GALILEO REGARDING BEAM STRENGTH

Comparing this with Eq. (4.16), it is evident it gives a maximum stress that is only two-thirds of the correct value. 

However, Galileo does not seek or use absolute values of strength but compares the strength of one beam with that of another. What is used is the proportionalify  

The rest of the second day is devoted primarily to discussion of the relative strengths of prisms and cylinders that fail under their own weight. By prism, he means a column having a square cross section. 

for the same material (same yand same S, when t is doubled in length, d must increase by a factor of 4. This is illustrated in Fig. 4.10, which shows the relative shapes of bodies of the same material about to fail under their own weights. 

In passage 173, Galileo observes thatthe total force required to break the beam of Fig. 4.11 + i ) depends on the loeation of the fulcrum (0). Since 

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