1. Thales Of Miletus thales of miletus. thales of miletus Born c 624 BC and died c. 547 inAsia minor. thales of miletus taught that all things are water http://phoenicia.org/thales.html

A Bequest Unearthed Phoenicia Encyclopedia Phoeniciana Thales of Miletus 900 pages on Phoenicians Search Phoenicia Get a Search Eine For Your Site TRANSLATE this page Thales of Miletus Born c 624 BC and died c. 547 in Asia minor. He was the son of Examyes and Cleobuline, distinguished Phoenicians. Thales was the first known philosopher, scientist and mathematician although his occupation was that of an engineer. He is believed to have been the teacher of Anaximander (611 BC - 545 BC) and he was the first natural philosopher in the Milesian School. However, none of his writing survives so it is difficult to determine his views or to be certain about his mathematical discoveries. Indeed it is unclear whether he wrote any works at all and if he did they were certainly lost by the time of Aristotle who did not have access to any writings of Thales. On the other hand there are claims that he wrote a book on navigation but these are based on little evidence. In the book on navigation it is suggested that he used the constellation Ursa Minor, which he defined, as an important feature in his navigation techniques. Even if the book is fictitious, it is quite probable that Thales did indeed define the constellation Ursa Minor. Proclus, the last major Greek philosopher, who lived around 450 AD, wrote:-

2. Thales Of Miletus [Internet Encyclopedia Of Philosophy] thales of miletus (62?546 BCE) There is considerable agreement that Thales was born in Miletus in Greek Ionia in the mid 620s BCE and died in about 546 BCE, but even those dates are indefinite. http://www.utm.edu/research/iep/t/thales.htm

Thales of Miletus (62?-546 BCE) Table of Contents (Clicking on the links below will take you to that part of this article) The Writings of Thales Possible Sources for Aristotle Thales says Water is the Primary Principle Thales and Mythology ... Abbreviations The Writings of Thales Doubts have always existed about whether Thales wrote anything, but a number of ancient reports credit him with writings. Simplicius (Diels, Dox. p. 475) specifically attributed to Thales authorship of the so-called Nautical Star-guide. Diogenes Laertius raised doubts about authenticity, but wrote that 'according to others [Thales] wrote nothing but two treatises, one On the Solstice and one On the Equinox ' (D.L. I.23). Lobon of Argus asserted that the writings of Thales amounted to two hundred lines (D.L. I.34), and Plutarch associated Thales with opinions and accounts expressed in verse (Plutarch, De Pyth. or. 18. 402 E). Hesychius, recorded that '[Thales] wrote on celestial matters in epic verse, on the equinox, and much else' (DK, 11A2). Callimachus credited Thales with the sage advice that navigators should navigate by Ursa Minor (D.L. I.23), advice which may have been in writing. Diogenes mentions a poet, Choerilus, who declared that '[Thales] was the first to maintain the immortality of the soul' (D.L. I.24), and in

3. Thales keep that in mind while reading these papers. thales of miletus. c.585 B.C.E. thales of miletus was a statesman, engineer, astronomer, mathematician and a philosopher http://www.perseus.tufts.edu/GreekScience/Students/Kathleen/thales.html

Please note: These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. We assume no responsibility over the content of these papers: we present them as is as a part of the course, not as documents in the Perseus Digital Library . We do not have contact information for the authors. Please keep that in mind while reading these papers. Thales of Miletus c.585 B.C.E. Kathleen Norton April 15, 1995 Look at the comments on this paper. Thales of Miletus was a statesman, engineer, astronomer, mathematician and a philosopher. Such activity in varied fields was not uncommon among academics in ancient Greece. However, according to Plutarch, "Thales was the only wise man of the time who carried his speculations beyond the realm of the practical ( Solon 3.4)." Because Thales did not always seek answers to practical questions, he was seen by some people as " wise but not prudent. " One tale by Plato describes Thales falling into a well because he was too busy examining the stars above.

