An Etymological Dictionary of the German Language/Säge
Säge, f., ‘saw,’ from the equiv. MidHG. sëge, sage, OHG. sëga, saga, f.; comp. Du. zaag, AS. sage, f., and sagu, f., E. saw; OIc. sǫg, f. (Goth. *saga, f., is wanting). A derivative of an Aryan root sek, sok, whence also Lat. secâre, ‘to cut,’ securis, ‘hatchet’; see further under Sichel. The ä of ModHG. Säge is based, as is indicated by the modern Alem. dials., on ë; hence there is the same gradation in OHG. sëga and saga as in OHG. rëhho and AS. racu (see Rechen), or in HG. Nacken and E. neck. With the Aryan root sek, sok, are also connected in Teut., OHG. sahs, ‘sword’ (see Messer), E. scythe, and AS. sîðe, from sigþe; comp. OIc. sigðr, m., ‘sickle,’ OHG. sëh, MidHG. sëch, ‘ploughshare,’ and the cognates of Sense.