Study - Alternate Solution

Part of Leonardo's workshop is accessible. Take the stick (leaning against the bench to your right as you enter) and the link lying on the floor. Go to the vertical saw and insert the stick between the two wooden blocks. Use the foot pedal to power the saw, then push the wooden blocks forward to cut the stick into two small sticks.
Leave the house and look for the ladder along the wall to the right. Next, go to the corner of the house and you see a room above with a light on. Place the ladder against the wall. Look at the ladder very carefully to see that one of the rungs is broken.

You should repair the broken rung with the link before climbing up. If you don't, you fall off the ladder and thereafter have to insert the two small sticks to replace the broken rungs.
Climb up the ladder to get to a bedroom adjoining Leonardo's study. Go to the door next to the fireplace, turn the key in the lock and open the door to enter the study.
Doing this causes the level of the red (diabolical) barometer on the conscience gauge to rise.