4. Thales Of Miletus thales of miletus. Little is known of Thales. The bust shown above is in the CapitolineMuseum in Rome but is not contemporary with Thales. thales of miletus. http://www.math.tamu.edu/~don.allen/history/thales2/thales2.html

Next: About this document Thales of Miletus Little is known of Thales. He was born about 624 BC in Miletus, Asia Minor (now Turkey) and died about 546 BC in Miletos, Turkey The bust shown above is in the Capitoline Museum in Rome but is not contemporary with Thales. Thales of Miletus Some impression and highlights of his life and work follow: Thales of Miletus was the first known Greek philosopher, scientist and mathematician. Some consider him to be the teacher of of Pythagoras, though it may be only that he advised Pythagoras to travel to Egypt and Chaldea. From Eudemus of Rhodes (fl ca. 320 B.C) we know that he studied in Egypt and brought these teachings to Greece. He is unanimously ascribed the introduction of mathematical and astronomical sciences into Greece. He is unanimously regarded as having been unusally cleverby general agreement the first of the Seven Wise Men, a pupil of the Egyptians and the Chaldeans. None of his writing survives; this makes it is difficult to determine his philosophy and to be certain about his mathematical discoveries. There is, of course, the story of his successful speculation in oil presses as testament to his practical business acumen.

5. Thales Of Miletus He was born about 624 BCE in Miletus and he considered the founder of the IonianSchool, also called the Milesian school. Thales was an avid traveler as http://www.forthnet.gr/presocratics/thaln.htm

Thales [His Life] Thales is the father of ancient Greek philosophy insofar as he was the first that raised the point that a material substance explains all the natural phenomena. He was born about 624 BCE in Miletus and he considered the founder of the Ionian School, also called the Milesian school. Thales was an avid traveler as Hieronymus of Rhodes indicates in his report that Thales measured the pyramids by their shadow, having observed the time when our shadow is equal to our height. For the ancient Greek Sages of the sixth-century (for example Solon, see Timaeus) it was a custom to visit Egypt and studding the traditional fountain-head. Proclus, in Euclidem, mentions that " Thales left Egypt and went to Greece to further his study of geometry" . Thales was regarded as one of the "Seven Sages" of ancient Greece. He died at an old age when watching athletic matches due to heat exhaustion. The inscription on his tomb is: Here in a narrow tomb great Thales lies; Yet his renown for wisdom reached the skies. [The Water As The First Principle] Thales was the first Greek philosopher to speculate about the primary material element of all beings and cosmic phenomena, which he identified as

6. Thales Of Miletus (634-546 BC) -- From Eric Weisstein's World Of Scientific Biog Astronomers. Branch of Science. Mathematicians. Branch of Science. Philosophers. Nationality. Greek. thales of miletus (634546 BC) To him is attributed Thales' theorem. Proclus attributed the following additional mathematical theorems to Thales (Boyer http://scienceworld.wolfram.com/biography/Thales.html

Branch of Science Astronomers Branch of Science Mathematicians ... Greek Thales of Miletus (634-546 BC) Greek philosopher who is considered the founder of Greek science, mathematics, and philosophy. He visited Egypt and probably Babylon, bringing back knowledge of astronomy and geometry. He invented deductive mathematics. To him is attributed Thales' theorem Proclus attributed the following additional mathematical theorems to Thales (Boyer 1968, pp. 50-51): (1) a circle is bisected by a diameter (2) the base angles of an isosceles triangle are equal, (3) pairs of vertical angles formed by two intersecting lines are equal, and (4) the ASA theorem for triangles According to Herodotus, Thales predicted the year of the May 28, 585 BC solar eclipse confirming his access to Babylonian records. Thales believed the Earth to be a flat disk floating on an infinite ocean, and established the Ionian (Milesian) school of Greek astronomy. Thales considered water to be the "first principle" ("arche") of nature. In his theories, Thales "naturalized" supernatural explanations, marking the beginning of scientific methodology. However, his teachings emphasized philosophical speculation over practical applications of science. It is therefore fitting that a legend tells of his falling into a well while pondering the heavens. A passing peasant is said to have fished him out with the comment "here is a man who would study the stars and cannot see what lies at his feet."

