The Medicines Co., of Parsippany, N.J., said it proposes to offer $350 million aggregate principal amount of convertible senior notes due 2023. The company also expects to grant to the initial purchasers an option to purchase up to an additional $52.5 million of the notes. The company expects to use a portion of the net proceeds to repurchase about $220 million of its 1.375 percent convertible notes due 2017 in privately negotiated transactions effected through one of the initial purchasers. The remainder will be used for general corporate purposes.