In Plato Succeeds, technology is roughly 500 years ahead of the OTL, so much that in the main timeline, nothing past the nineteenth century is currently given yet as some areas would go into science fiction, and in other areas so little that it's comparable to the OTL equivalent time. Progress may also be slower, as shown by the steam engine that was used far longer than when it was reintroduced in the OTL's 18th Century. Each nation is competing with outsiders and each other to be the best of all in improving the lives of people via any means necessary in order to help reach either Eudaimonia or an to reach the world of the forms. The overall unity also allowed stable ground for industrialisation though the ease of slavery made this slow. Plato himself said that when it comes to geometry only ruler and compass should be needed and used, but Aristotle believed we should use what we need to. If we are all indeed prisoners in a cave watching shadows, to use Plato's analogy, then we should use what we can when we can to break out and enter the real world. Some examples are given here.
The burning glass
Invented by Archimedes in 212 BC, this device may or may not work. Many factors are involved and all must be correct. Weather, heat, ability to focus glass, the enemy. Otherwise it won't work as intended, if at all. An attempt to incinerate wooden siege engines may just blind the operators. Of course, it all goes well, this is an absolutely devastating weapon, but its probability of malfunctioning and expense means that they're rare. Stationary ones can also be found on coastal city defences and some warships also possess them, but these are even less reliable as they're moving with the rest of the vessel. In fact, it would be incredible if they worked at all, the only way they could being in the presence of intense sunlight. When they did work, it was considered newsworthy. As such, most vessels do not mount them and the ones that do almost never take them into account in tactical planning. The (very sensible) ships that did not carry burning glasses often carried light steam cannon instead. None carry giant grappling hooks, though a team of ships might. Land based ones have more success.
Miniature or telescopic weapons
The Chinese accidentally invented this when an alchemist looking for the key to eternal life blew up his house instead. It was first deployed in battle in 400 and was quickly copied by the Confederation. Development follows the periods of peace and war respectively, however technology is not lost. This was supplemented by new armaments in the 13th century. Hyper-gunpowder (nitroglycerine) was the most powerful conventional explosive for 600 years and was used in the 1605 failed attack on the British Parliament.
More advanced weapons
Unsuccessful research into particle beam weapons was pursued in the 15th century. A practical form was achieved 100 years later. Hand held Boetian fire raisers are sometimes deployed though never indoors. In the wars against the Mesoamerican flame-throwers were formidable weapons in the hands of an experienced user, some using Greek fire.
Hero of Alexandria pioneered this and in this timeline, this tech was welcomed rather than suppressed (Terry Jones claims that Vespasian scrapped it, claiming he had to "feed the common people", a further source may be found here http://www.mlahanas.de/Greeks/HeroAndLoon.htm). Although invented for entertainment and to help Civilians, the Guardians quickly adopted this to aid in the war against China, looking for any way to break the stalemate. Essentially, steam power was used to power artillery machines, allowing far more to be used with the same amount of crew, who only step in to change trajectory or operate the machines manually if needed. For Civilians, steam power was used to power machinery, often vehicles, creating a form of public transport. Plus, the original aeoliple entertainment device was kept. Archimedes also developed a steam powered cannon which has a greater range and damage than other weapons of the Second Punic War. This cannon, the burning glass and large grappling hooks were invented during that war. Syracuse had broken off from the Confederation and grown closer to Carthage. Rome and Epirus won it back after a long and costly siege. The coalition general ordered that Archimedes be spared. When he was found doing math in the dirt, the Epiran peltast who found him took him alive despite being insulted and treated like a pest rather than an enemy to be feared,
Water power was known beforehand, but by the 5th century, someone decided to experiment with magnets and steam to see if there was a way to use that sparking thing often found in amber elektron. There wasn't really anything practical to do with it. That required better metallurgical knowledge and industry. But once a way was found to conduct electricity on a practical level (the next month) was discovered by accident, it was found that it can power lights and perform executions. With mills soon using electricity and others using steam, a fairly automated society was created, allowing Civilians the chance to have more spare time. This automation was limited to avoid a "Luddite" style revolt .Hydroelectricity is also the main power source for Confederate ships but are supplemented by other means of generating power as well as the scaled down generators are not always capable of handling the demands made of them.