7. Thales Of Miletus --  Encyclopædia Britannica MLA style " thales of miletus." Encyclopædia Britannica. 2004 APA style thales of miletus. Encyclopædia Britannica. Retrieved May 6, 2004, from Encyclopædia Britannica Premium http://www.britannica.com/eb/article?eu=73782

8. Thales Article by J.J. O'Connor and E.F. Robertson, from the MacTutor History of Mathematics archive. A discussion of the life and teachings of this thinker, with links to related articles. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Thales.html

Thales of Miletus Born: about 624 BC in Miletus, Asia Minor (now Turkey) Died: about 547 BC in Miletus, Asia Minor (now Turkey) Click the picture above to see five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Thales of Miletus was the son of Examyes and Cleobuline. His parents are said by some to be from Miletus but others report that they were Phoenicians. J Longrigg writes in [1]:- But the majority opinion considered him a true Milesian by descent, and of a distinguished family. Thales seems to be the first known Greek philosopher, scientist and mathematician although his occupation was that of an engineer. He is believed to have been the teacher of Anaximander (611 BC - 545 BC) and he was the first natural philosopher in the Milesian School. However, none of his writing survives so it is difficult to determine his views or to be certain about his mathematical discoveries. Indeed it is unclear whether he wrote any works at all and if he did they were certainly lost by the time of Aristotle who did not have access to any writings of Thales. On the other hand there are claims that he wrote a book on navigation but these are based on little evidence. In the book on navigation it is suggested that he used the constellation Ursa Minor, which he defined, as an important feature in his navigation techniques. Even if the book is fictitious, it is quite probable that Thales did indeed define the constellation Ursa Minor.

9. Thales Of Miletus Comprehensive studies on of everything Canaanite Phoenicians in Lebanon, Israel, Syria, world A Bequest Unearthed Phoenicia Encyclopedia Phoeniciana. thales of miletus. 900 pages on TRANSLATE this page. thales of miletus. Born c 624 BC and died c http://www.phoenicia.org/thales.html

A Bequest Unearthed Phoenicia Encyclopedia Phoeniciana Thales of Miletus 900 pages on Phoenicians Search Phoenicia Get a Search Eine For Your Site TRANSLATE this page Thales of Miletus Born c 624 BC and died c. 547 in Asia minor. He was the son of Examyes and Cleobuline, distinguished Phoenicians. Thales was the first known philosopher, scientist and mathematician although his occupation was that of an engineer. He is believed to have been the teacher of Anaximander (611 BC - 545 BC) and he was the first natural philosopher in the Milesian School. However, none of his writing survives so it is difficult to determine his views or to be certain about his mathematical discoveries. Indeed it is unclear whether he wrote any works at all and if he did they were certainly lost by the time of Aristotle who did not have access to any writings of Thales. On the other hand there are claims that he wrote a book on navigation but these are based on little evidence. In the book on navigation it is suggested that he used the constellation Ursa Minor, which he defined, as an important feature in his navigation techniques. Even if the book is fictitious, it is quite probable that Thales did indeed define the constellation Ursa Minor. Proclus, the last major Greek philosopher, who lived around 450 AD, wrote:-

10. Foundations Of Greek Geometry Introduction. The birth of Greek astronomy has been attributed to thales of miletus.Thales brought from Egypt a number of fundamental geometric principles. http://www.perseus.tufts.edu/GreekScience/Students/Mike/geometry.html

Please note: These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. We assume no responsibility over the content of these papers: we present them as is as a part of the course, not as documents in the Perseus Digital Library . We do not have contact information for the authors. Please keep that in mind while reading these papers. Foundations of Greek Geometry Michael Tirabassi Look at the comments on this paper. Introduction The birth of Greek astronomy has been attributed to Thales of Miletus. Thales brought from Egypt a number of fundamental geometric principles. He was able to take what he learned, develop upon it, and put it to practical use for the Greeks. Another important contributor to the foundation of Greek geometry was Pythagoras. Pythagoras is credited with the discovery of the famous Pythagorean theorem which equates the sides of a right triangle. Pythagoras and his followers, the Pythagoreans, developed and proved a few significant theorems and may have discovered the existence of irrational numbers. Plato also played a crucial role in laying out the beginnings of Greek geometry. His main contribution was not the in the content of his discoveries, but in his contribution to the philosophy of mathematics. Thales Thales, an Ionian who was active near the start of the sixth century B.C.,(Herodotis I, 74) has been credited with completing a number of tasks that imply he must have had a basic knowledge of the underlying geometric theorems. Thales was able to determine the height of a pyramid by measuring the length of its shadow at a particular time of day (Heath pp. 128-139). He may have been able to do this in a couple ways. The simplest way would be to measure the shadow of the pyramid at the time of day when an objects shadow was the same length as the height of the object. Thales may have been able to observe that at a certain position of the sun an objects height is equal to the

