Nina.Wan
Paper: Rough Draft
2016.11.10
Tutor: Ms.Courm
Claudius Ptolemaeus Claudius Ptolemaeus was born in Ptolemais Hermiou, lived in Alexandria, Egypt ,and has an important role in the history of astronomy and geography and lived with the prerogative and political rights of Roman citizenship. It has been speculated that his parents were Greek, but moved to Egypt, his name affirms his parents’ relocation because Ptolemaeus is a Greek Egyptian name and Claudius is a Roman name, indicating he was a Roman . After the Romans conquered at 27 BC, even though the Alexandria is the second-large city at that time ,it only just had a little funding which was used for science and the development of scientific study of the stars. Ptolemy was the only great scientist…show more content… First we need to find make a E on the BD and this E has to make a △ABE then ∠BAE=∠CAD and ∠ABE=∠ ACD ,and △ABE has a an intersection between B and D knew as E. At this time ∠ABE=∠ACD and ∠BAE=∠CAD. Thus, △ ABE is similar to△ ACD(1). When we know the △ ABE is similar to△ ACD, the properties of similar triangles can give us that AB/AC=BE/CD and after changing the denominators up to each side, we got AB*CD=AC*BE.
Then we have to do the same thing with △ABC and △AED. Because of △ABE is similar to △ACD,we can have AD/AC=AE/AB because of the similar triangles, and we have already knew that ∠BAC=∠EAD, so △ABC is similar to △AED. Then we can have BC/ED=AC/AD then BC*AD=AC*DE was gotten.
From BC*AD=AC*DE and AB*CD=AC*BE, we can have this equation - AB*CD+BC*AD=AC*BE+AC*DE and after we simplified it twice ,we got AC（BE+DE）=AC*BD. This also has a converse theorem “In a quadrilateral, if the sum of the products of the two pairs of opposite sides is equal to the product of the diagonals in a same quadrilateral then the quadrilateral can be inscribed in a
