proofs were created by mathematicians trying to prove the parallel postul...

Euclid biography Euclid (c. 325 BC – 265 BC) – Greek Mathematician considered the “Father of Geometry”. His textbook ‘Elements’ remained a highly influential mathematics teaching book until the late 19th Century and is one of the most widely published books in the world. It has had a lasting influence on the sciences -, especially in mathematics. In a list by Michael H. Hast – Euclid is considered to be 14th most Euclid was born in the mid 4th Century BC and lived in Alexandria; he was mostly active during the reign of Ptolemy I (323-283BC) His name Euclid means “renowned, glorious” – he is also referred to as Euclid of Alexandria. Details about Euclid’s life are sparse – the main biographical information was not written until many centuries later, e.g. Proclus c. 450 AD. Proclus writes about Euclid: “Not much younger than these [pupils of Plato] is Euclid, who put together the “Elements”, arranging in order many of Eudoxus’s theorems, perfecting many of Theaetetus’s, and also bringing to irrefutable demonstration the things which had been only loosely proved by his predecessors. This man lived in the time of the first Ptolemy; for It is likely Euclid worked with a team of mathematics in Alexandria and he received a degree of help in his mathematical works. Some historians feel the works of Euclid may have been the result of several authors, but most agree that one person – Euclid – was the principal author. It is likely that Euclid would have studied at Another later hist...