Pulse pine nuts in a food processor until finely ground (be careful not to grind to a paste). Add arugula, oil, cheese, and salt and pulse until almost smooth.
Heat oil in a 12-inch heavy skillet over moderate heat until hot but not smoking, then cook garlic, stirring, until golden, about 2 minutes. Discard garlic. Add tomatoes and salt and cook, stirring occasionally, until tomatoes are collapsed but not falling apart, 15 to 20 minutes.
Cook fettuccine in a 6- to 8-quart pot of boiling salted water until al dente. Drain pasta in a colander and return to pot. Add arugula purée and toss until well coated. Transfer to a platter or plates and top with tomato sauce.
