Working of Hex Schmitt−Trigger Inverter as a Sawtooth and Square Wave Producer
The sawtooth is actually positive and negative exponential decays, not lines.  However, for many purposes this is close enough to a sawtooth.

To visualize this better, let's do a example with hard numbers.  Let's say this is a ideal Schmitt trigger inverter running from 5 V with thresholds at 2 and 3 volts.  Let's start with the input at 0 (the cap discharged).  This will make the output high, so now the cap charges up with a exponential decay towards 5 V.  When it gets to 3 V, the inverter output will go low.  Now the cap discharges with a exponential decay towards 0.  When it gets to 2 V, the output will go high until the cap reaches 3 V.

This process of charging, discharging, charging, etc between 2 and 3 volts will repeat indefinitely.  The charge and discharge times are the same, so the output will be a square wave.

Each charge and discharge is terminated 1/3 of the way to the final value, which is .41 time constants.  With the values you show of 1 &micro;F and 100 &Omega;, the time constant is 100 &micro;s.  Each phase will therefore last 41 &micro;s.  The period will be 81 &micro;S, and the frequency will be 12 kHz.

Keep in mind that the 2 V and 3 V thresholds were only numbers for the example above.  See the datasheet for the real thresholds, from which you can compute the real high and low times, and from that the period and frequency.  Also note that 100 &Omega; is a excessive load for most real inverters.