11. Thales Biography of thales of miletus (624BC547BC) thales of miletus. Born about 624 BC in Miletus, Asia Minor (now Turkey) Main index. thales of miletus was the son of Examyes and Cleobuline http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Thales.html

Thales of Miletus Born: about 624 BC in Miletus, Asia Minor (now Turkey) Died: about 547 BC in Miletus, Asia Minor (now Turkey) Click the picture above to see five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Thales of Miletus was the son of Examyes and Cleobuline. His parents are said by some to be from Miletus but others report that they were Phoenicians. J Longrigg writes in [1]:- But the majority opinion considered him a true Milesian by descent, and of a distinguished family. Thales seems to be the first known Greek philosopher, scientist and mathematician although his occupation was that of an engineer. He is believed to have been the teacher of Anaximander (611 BC - 545 BC) and he was the first natural philosopher in the Milesian School. However, none of his writing survives so it is difficult to determine his views or to be certain about his mathematical discoveries. Indeed it is unclear whether he wrote any works at all and if he did they were certainly lost by the time of Aristotle who did not have access to any writings of Thales. On the other hand there are claims that he wrote a book on navigation but these are based on little evidence. In the book on navigation it is suggested that he used the constellation Ursa Minor, which he defined, as an important feature in his navigation techniques. Even if the book is fictitious, it is quite probable that Thales did indeed define the constellation Ursa Minor.

12. Thales Of Miletus --  Encyclopædia Britannica thales of miletus Encyclopædia Britannica Article. MLA style thales of miletus. Encyclopædia Britannica. 2004. Encyclopædia Britannica Premium Service. http://www.britannica.com/eb/article?eu=73782&tocid=0&query=ursa minor

13. Thales thales of miletus and the Development of Science in the Greek World. Thales was supposedly born in 625 B.C.E. Historians credit him as the first philosopher to account for phenomenon in natural terms. http://www2.drury.edu/dhale/thales.htm

Thales of Miletus and the Development of Science in the Greek World Thales was supposedly born in 625 B.C.E. Historians credit him as the first philosopher to account for phenomenon in natural terms. He was the first to apply the principles of logos to his account of the world. Thales proposed that water supplied the underlying reality for the entire cosmos. His account existed as one of the first of a series of accounts that attempted to satisfy the Greek craving for a more physical account of phenomenon. Earlier, knowledge based itself upon the principles of mythos and inspiration. However, with the rise of natural philosophy in Greece, individuals could think of reality as an entity somewhat apart from the seemingly arbitrary will of the Gods. As Anthony Alioto, in his A History of Western Philosophy points out: "Although natural law seems to be an act of legislation by the will of Zeus, the god himself has become a personality, drifting away from the sky he representsas do the other gods. They live upon Mount Olympus in Thessaly, separated from the elements they govern. The implications could be that nature itself, the living and self-changing world the Greeks called...( physis ) is something apart from the gods, like a common stage upon which both humans and gods act out their roles" (25).

14. Thales thales of miletus. Born about 624 BC in Miletus thales of miletus wasthe son of Examyes and Cleobuline. His parents are said by some http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Thales.html

Thales of Miletus Born: about 624 BC in Miletus, Asia Minor (now Turkey) Died: about 547 BC in Miletus, Asia Minor (now Turkey) Click the picture above to see five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Thales of Miletus was the son of Examyes and Cleobuline. His parents are said by some to be from Miletus but others report that they were Phoenicians. J Longrigg writes in [1]:- But the majority opinion considered him a true Milesian by descent, and of a distinguished family. Thales seems to be the first known Greek philosopher, scientist and mathematician although his occupation was that of an engineer. He is believed to have been the teacher of Anaximander (611 BC - 545 BC) and he was the first natural philosopher in the Milesian School. However, none of his writing survives so it is difficult to determine his views or to be certain about his mathematical discoveries. Indeed it is unclear whether he wrote any works at all and if he did they were certainly lost by the time of Aristotle who did not have access to any writings of Thales. On the other hand there are claims that he wrote a book on navigation but these are based on little evidence. In the book on navigation it is suggested that he used the constellation Ursa Minor, which he defined, as an important feature in his navigation techniques. Even if the book is fictitious, it is quite probable that Thales did indeed define the constellation Ursa Minor.

