We have measured directly via laser absorption spectroscopy the 6s2S1/2 → 7p2P3/2 to the 6s2S1/2 → 7p2P1/2 transition strength ratio in atomic cesium along with the individual electric dipole matrix elements for both of those transitions. The laser absorption spectrometer constructed for this experiment is described. Our motivation for constructing this apparatus is to perform high precision measurements of transition strengths and ratios important to the interpretation of parity nonconservation measurements and for testing electronic structure calculations in atomic cesium. We find a value for this ratio of 4.461 (23), for the 6s2S1/2 → 7p2P3/2 transition of 0.5759(30) a.u., and for the 6s2S1/2 → 7p2P1/2 transition of 0.2743(29) a.u., all of which are consistent with previously performed measurements.