In the unorganized portion of his second notebook [6], Ramanujan has recorded modular equations corresponding to signatures 3 and 4. The proofs of the same can be found in Chapter 33 of [3]. In this article, we use the method of parametrization to establish a few new modular equations in signature 3 and 4 which are analogous to modular equations in signature 2 due to Ramanujan. Using the same method, we also prove a few modular equations in signatures 3 and 4, recorded by Ramanujan in his second notebook [6].
