Saccheri investigated the summit angles of a quadrilateral; his result depended on the postulate chosen. ... Many historians praised Saccheri's book of 39 theorems. ... In his 33rd theorem is where his flaw can be found. ... Even though his book came to an abrupt conclusion, Saccheri's investigation was a crucial step in the evolving of non- Eluclidian geometries. His major achievement was to break ground for the later geometers who now were free to investigate the new geometries. ...

• Word Count: 366
• Approx Pages: 1
• Grade Level: High School

In one particular result he was able to compute the maximum angle that a (paraboloid) ship could list before it capsized - and he did it without calculus! ... On plane equilibriums, shows the fundamentals of mechanics using geometry. In this book are theorems he discovered for the center of gravity of plane figures. ... He tells how he was in the habit of sending them statements of his latest theorems, but without giving proofs. ... Archimedes considered these to be amusements in geometry. ...

• Word Count: 1479
• Approx Pages: 6
• Has Bibliography
• Grade Level: High School

At age thirteen, before Albert had studied geometry, his uncle Jakob taught him the pythagorean theorem: that the sum of the squares n the sides of a right-angled triangle is equal to the square on the hypotenuse. ...

• Word Count: 1127
• Approx Pages: 5
• Grade Level: High School