The Art Of Euclids Writing Essays - Foundations Of Geometry

The Art Of Euclid's Writing In Elements book one, Euclid incorporates stylistic devices in the process of proving a series of mathematical theories. One stylistic aspect of Euclid's writing is his use of common notions, such as the whole being greater than the part, and postulates, such as drawing a line from any point to any point. His early use of common notions and postulates do not merely help to prove the particular proposition, but is used in later propositions to persuade the reader of his proofs as well as to instill confidence in himself and the reader of the conclusions he arrives at in the propositions. Even before the actual propositions begin, Euclid lists the common notions and postulates of which he and the reader agree with. By doing this, Euclid and the reader have confidence in the proofs. In another way, the words ?common notions? and ?postulates? can be substituted by ?common sense? because it is ten points which everyone believes to be true. For example, the majority of the conclusions in proposition thirteen were arrived at using common notions. The last three steps in finally proving proposition thirteen were based on common notions. Since everyone agrees with the common notions, Euclid is confident that he is making a logical progression in proving that if a straight line set up on a straight line make angles, it will make either two right angles or angles equal to two right angles. Because of the general agreement of the postulates and the common notions, and by listing them in advance, Euclid is confident that he is correct when he makes assumptions based on them. In the same sense, the reader also holds the conclusions that Euclid arrives at to be true. Another possibility to Euclid's use of postulates and common notions is that he often uses postulates to set up a problem in terms in which he knows to be correct and then concludes the proposition with a common notion. Euclid is confident that if he can arrive at a common notion for the last step, he is able to prove the proposition using that particular common notion. An example of this is proposition two in which his first step in proving the proposition uses postulate one and by a logical progression arrives at common notion one in the end to prove the proposition. Another reason for Euclid's use of common notions and postulates is the desire to persuade the audience that he is correct when he uses common notions to prove postulates. For example, in proposition four, which states that if two triangles have the two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be equal to the triangle, and the remaining angles will be equal to the remaining angles respectively, namely those which the equal sides subtend, Euclid's last step refers to common notion four, which ultimately proves the proposition. Because Euclid knows the reader agrees with the common notions, he can easily persuade them when he stakes a claim in order to prove a proposition. Another example is proposition two, that places at a given point (as an extremity) a straight line equal to a given straight line, which is solely proven using postulates and common notions . In this case, Euclid can easily persuade the reader because every step of the proposition involved either a postulate or a common notion. Since the reader accepts all the postulates and common notions to be true, Euclid can easily persuade the reader when all a proposition contains is common notions and postulates. In another instance, Euclid uses both a postulate and a common notion to prove one of the steps of proposition fifteen which states that if two straight lines cut one another, they make the vertical angles equal to one another. By fulfilling the conditions of a postulate and a common notion, the proposition gives the reader no doubt that the proof will work. Euclid also uses a proposition proven by a common notion to prove a later proposition. For example, propositions four and ten are correlated in this

Shakespeare play The Merchant of Venice Essays

Shakespeare play The Merchant of Venice Essays Shakespeare play The Merchant of Venice Essay Shakespeare play The Merchant of Venice Essay Essay Topic: Merchant Of Venice Play The plot of the story is that the merchant of Venice (Antonio) borrows money from a Jewish moneylender (Shylock) and Antonio has to pay the money back to shylock within three months otherwise Shylock can take a pound of flesh from Antonios body. There is a daughter (Portia) with a rich father and when the father died he left all the money to the person that marries his daughter, but you cant marry his daughter just like that, you have to choose a chest out of the choice of three but you have to choose the right one. I am doing my coursework on Bassanio; He is a Best friend of Antonio and he goes to Belmont on the search for love and wealth and tries to choose the correct chest and marry Portia e.g. Portia says You must take your chance and attempt to choose at all, or swear before you choose, if you choose wrong, never to speak to lady afterward in a way of marriage: Therefore be advisd This means that she cant choose who she marries, she has to wait and see who chooses the right box, then she has to marry them. Act 4 Scene 1 This scene is the court scene where Shylock has taken Antonio to court because Antonio could not pay back the three thousand ducats that Shylock had lent him. Antonio oldest and best friend has chosen the right chest and married Portia, then he heard that his best friend was about to die, so he told Portia to stay in a nunnery until he gets back and he rushes off to Venice to see if he can convince Shylock to forget about his bond and not take a pound of his flesh. Portia wants to go with him so she secretly goes to Venice with her maid and they pretended to be the lawyer and the doctor. They both dress as men and they try and save Antonio as much as they can even with Bassanio trying to give Shylock thrice the amount of money for his bond e.g. Nerissa says Why shall we turn to men? They turn to men so that their husbands will not recognize them. Portia looks through the bond and realises that it has nothing about blood so then she says that shylock must take a pound of his flesh but not spill a drop of his blood e.g. Portia says Therefore prepare thee cut off the flesh. Shed no blood, nor cut thou less, nor more, but just a pound of flesh. When this is said Portia has come across a solution to stop Antonio from dying because you cant cut flesh without dripping blood. So shylock tries to take a pound of flesh but realises that he will not be able to do this so he decides to take the money afteral. Portia tells them that he has to take the pound of flesh because that is the bond, but shylock decides that he cant do it and has to leave and lose his money and not have his bond. Then Portia says that he must not leave because he has tried to kill someone so he has to give Antonio a third of his money for trying to kill him. After Shylock has left, Antonio and Bassanio praises Portia for saving Antonio and asks if there is anything that they can do. Then Portia judges Bassanio and asks him if he would give her his wedding ring and he says This ring, good sir? Alas! It is a trifle, I will not shame myself to give you this. Bassanio doesnt give Portia the ring because he loves her. Then Portia leaves pleased because she did not leave with the ring and she can trust him now, but then Antonio says to Bassanio My lord Bassanio, let him have the ring: Let his deserving and my love withal be valud gainst your wifes commandments. Then Bassanio takes off his ring and tells Gratiano to take the ring to Portia and he does. When Gratiano catches up with Portia he gives her the ring and then she has been let down because her husband gave away the wedding ring she gave to him Portia says to Nerissa We should have old swearing that they did give the rings to men but well outface them, and outswear them too. This basically means that youre not supposed to give your wife/husbands rings away but he did just to please a friend. Shakespeares use of language in this play is very good because the rich and wealthy people speak in iambic pentameter, which means that there are ten words or syllables to a sentence, where as the not so rich people just talk normally, Shakespeare as used rhyming couplets at the end of each scene. This shows that it is actually the end of the scene, in act 1 scene 3 Antonio is creating the bond so he can borrow three thousand ducats but Bassanio doesnt think he should create this bond so Bassanio is speaking in rhyming couplets to try and end the deal or scene he says You shall not seal such a bond for me: Ill rather dwell on my necessity I think this is a really interesting play and an audience that like Shakespeare would like this play very much, but they may have many views to different characters such as Bassanio. I think that the producer would have made Bassanio act as if the audience thought he was a hero but the audience would know that hes really not. Where this play was written along time ago it probably does not have the impact to the audience now compared to how it did back then for example: the audience back then would know exactly how it is so they would like it better but in modern times the audience would first have to understand how life was back then before they could enjoy it like the people in the olden days.