Euclid's Optics - Wikipedia
Confirmation of Proclus' upper dale comes from the relationship of Euclid to exact scholar not vaunting himself,” as Apollonius was alleged to do; and although. Conic Sections After Euclid, 1. Hippocrates. Menaechmus. Archimedes. Euclid. Apollonius The characteristic relation between the “abscissa” and the. “Like the crest of a peacock, like the gem on the head of a snake, so is mathematics at the head of all knowledge.” (Vendanga Iyotisa).
However, their works were mostly philosophical in nature and lacked the mathematics that Euclid introduced in his Optics. Because Optics contributed a new dimension to the study of vision, it influenced later scientists. In particular, Ptolemy used Euclid's mathematical treatment of vision and his idea of a visual cone in combination with physical theories in Ptolemy's Optics, which has been called "one of the most important works on optics written before Newton".
The postulates in Optics are: Let it be assumed 1. That rectilinear rays proceeding from the eye diverge indefinitely; 2. That the figure contained by a set of visual rays is a cone of which the vertex is at the eye and the base at the surface of the objects seen; 3. That those things are seen upon which visuals rays fall and those things are not seen upon which visual rays do not fall; 4.
That things seen under a larger angle appear larger, those under a smaller angle appear smaller, and those under equal angles appear equal; 5. That things seen by higher visual rays appear higher, and things seen by lower visual rays appear lower; 6.
That, similarly, things seen by rays further to the right appear further to the right, and things seen by rays further to the left appear further to the left; 7.
That things seen under more angles are seen more clearly. Content[ edit ] According to Euclid, the eye sees objects that are within its visual cone. The visual cone is made up of straight lines, or visual rays, extending outward from the eye.
Conic Sections in Ancient Greece
These visual rays are discrete, but we perceive a continuous image because our eyes, and thus our visual rays, move very quickly. This accounts for the difficulty in searching for a dropped needle. Although the needle may be within one's field of view, until the eye's visual rays fall upon the needle, it will not be seen.
This man lived 2 in the time of the first Ptolemy. For Archimedeswho came immediately after the first Ptolemy 3makes mention of Euclid: He is then younger than the pupils of Plato but older than Eratosthenes and Archimedes ; for the latter were contemporary with one another, as Eratosthenes somewhere says. He proceeds by inference.
Since Archimedes lived just after the first [p.
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We may infer then from Proclus that Euclid was intermediate between the first pupils of Plato and Archimedes. Thus Euclid must have flourished c. It is most probable that Euclid received his mathematical training in Athens from the pupils of Plato ; for most of the geometers who could have taught him were of that school, and it was in Athens that the older writers of elements, and the other mathematicians on whose works Euclid's Elements depend, had lived and taught.
He may himself have been a Platonist, but this does not follow from the statements of Proclus on the subject. Proclus says namely that he was of the school of Plato and in close touch with that philosophy 5.
It is true that Euclid's Elements end with the construction of the five regular solids; but the planimetrical portion has no direct relation to them, and the arithmetical no relation at all; the propositions about them are merely the conclusion of the stereometrical division of the work.
One thing is however certain, namely that Euclid taught, and founded a school, at Alexandria.
Apollonius of Perga
This is clear from the remark of Pappus about Apollonius 8: Pappus says on this 9: Another story is told of Euclid which one would like to believe true. This description arose out of a confusion between our Euclid and the philosopher Euclid of Megara who lived about B. But, if Valerius Maximus took Euclid the geometer for a contemporary of Platoit could only be through confusing him with Euclid of Megara.
But one Constantinus Lascaris d. Hence also GreekRoman and Arabian geometers not a few, who undertook the task of illustrating this work, published commentaries, scholia, and notes upon it, and made an abridgment of the work itself.
For this reason the Greek philosophers used to post up on the doors of their schools the well-known notice: Damascus and Tyre were no doubt brought in to gratify a desire which the Arabians always showed to connect famous Greeks in some way or other with the East. The readiness of the Arabians to run away with an idea is illustrated by the last words [p.