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Euclid of alexandria
- 2. Euclid of Alexandria Alexandria Death of Alexander the Great Ptolemies Museum and Library Ptolemy II Euclid Elements (Stoichia) Obscure!!! Ptolemy I
- 3. Euclid of Alexandria Lost works DID YOU KNOW THAT!!! Of what Euclid wrote, more than half has been lost!!! Treatise on conics in four books Treatise on Solid Loci (the Greek name for the conic sections) Surface Loci Pseudaria (or fallacies) three books on Porisms the loss of Euclidean Porisms Pappus Porism is intermediate between a theorem, in which something is proposed for demonstration , and a problem, in which something is proposed for construction. A proposition in which one determines a relationship between known and variable or undetermined quantities
- 4. Euclid of Alexandria Extant works Elements Data Division of Figures Phaenomena Optics Optical Phenomena optics catoptrics dioptrics The geometry of direct vision The geometry of refracted rays The geometry of reflected rays
- 5. Euclid of Alexandria Extant works Euclid’s Optics “emission” theory of visionEuclidean Division of Figures Arabic Scholars Arabic Translations Latin Current modern languages
- 6. Euclidean Division of Figures Euclid of Alexandria Includes a collection of thirty-six propositions concerning the division of plane configurations Proposition 1 Calls for the construction of a straight line that shall be parallel to the base of a triangle and shall divide the triangle into two equal areas. Proposition 6 Call for the division of a parallelogram into two equal parts by a line drawn through a given point on one of the sides or (proposition 10) through a given point outside the parallelogram. Final Preposition (36) Asks for the division of a quadrilateral in a given ratio by a line through a point on one of the sides of the quadrilateral.
- 7. Euclid of Alexandria Euclid’s Data Fifteen definitions magnitu des lo ci Ninety-five statements Conditions and magnitudes If two magnitudes a and b are given, their ratio is given, and that if one magnitude is given and
- 8. Euclid of Alexandria E B D CFA We are told that if a given (rectangular) area AB is laid off along a line segment of given length AC and if the area BC by which the area AB falls short of the entire rectangle AD is given, the dimensions of the rectangle BC are known.
- 9. Euclid of Alexandria The elements First textbook Introductory textbook covering all elementary mathematics A bearing to the rest of mathematics the same sort of relation as that which the letters of the alphabet have in relation to language.
- 10. Euclid of Alexandria The elements Thirteen books First half- dozen Elementary Plane Geometry “The extremities of a line are points” “A straight line is a line in which lies evenly with the points on itself.” “The extremities of a surface are lines”
- 11. Postulat es 1. To draw a straight line from any point to any point 2. To produce a finite straight line continuously in a straight line. 3. To describe a circle with any center and radius. 4. That all angles are equal. 5. That, if a straight line falling on two straight line makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than the two right angles. Euclid of Alexandria
- 12. Common notions: 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another. 5. The whole is greater than the part. Euclid of Alexandria
- 13. End.. Sa Wakas!!!! Euclid of Alexandria
- 15. Euclid of AlexandriaEuclid of Alexandria
Hinweis der Redaktion
- DEATH OF ALEXANDER THE GREAT-led to internecine strife among the generals in the Greek army, but after 300 BCE, control of the Egyptian portion of the empire was firmly in the hands of thePTOLEMIES- Macedonian rulers of EgyptPTOLEMY I- laid the foundations for two institutions at Alexandria that would make it the leading center of scholarship for generations.MUSEUM and LIBRARY- both amply endowed by him and his sonPTOLEMY II-brought to this great research center men of outstanding scholarship in a variety of fields. And one of them is…EUCLID- author of the most successful mathematics textbook ever written entitledELEMENTS (Stoichia)- Perokahitnapakasikatnieuclid at kahit best-seller xa, remarkably little is known of his life.. He is so..OBSCURE- no birthplace associated with his name/Though samga edition saiyang books ginapadayagiyangpagkataongasiyadwsi Euclid of Megara, but this is a case of mistaken identityFrom the nature of his work, it is presumed that Euclid of Alexandria had studied with students of Plato,
