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THE NORMAL RECORD. theorems deduced by Pythagoras are: (1) The sum of the interior angles of a triangle equals two right angles. (2) The square on the hypothenuse of a right triangle equals the sum of the squares on the two legs. This is sometimes called the "Pythagorean Theorem." Pythagoras was so rejoiced when he proved this theorem that he sacrificed a hecatomb. A thousand oxen seems a great many animals to slaughter, but the act was justifiable. It was well that more great theorems were not then discovered, or else the price of beef would have been so high that the common people would have judged geometry an expensive luxury. (3) The problem, to find a mean proportional betwean two given lines. Pythagoras had to sacrifice another ox. (4) The plans about a point can be exactly filled by equilateral triangles, by squares, or by regular hexagons. This was evidently suggested to him by the shape of the tiles on the floors. The theorem which bears his name was probably suggested to him in the same manner. In 501 B. C, amid some popular revolt in Italy, the Pythagoreans were attacked. Pythagoreas was driven from Croton, where he lived, and was murdered in Metapontum in another popular outbreak in 500 B. C. Some of his political and social teachings did not meet the approval of the democratic populace, so Pythagoras mat an ignoble death. After the repulse of Xerxes in 480 B. C, Athens, after being rebuilt, began to increase in wealth; she sought, through the efforts of her men of wealth, to make herself the center of beauty, wealth and education. The remnant of the Pythagoreans went from Lower Italy to Athens and helped form the third Grecian school—the sophists or "wise men". These men were primarily philosophers. They accomplished little in philosophy as well as in geometry, but they deserve credit for trying to solve three problems that we know today cannot be solved by ordinary geometry. But in trying to solve these they worked many important theorems and problems concerning circles. Bat their efforts cannot be compared with the work of Pythagoras, or that later of Euclid, Archimedes or Apollonius of Perga. The three problems mentioned are: (1) To trisect any arc or angle. (2) To duplicate a cube, i. e. to find a cube whose volume is double that of a given cube. (3) To " square a circle ", i. e. to find a square exactly equal in area to a given circle, this being impossible on account of the incommensurability of pi. Thales and Pythagoras were philosophers as well as geometers, but the greatest philosophers and mathematicians of antiquity included such names as Plato, Socrates and Aristotle as philosophers: and Plato, Eudoxus, Euclid, Archimedes and Apollonius of Perga, as geometers. These liyed during the "golden age" in Greece from about 450 B. C. to 200 B. C. Plato was the first to lay down the fundamental definitions, axioms and postulates of geometry, and the first to use the method of analysis as applied to geometry. His philosophy helped his geometry not inconsiderably. His philosophy and his mathematics worked in accord, the results were lasting. His interest was shown in geometry by at least one overt act—he placed this inscription over the door of his school—"Let none ignorant of geometry enter here." Eudoxus was the author of the 5th book of "Euclid," the discoverer of the famous problem, "To divide a line in 'Golden Section,'" that is to divide a line in extreme and mean ratio, and the first one to use the "method of exhaustion" as applied to geometry. The name of Euclid is familiar, or at least should be familiar to all students in geometry today. Archimedes and Apollonius were undoubtedly greater geometers than Euclid; they introduced a new kind of geometry, the geometry of the "conic sections" while Euclid compiled the work of his predecessors and produced the geometry that bears his name today. Euclid was born about 330 B. C. and died 275 B. C. As did Thales and Pythagoras, he studied in Egypt, but in addition, had the advantages of the new university at Alexandria. While at Alexandria, Ptolemy I. once asked Euclid if geometry could not be mastered by an easier process than by studying the "Elements," Euclid's book. This was after Ptolemy had been working for some time on the first few theorems. Euclid replied, " There is
Object Description
Title  The Normal Record. December 1898 
Original Date  189812 
Description  The Record. Published by the Associated Students of Chico State College. 
Creator  Chico State College 
Location of Original  Archives 
Call Number  LD723 C57 
Digital Collection  The Record: Chico State Yearbook Collection 
Digital Repository  Meriam Library, California State University, Chico. 