15. Thales - Wikipedia, The Free Encyclopedia From Wikipedia, the free encyclopedia. thales of miletus (circa 635 BC 543 BC)was a pre-Socratic Greek philosopher and one of the Seven Sages of Greece. http://en.wikipedia.org/wiki/Thales

16. Adventures In CyberSound: Thales Of Miletus ADVENTURES in CYBERSOUND. Thales of Miletus 624 c.546 BC. Philosopherremembered for his cosmology based on water as the essence of all matter. http://www.acmi.net.au/AIC/THALES_BIO.html

A D V E N T U R E S in C Y B E R S O U N D Thales 'of Miletus' : 624 - c.546 BC Philosopher remembered for his cosmology based on water as the essence of all matter. According to the Greek thinker Apollodorus , Thales was born in 624; the Greek historian placed his death in the 58th Olympiad (548-545) at the age of 78. No writings by Thales survive, and no contemporary sources exist; thus, his achievements are difficult to assess. Inclusion of his name in the canon of the legendary Seven Wise Men led to his idealization, and numerous acts and sayings, many of them no doubt spurious, were attributed to him. According to Herodotus , Thales was a practical statesman who advocated the federation of the Ionian cities of the Aegean region. The Greek scholar Callimachus recorded a traditional belief that Thales advised navigators to steer by the Little Bear (Ursa Minor) rather than by the Great Bear (Ursa Major), both prominent constellations in the north. He is also said to have used his knowledge of geometry to measure the Egyptian pyramids and to calculate the distance from shore of ships at sea. Although such stories are probably apocryphal, they illustrate Thales' reputation. The Greek writer Xenophanes claimed that Thales predicted the solar eclipse that stopped the battle between the Lydian Alyattes and the Median Cyaxares, evidently on May 28, 585.

17. Thales Of Miletus thales of miletus. fl. 6th century BC. Philosopher remembered for hiscosmology based on water as the essence of all matter. According http://www.kat.gr/kat/history/Greek/Ph/ThalesMiletus.htm

Thales of Miletus fl. 6th century BC Philosopher remembered for his cosmology based on water as the essence of all matter. According to the Greek thinker Apollodorus, he was born in 624; the Greek historian Diogenes Laertius placed his death in the 58th Olympiad (548-545) at the age of 78. No writings by Thales survive, and no contemporary sources exist; thus, his achievements are difficult to assess. Inclusion of his name in the canon of the legendary Seven Wise Men led to his idealization, and numerous acts and sayings, many of them no doubt spurious, were attributed to him. According to Herodotus In geometry Thales has been credited with the discovery of five theorems: (1) that a circle is bisected by its diameter, (2) that angles at the base of a triangle having two sides of equal length are equal, (3) that opposite angles of intersecting straight lines are equal, (4) that the angle inscribed in a semicircle is a right angle, and (5) that a triangle is determined if its base and the angles relative to the base are given. His mathematical achievements are difficult to assess, however, because of the ancient practice of crediting particular discoveries to men with a general reputation for wisdom.

18. - Great Books - thales of miletus (c. 634 BCc. 546 BC), Thales, presocratic Greek philosopherwho lived around 600 BC. Thales lived in the city of Miletus, in Ionia. http://www.malaspina.com/site/person_1113.asp

