This appears to be a bacterial spot. Bacteria can enter through wounds or stomates. Moisture in the form of rainfall or relative humidity greater than 95 percent for several days is required for infection and later disease development. Dry weather for 2 weeks can arrest the disease. Controls include the selection of resistant cucumber varieties, use of disease-free seed, and a 2 year rotation out of all cucurbits. Removal of the infected leaves if possible is helpful also. Copper fungicides can be applied to slow disease spread during particularly wet periods but can be dropped if dry weather continues for 2 weeks. Always read and follow label directions when applying chemicals.