DescriptionAbstract  The Record served as both a student magazine and a commencement program for Chico Normal School. In the year 1898, it was published almost monthly. 
Date Digital  2013 
Language  eng 
Rights  For information on the use of the images in this collection contact the Special Collections Department at 530.8986342 or email: specialcollections@csuchico.edu 
Format  image/tiff 
Filename  index.cpd 
Description
Title  1898_12_NormalRecord.007 
Original Date  189812 
OCR Transcript  THE NORMAL RECORD. theorems deduced by Pythagoras are: (1) The sum of the interior angles of a triangle equals two right angles. (2) The square on the hypothenuse of a right triangle equals the sum of the squares on the two legs. This is sometimes called the "Pythagorean Theorem." Pythagoras was so rejoiced when he proved this theorem that he sacrificed a hecatomb. A thousand oxen seems a great many animals to slaughter, but the act was justifiable. It was well that more great theorems were not then discovered, or else the price of beef would have been so high that the common people would have judged geometry an expensive luxury. (3) The problem, to find a mean proportional betwean two given lines. Pythagoras had to sacrifice another ox. (4) The plans about a point can be exactly filled by equilateral triangles, by squares, or by regular hexagons. This was evidently suggested to him by the shape of the tiles on the floors. The theorem which bears his name was probably suggested to him in the same manner. In 501 B. C, amid some popular revolt in Italy, the Pythagoreans were attacked. Pythagoreas was driven from Croton, where he lived, and was murdered in Metapontum in another popular outbreak in 500 B. C. Some of his political and social teachings did not meet the approval of the democratic populace, so Pythagoras mat an ignoble death. After the repulse of Xerxes in 480 B. C, Athens, after being rebuilt, began to increase in wealth; she sought, through the efforts of her men of wealth, to make herself the center of beauty, wealth and education. The remnant of the Pythagoreans went from Lower Italy to Athens and helped form the third Grecian school—the sophists or "wise men". These men were primarily philosophers. They accomplished little in philosophy as well as in geometry, but they deserve credit for trying to solve three problems that we know today cannot be solved by ordinary geometry. But in trying to solve these they worked many important theorems and problems concerning circles. Bat their efforts cannot be compared with the work of Pythagoras, or that later of Euclid, Archimedes or Apollonius of Perga. The three problems mentioned are: (1) To trisect any arc or angle. (2) To duplicate a cube, i. e. to find a cube whose volume is double that of a given cube. (3) To " square a circle ", i. e. to find a square exactly equal in area to a given circle, this being impossible on account of the incommensurability of pi. Thales and Pythagoras were philosophers as well as geometers, but the greatest philosophers and mathematicians of antiquity included such names as Plato, Socrates and Aristotle as philosophers: and Plato, Eudoxus, Euclid, Archimedes and Apollonius of Perga, as geometers. These liyed during the "golden age" in Greece from about 450 B. C. to 200 B. C. Plato was the first to lay down the fundamental definitions, axioms and postulates of geometry, and the first to use the method of analysis as applied to geometry. His philosophy helped his geometry not inconsiderably. His philosophy and his mathematics worked in accord, the results were lasting. His interest was shown in geometry by at least one overt act—he placed this inscription over the door of his school—"Let none ignorant of geometry enter here." Eudoxus was the author of the 5th book of "Euclid," the discoverer of the famous problem, "To divide a line in 'Golden Section,'" that is to divide a line in extreme and mean ratio, and the first one to use the "method of exhaustion" as applied to geometry. The name of Euclid is familiar, or at least should be familiar to all students in geometry today. Archimedes and Apollonius were undoubtedly greater geometers than Euclid; they introduced a new kind of geometry, the geometry of the "conic sections" while Euclid compiled the work of his predecessors and produced the geometry that bears his name today. Euclid was born about 330 B. C. and died 275 B. C. As did Thales and Pythagoras, he studied in Egypt, but in addition, had the advantages of the new university at Alexandria. While at Alexandria, Ptolemy I. once asked Euclid if geometry could not be mastered by an easier process than by studying the "Elements," Euclid's book. This was after Ptolemy had been working for some time on the first few theorems. Euclid replied, " There is 