- Including some of his more important compositions such as TREATISE ON CONICS IN FOUR BOOKSTHE LOSS OF EUCLIDEAN PORISMS-particularly tantalizingtantalizing present participle of tan·ta·lize(Verb)VerbTorment or tease (someone) with the sight or promise of something unobtainable.Excite the senses or desires of (someone).PAPPUS-later reported that (NEXT)Others described porisms as a (NEXT)a (1) : something offered for consideration or acceptance :proposal (2) : a request for sexual intercourseb : the point to be discussed or maintained in argument usually stated in sentence form near the outsetc : a theorem or problem to be demonstrated or performed2a : an expression in language or signs of something that can be believed, doubted, or denied or is either true or falseb : the objective meaning of a proposition3: something of an indicated kind to be dealt with <the farm was never a paying proposition>
- Five works of Euclid that have survived to our day: ELEMENTS, DATA,DIVISION OF FIGURES, PHAENOMENA AND OPTICSThe last mentioned is of interest to the ancients so they had divided the study of optical phenomena into three parts: OPTICS, CATOPTRICS nd DIOPTRICSNOTE:::!!!!!CATOPTRICA-in doubtful authenticity, being perhaps by Theon of Alexandria, who lived some six centuries later
- EUCLID’S OPTICS-noteworthy for its espousal of an“EMISSION” THEORY OF VISION- according to which the eye sends out rays that travel to the object. Contrasted by the ARISTOTELIAN DOCTRINE-in which an activity in a medium travels in a straight line from the object to the eye.But it should be noted that the mathematics of perspective is the same, no matter which of the two theories is adopted.tanαtan 𝛽<𝛼𝛽 𝑖𝑓 0<𝛼<𝛽<𝜋2=one widely used in antiquity among the theorems found in Euclid’s OpticsEUCLID DIVISION OF FIGURES-work that would have been lost kung hindidahilsaArabic Scholars.hindiito nag survive nungtymsnggreekperobago pa nawala, may arabic translationna then later translated into latin then ultimately into current modern languagesEUCLID’S OPTICS-noteworthy for its espousal of an“EMISSION” THEORY OF VISION- according to which the eye sends out rays that travel to the object. Contrasted by the ARISTOTELIAN DOCTRINE-in which an activity in a medium travels in a straight line from the object to the eye.But it should be noted that the mathematics of perspective is the same, no matter which of the two theories is adopted.tanα/(tan 𝛽)<𝛼/𝛽 𝑖𝑓 0<𝛼<𝛽<𝜋/2=one widely used in antiquity among the theorems found in Euclid’s OpticsOne object of the Optics was to combat an Epicurean insistence that an object was just as large as it looked, with no allowance to be made for the foreshortening suggested by perspective.EUCLID DIVISION OF FIGURES-work that would have been lost kung hindidahilsaArabic Scholars.hindiito nag survive nungtymsnggreekperobago pa nawala, may arabic translationna then later translated into latin then ultimately into current modern languages
- EUCLID’S DATA- somewhat similar in nature and purpose to the Division of Figures -a work that has come down to us through both the Greek and the Arabic. -composed for use at the Museum of Alexandria, serving as a companion volume to the first six books of the Elements in much way that a manual of tables supplements a textbook. -opens with FIFTEEN DEFINITIONS concerning MAGNITUDES AND LOCIThe body of the textcomprises NINETY-FIVE STATEMENTS concerning the implications of CONDITIONS AND MAGNITUDESThe first two state that ….LOCI-d set of all points whose location is determined by stated conditions
- Some of the statements are geometric equivalents of the solution of quadratic equations. For example (NEXT)The shortcutThe geometric solution given by Euclid is equivalent to this, except that the negative sign before the radical is used.
- (Surprise)a textbook that by no means the first oneElements of Euclid so far outdistanced competitors that it alone survivedELEMENTS was not, as sometimes thought, a compendium of all geometric knowledge instead (NEXT)ARITHMETIC-in the sense of the English “higher arithmetic” or the American “theory of numbers”SYNTHETIC GEOMETRY-of points, lines, planes, circles, and spheresProclus described the elements as (NEXT)Elements were intended as an exhaustive store of information ..daghankauang authors. Euclid himself made no claim of originality. Yes, the arrangements are his and He supplies the proofs but beyond that, it is difficult to estimate the degree of originalityBEARING-connection