Protractor on the dial from 180°, as the dial is graduated from opposite zero marks to 90° each way. Since the spaces, both on the main scale and the Vernier scale, are numbered both to the right and to the left from zero, any angle can be measured. The readings can be taken either to the right or to the left, according to the direction in which the zero on the main scale is moved. Reading the Vernier scale: The bevel protractor Vernier scale may have graduations of 5′ (minutes) or 1/12°. Each space on the Vernier scale is 5′ less
Foundations of geometry a more abstract treatment of one of Pieri's systems (from 1909) based on the primitives "point" and "congruence". Starting with Peano, there has been a parallel thread of interest amongst logicians concerning the axiomatic foundations of Euclidean geometry. This can be seen, in part, in the notation used to describe the axioms. Pieri claimed that even though he wrote in the traditional language of geometry, he was always thinking in terms of the logical notation introduced by Peano, and used that formalism to see how to prove things. A typical example of this type of notation can be found in