what two renaissance artists does raphael include in his painting the school of athens
The building is in the shape of a Greek cross, which some have suggested was intended to show a harmony between pagan philosophy and Christian theology  (see Christianity and Paganism and Christian philosophy). The architecture of the building was inspired by the work of Bramante, who, according to Vasari, helped Raphael with the architecture in the picture.  The resulting architecture was similar to the then new St. Peter’s Basilica. 
The popular idea that the rhetorical gestures of Plato and Aristotle are kinds of pointing (to the heavens, and down to earth) is very likely. However, Plato’s Timaeus – which is the book Raphael places in his hand – was a sophisticated treatment of space, time, and change, including the Earth, which guided mathematical sciences for over a millennium. Aristotle, with his four-elements theory, held that all change on Earth was owing to motions of the heavens. In the painting Aristotle carries his Ethics, which he denied could be reduced to a mathematical science. It is not certain how much the young Raphael knew of ancient philosophy, what guidance he might have had from people such as Bramante and whether a detailed program was dictated by his sponsor, Pope Julius II.
In 1508, during the High Renaissance (c.1490-1530), the 25-year old painter Raffaello Sanzio, better known as Raphael, was summoned to the Vatican by the ageing pontiff Pope Julius II (1503-13), and given the largest, most important commission of his life – the decoration of the Papal Apartments, including the Stanza della Segnatura. Located on the upper floor of the Vatican palace, this room was used by the Pope as a library. It was here, between 1509 and 1511, that Raphael painted his famous fresco The School of Athens (Scuola di Atene). It was the second mural painting to be finished for the Stanza della Segnatura, after La Disputa, on the opposite wall, and is regarded as one of the greatest Renaissance paintings. The general theme of the picture, indeed the whole room, is the synthesis of worldly (Greek) and spiritual (Christian) thinking, and ranks alongside the finest examples of classically inspired Renaissance art. A rival of the older Michelangelo (1475-1564), Raphael went on to complete three other Papal apartment rooms in the Vatican (known as the Raphael Rooms) and was to remain in Rome serving successive popes until his sudden death in 1520.
In fact Raphael’s painterly skills were soon in such demand that he was obliged to leave more and more work to his assistants, such as Giovanni Francesco Penni (1496-1536), Giulio Romano (1499-1546) and Perino del Vaga (Piero Buonaccorsi) (1501-47). Responsible for numerous altarpieces, such as The Sistine Madonna (1513-14, Gemaldegalerie Alte Meister, Dresden) and The Transfiguration (1518-20, Pinacoteca Apostolica, Vatican), as well as other examples of religious art, he also produced several famous Renaissance portraits of ecclesiastical and secular subjects – such as Portrait of Baldassare Castiglione (1514-15, Louvre) and Pope Leo X with Cardinals (1518, Galleria Palatina, Pitti Palace, Florence). Arguably the finest painter of the Italian Renaissance, Raphael remains one of the best artists of all time.
To the left of Plato, Socrates is recognizable thanks to his distinct features. It’s said that Raphael was able to use an ancient portrait bust of the philosopher as his guide. He’s also identified by his hand gesture, as pointed out by Giorgio Vasari in Lives of the Artists. “Even the Manner of Reasoning of Socrates is Express’d: he holds the Fore-finger of his left hand between that, and the Thumb of his Right, and seems as if he was saying You grant me This and This.”
Mirroring Pythagoras’ position on the other side, Euclid is bent over demonstrating something with a compass. His young students eagerly try to grasp the lessons he’s teaching them. The Greek mathematician is known as the father of geometry, and his love of concrete theorems with exact answers demonstrates why he represents Aristotle’s side of The School of Athens. Experts believe that Euclid is a portrait of Raphael’s friend Bramante.
Diogenes of Sinope (412-323 BC), a cynic philosopher, a student of Antisthenes, who lived in Corinth. His father Icesias was a banker. With his вЂњbeggarвЂќ cup, lying deep in thought on the steps; this is a finely conceived figure which deserves high praise for its beauty and the appropriate negligence of its clothing. Diogenes is seen alone, set apart: [. ] a cynic in his expression, in his bearing, in his attitude. What is he reading? Diogenes, a philosopher, lived in a big barrel, instead of the traditional house. He spent his nights wandering from house to house with a lantern, knocking on peoples’ doors to find out if there was “an honest human inside.” With his audacious intrusion in peoples’ private affairs, he meant to show them that no honest person could be found anywhere in his city. When Alexander the Great went to meet him, he found him sitting in front of his barrel, facing the sun. As a great admirer of Diogenes, Alexander then asked him if there is anything he could give him, which today might be equivalent to being asked whether you would like to win the lottery. Diogenes thought for a while, and then asked politely if the Great King could simply. step aside, because by standing over him with his horse, he was hiding the sun from his face! This answer so impressed Alexander, that he exclaimed that if he were not Alexander, he would have liked to be Diogenes!
Back view of Ptolemy holding earth sphere, facing Strabo (or Zoroaster, represented as an astrologer), holding a celestial sphere. An explanation is that Raphael used the motif of the crown found on coins from the “dynasty of Macedonian kings of the same name who ruled Egypt from 323 to 30 BC
Raphael’s work has always been highly regarded by his contemporaries and followers alike. However, the School of Athens proved less influential in his own century than works by Michelangelo or da Vinci. It is also accepted that with Raphael’s death and the end of magnificent frescoes such as the School of Athens, the classic art of the High Renaissance subsided and was taken in a new direction by Mannerism and Baroque art.
Leonardo da Vinci’s portrait is also self evident in the School of Athens. His reincarnation as Plato is somewhat curious though, given that Leonardo left Florence, and its overt Platonism, for the more congenial Aristotelian circle of scholars, scientists and engineers at Milan. Perhaps it was Raphael’s duel admiration and preference for Plato, combined with his respect for his teacher (Leonardo) that led him to identify the two men.