Other fuel sources
As hydroelectricity is demanding on the environment, blocks rivers and can be difficult to use on a small scale level (plus the fact it's risky to use only one means of generating electricity). As well as steam, some nations, especially those in the Middle East have experimented with using oil, others try coal or gas. Slavery was used by the many European and some Oriental nations with people being used to generate power (though Egypt uses paid workers who could easily be mistaken for slaves while Hindu nations with a caste system may use Dalits). The ultimate problem is getting a turbine to move in order to turn a generator. While people try that, more sunny areas such as the Iberian Peninsula or the Mediterranean coast have experimented with using the Sun to generate power. True solar cells were invented in the 17th century, with most making do with intensifying the heat to an extent it can boil water located under a black surface ... to become steam to turn a generator.
Metal built radar equipped naval vessels are in use by the 16th century. Examples of British ships are the Mary Rose (flagship dreadnought, named after the sister of a senior admiral), the Diogenes class battleship, Stonehenge class light cruiser or the CuChullain class aircraft carrier. In China, there are similar craft, resembling Oriental designs of the OTL combined with modern battleships, the same applies to European ones (modern battleships combined with Age of Discovery elements). An oddity is that by the 18th century the research and development on shipping had stagnated with some classes being in service for centuries on end.
Also available by 1558 and carried on ships. Most in the Tudor era are OTL World War 1 & World War 2 hybrids, with some Tudor aspects used for symbolism.
Public transport includes buses and rail, while cars, vans, goods vehicles and human powered vehicles are available for individual usage. Military craft includes tanks, armoured personnel carriers, minesweepers and utility vehicles. Horses and camels were used even up to the 18th century, often armoured alongside other light transport such as bicycles, tricycles and quad bikes. Some areas still use traditional methods such as carriages and chariots.
This is a complicated issue. See the various nations articles and the timeline. Space travel originated in the 16th century and continued from there on.
Due to the technological leaps, armour is also 500 years ahead, going through mail, plate and modern fast. All armour with power systems are equipped with stealth systems (see below), the favourite bending light and sending out false signals to confuse vision and detection systems. It's also possible to project an image of the background onto the armour surface, which is often used for the eyepieces so they can still see. Most suits mount weapons allowing users to free their hands for other tasks.
In Republic, Plato tells the story of a shepherd boy named Gyges. This boy finds a ring that can turn him invisible, so he kills the king, marries the queen and seizes power. Nobody can stop him as nobody can find him. Although a story, all philarchons became concerned such a thing may happen to them if they weren't careful. All of them also wanted to find a way to copy the events in the story and use it on their enemies. All OTL stealth techniques are employed. To counter, all OTL detection systems are employed as well. This is where the most advancements in technology are made, even during peacetime, as nobody wants a Gyges situation to happen to them, but may want to do it to their rivals.
For some reason, while there are alternate leaps and stagnation in technology, clothing remains more or less the same as in the OTL. There are some variations like zips but a 16th century OTL peasant looks remarkably similar to a Plato Succeeds 16th century peasant, though they may be carrying more modern equipment and have better quality clothes.
There has been progress on this area, with the most leaps made when necessary. The 12th century world was able to use nonverbal mass communications like sound and light codes, semaphore and flags. Radio was invented in the 13th and expanded on. Radio entered the various world languages as a general term for all wireless communication.
If Terry Jones and his book Barbarians is correct, then the Roman Republic and Empire set back technology 1500 years while dishing out propaganda saying they advanced it. Also, if the many theories of the Library of Alexandria are true, both the Romans for letting it decay and the Arabs for destroying most of what survived was responsible for a massive loss of human knowledge. In this timeline no such events occur. While it may be an exaggeration to say the Greeks were about to launch an industrial revolution (Jones) or that if the Library survived we'd have space travel by the Middle Ages (Stephen Fry on QI- whatever readers may think of the show or Fry himself, he was expressing personal views and could be considered reasonably credible), it is possible that technology and science would have been more advanced. The Concise Encyclopaedia of Islam by Cyril Glasse (with an introduction by Professor Huston Smith) under the section "Fallacies and Inaccuracies about Islam (p111), blames the loss of knowledge more on Rome than the Arabs, pointing the most devastating blame to the later Emperor Theodosius I and says the Library began to fall apart from the Roman conquest of Egypt onward. In this timeline Rome is solely a Western European empire, so they had no effect. Everyone in Egypt worked to maintain the Library. Since all knowledge is important, even more so than technology, the Library remains reasonably intact and makes many contributions to the advancement of science and engineering.