The common inferences in Euclid's Stoikeioon are great. They set the tone for the whole work, The material is to exposit the theurgical nature of the Pythagorean philosophy. It does divide into 2 (dual/ isos) :
•exploration of the relationships distinguished within any object(subjectively output);
•-exposition of the analysis and synthesis of an object into distinct and distinguished parts that recombine into the whole through duality relationships in the comon inferences, and other defined and exposited multiple form relationships, including factorisation into protoarithmoi.
The common inferences for dynamic situation and for explosive situations are not in the Stoikeioon. They are in Euclid's other works, and the works of others . The dynamic whole is greater than the dynamic part, etc.
When considering the dynamic situation one can look at the change in space with respect to position, that is without time, or we can look at the change in space solely with respect to time. This we can call motion/growth.
We can look at the change in space with respect to both space and time, in which case we can identify 3 cases: time before space, space before time ,space and time (at the same time?) The last one highlights an issue: what is time and can one stand apart from it?
As an observation, if i took a film of an event with a clock clearly visible, i can embed time within a common frame of reference. The frame of reference is a window onto a time and space, it is a screen on which a sensory intensity is that has been processed is projected. Therefore it does not say anything about the intensities, it says a whole lot about the processing system that is representing it.
We have developed a sophistication through photography and film, that enable us to posit that we have a subjective process that is akin to this filming process, in all its detail.
Time then drops out o the equation, and film sequence becomes important. This equates to subjective process sequence for each individual, and a statistically averaged sequence for a communal output of the individual proceeses.
Do we create such a statistically averaged sequence? Empires and emperors attempted to create this sequence through mythological ritual attached to the processional motions of the stars and planets.
Although this is not a film like sequence, it is a common or cultural sequence which helps to order events. It is however unlikely that it would record a film sequence.It is the memory of the sequence that creates our notion we call "Time".
Thus ultimately we can look at a dynamic situation as a change of space , or/and time with respect to sequence.
Now sequence theory does not posit one unique sequence, therefore one can look at dynamic situations as space-time changes with respect to sequence changes, that is sequence change with respect to a sequence that moves through a set of sequences.
The common inferences for motion began to be established by Newton, The common inferences for space were developed onder differenial geometry principally by Leibniz. Galculus has developed some common inferences, but not in the same format as Euclid.. There is work to be done