The Last Supper by Leonardo Da Vinci and Jacopo Tintoretto Term Paper

The Last Supper by Leonardo Da Vinci and Jacopo Tintoretto - Term Paper Example Focusing on the theme of the last days of Christ's life, Leonardo da Vinci makes it clear that the ideals of humanism are extremely important to him. The compositional structure of the painting created between 1495 and 1498 corresponds to the aesthetic principles of humanism. The symmetrical organization of the picture confirm this. Jesus is the central figure and six of the apostles are sitting on the left and right of him. In general, the apostles are divided into four groups of three. Behind Jesus, one can see three windows that visually enlarge the space, while there are four doors or curtains on the left and right sides of the picture. All this is consistent with the principles of humanity in relation to the organization of the space. However, the influence of humanism is not limited to these items. Its main value is observed in a special emotionality of the images. Da Vinci has made a special emphasis on the reaction of the apostles in response to Jesus' words about the fact th at one of them would betray him. The phrase â€Å"One of you will betray me† causes a different reaction from all the apostles and this reaction is expressed by a variety of their gestures and facial expressions. In other words, â€Å"together with facial attributes and expressions these gestures depict the essential character of each apostle†. â€Å"These reactions are quite specific to each apostle, expressing what Leonardo called the ‘motions of the mind'†. In spite of the expressivity of these images, the painting shows a certain order.

Newton, Leibniz, and the Invention of Calculus Essay

Newton, Leibniz, and the Invention of Calculus - Essay Example The theorem was the start of the Newton’s mathematical innovation (Dunham 6). In 1666, Newton made his first contribution to calculus through the introduction of fluxions. In the late 1665 before his first publication, Newton had made studies on the tangent problems by combining velocity components of the moving points in a proper coordinate system. This was vital for the introduction of fluxions which is a key component in geometric applications (Edwards 191). Newton was capable of exploiting the concepts of antidifferentiation and differentiation by the substitution methods. This is the equivalent of what is called integration and chain rule by substitution. This is essential in the building of calculus of fluxions (Edwards 196). Newton applied the method of successive approximations in his De Analysi to the reversion of series. Newton proceeds further to use the technique of reversion of series in the discovery of sine and cosine series (Edwards