The goddess Isis has a mythological story that reveals one aspect of her worship. She synthesised Osiris. While this is only a small part of her story it is a crucial one for understanding Euclid and the Greek use of the word isos.
The etymology appears to be a Hellenization of the Egyptian Aset meaning throne. But Iso in Greek is usually taken to mean "even". However it's etymology seems to mean "vein or filament like", establishing a link with equality through splitting into 2. The mixing of these meanings occurs only in Greece as the loan word for Aset is absorbed into the earlier notion of splitting or dividing into veins. We're it not for the myth of Isis restoring the pieces of Osiris, the mathematical connection would have been lost and the notions distinct.
The adoption of Isis as a goddess by all walks of life reflects the accessibility she denotes mythologically. This accessibility extended to Astrologers for whom the title queen of the Heavens becomes highly significant. For Euclid, the secret magic enshrined in her was evoked in the power she gave him to analyse the world like Set, knowing the goddess Isis would restore it to its proper condition as she did with Osiris. This theme runs all the way through the Stoikeioon, but particularly as the notion of Isos, the filaments from the goddess isis which bind all things together.
The pattern runs deeper, because not just filaments, but also veins and skeletal bones are envisaged in the reconstructions and synthesis of Isis, as prepared by Euclid. The secret relationship appears to be the binary relationship of items or sites, as they join, ennoia in the magical faculty of the consciousness, that gonu or rotating corner of judgement we call intellect. The intimations are scant and febrile, and yet they cannot be dispelled. The analogies suggestive and potent and fecund. From this intense religious devotion Euclid fabricates the basis of the astrologers philosophy assenting to Plato's similarly tantalising analogies about form or ideas.
Isis was a real religious phenomenon prior to Christ, and many motifs of her worship are reflected in Christian worship of the Madonna and child. The promise of magical restoration on an individual scale was also appealing. Thus every element of the Christian salvation myths were evident in the Isis osiris Horus myths.
The Stoikeioon, the beginning philosophy of how the world is constructed, is an enduring presentation of a mix of beliefs expectations, hopes and insights which also was pragmatically accessible. The further works of Euclid in the progression of the course material did not enjoy the same popularity as the Stoikeioon. This has distorted the apprehension of the Stoikeioon and obscured its true nature as an introductory course in philosophy 101!
The philosophy of Isis is the pragmatic application of the content of her mysteries, focussing on the reconstruction and synthesis of reality after it has been torn apart by analysis! That we still use this synthesis method 3000 years after it was developed and 2000 years after it was written down testifies to an essential true synthesis method found for spatial objects. It also implies an essential analytical process that underpins it.
Both is and os derive from a common idea: an observation of the analytical structure of form . Form is analysable into fibre and this fibre is flexible (is) or rigid ( os) , and it is also connected. Thus analysis or breaking a form reveals its substructures (is and os) but also how they are synthesised. The notion iso relates to this connected fibrous structure and connotes how one becomes many and many one.
Closer inspection revealed a statistical process: one mainly split into 2 equal or nearly equal fibres. This is not always the case, but it is a common enough observation to form the notion of ISP:- dividing into 2. The notion of duality is not distinct here, iso covers all kinds of splitting into 2 parts.mit is only in rhetorical descriptions of pragmatic activities that it's meaning has to be pinned down as duality a precursor to equality.
A philosophy of quantity as standard measures has to define these things, but culturally the terms have a context based use and interpretation loosely around the idea of splitting into related parts. The connection of the Goddess Isis synthesising the related parts of Osiris is too obvious to ignore. The religious or prayerful act of combining pieces of knowledge and definitions was part of Euclid's devotional act of meditation as well as the material of his course in basic philosophy. Much of what follows is based on his apprehension of the mystery of synthesis and the inner understanding of isos–Isis and Osiris.
The methods of exhaustion rely on these immutable principles, and the old saw proving pi to be equals to 4 is an excellent example of this and how little we understand the mystery of duality, Isos.
It is a fascinating exercise to work out the relationship between a circular arc and the diameter. It is a quintessential relationship which gives rise to the ratio i, the ratio of units pi, the function call sqrt(–), the apprehension of orientation, and the specialness of the unit constant spiral we call a circle.
The motion of symmetry is founded on it , and every form derived from it by some extension. Despite all this, it is still a mysterious relationship defeating even the analytical tools of the calculus of differentials and integrals.
Newton made great use of it in developing his philosophy of quantity, and developing his secure methods of synthesis and soundness of analysis. Pythagoras was able to defeat his rebellious followers by it, maintaining the theorem of areas in a plane inviolate despite the challenge by contradiction. This form was the mysterious shape of the never ending process.
Newton, by it determined that 2 forces or motives must exist and counterbalance: the centripetal and the centrifugal. Many have rejected this exposition, only to find themselves enveloped in darkness, dark matter and dark energy! The synthesis of the reality is not in question. Our synthesis is! How can we synthesise reality from our analytical parts? This is why for Euclid the godess Isis was so important, revealing to him, so he thought, the secret of her magic in putting forms together. This was a philosophy that made sense of the world of forms/ideas.