Thales of Miletus (c. 634 BC-c. 546 BC) Thales, presocratic Greek philosopher who lived around 600 BC. He is generally considered the first philosopher in the Greek tradition and is considered the father of science as well. He is numbered among the Seven Sages of Greece. Thales is remembered for arguing that water is the essence of all things. This argument is significant because it is the first attempt to explain the physical world without reference to a supernatural power. Prior to Thales all such explanations relied on gods or other mythological forces. Thales lived in the city of Miletus, in Ionia. The Ionians were well-traveled and had many dealings with Egypt and Babylon, and it is possible that Thales had studied in Egypt as a young man. In any event, Thales was almost certainly exposed to Egyptian mythology, astronomy, and mathematics, as well as other traditions alien to the Homeric traditions of Greece. It is perhaps because of this that his inquiries into the nature of things took him beyond traditional mythology. Thales had a profound influence on other Greek thinkers and therefore on Western history. Anaximander is sometimes considered to be a pupil of Thales. And it is reported by early sources that one of Anaximander's more famous pupils, Pythagoras , visited Thales as a young man, and was advised to travel to Egypt to further his philosophical and mathematical studies. Many philosophers followed his lead in searching for explanations in nature rather than in the supernatural; others returned to supernatural explanations, but couched in the language of philosophy, rather than myth or religion.

19. Introductory Remarks: Thales Of Miletus, Father Of Physics, By Robert Kern Curti Introductory Remarks thales of miletus. The modern title, physics,of the course of study upon which the reader is embarking reveals http://www.rain.org/~rcurtis/thales.html

Introductory Remarks: Thales of Miletus The modern title, physics, of the course of study upon which the reader is embarking reveals something of the nature of that course. The word is derived from the Latin physica , natural science, which in turn is derived from the Greek plural phusika of the adjective phusikos meaning "of or pertaining to nature." In recent decades the scope of the meaning of the word physics has narrowed considerably until it is a "science that deals with matter and energy and their interactions in the fields of mechanics, acoustics, optics, heat, electricity, magnetism, radiation, atomic structure, and nuclear phenomena." As such a definition implies, the way to know and understand what physics is, is to do physics. This, it is suggested, is the true destination of this course of study. The earlier title of a course such as this, still found in an occasional college catalogue, is "natural philosophy." While the philosopher is the "lover of wisdom," the word "philosophy" has come to mean a "search for truth through logical reasoning" and so the name "natural philosophy" is richer in meaningit not only tells us that our study is the study of nature but also implies that this study will be one not merely of simple observation but will also emphasize logical reasoning. The philosopher and the physicist of today share another common link: the same man, Thales of Miletus, is claimed by each as the FATHER of his profession. His biographer, Diogenes Laertius, narrated anecdotes about him which are worthy of mention for the sake of tradition rather than fact. Two of these anecdotes are quite famous, namely, that he fell into a well or irrigation ditch while star-gazing, and that, predicting a scarcity of olives, he cornered the olive market.

20. TMTh:: THALES OF MILETUS MATHEMATICIAN, PHYSICIST. thales of miletus (fl. 640546 BC) Life Oneof the Seven Sages of Ancient Greece, and chronologically the http://www.tmth.edu.gr/en/aet/1/89.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ... PHYSICISTS MATHEMATICIAN, PHYSICIST THALES OF MILETUS (fl. 640-546 BC) Life One of the Seven Sages of Ancient Greece, and chronologically the first of the Greek philosophers, Thales of Miletus is considered the founder of European philosophy and science. He was born in Miletus, in Asia Minor; his father being called Hexamios and his mother Cleoboulene. The family was of Boeotian origin, and Thales considered himself a descendant of Cadmus and Agenor. Work Thales was the first to abandon a blind empiricism and turn to a theoretical investigation of causes. This is his most important contribution to the development of a universal philosophical and scientific spirit. He attempted to explain things, and give them a justification in theory. He held water to be the prime origin of all things, positing that every kind of matter is produced through the transformation of this uncreated and imperishable elemental substance. He made a number of purely scientific discoveries in geometry, astronomy and physics; he developed his own philosophical system; and he took part in the political life of Ionia. He also built large engineering works, devised instruments for calculating distances, and travelled widely for both commercial and scientific purposes. In geometry, Thales is credited with 5 theorems: 1) that a circle is bisected by its diameter; 2) that the angles at the base of a triangle having two sides of equal length are equal; 3) that opposite angles of intersecting straight lines are equal; 4) that the angle inscribed in a semicircle is a right angle; and 5) that a triangle is determined if its base and the angles relative to the base are determined.

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