The two retained some of their own rhetoric but they borrowed from each other's lexicon, using not just words but concepts that have often seemed foreign and unwelcome to them.
The Unionist spoke of recognising the legitimacy of Irish nationalism, of commitment to the principles of inclusivity and equality, of a new era of respect and tolerance of difference.
The republican spoke of Sinn Fein accepting that de-commissioning was an essential part of the peace process, of being opposed to the use of force and of wishing to work with Unionists toward an accommodation.
They both acknowledged that everyone had suffered from the conflict and both said this was a matter of regret, a form of words which is probably as close as these people and their traditions will ever get to saying sorry to each other.
There was no handshake; there was definitely no manly hug; in fact the two leaders did not even appear in public together. If the two sides are reaching out to each other they are doing so not in a spirit of friendship and fraternity but rather from self-interest. The deal they are attempting to strike together may be all the stronger for that.
The paper on which they issued their texts testified to their sharply differing aspirations. The Adams words were on notepaper with a Sinn Fein logo stamped over an outline of a united Ireland. The Trimble speech was on Unionist party notepaper stamped "Building your future within the union".
Out there on the streets many are still spoiling for a fight. It is still possible for the unwary Protestant or Catholic to get punched and kicked if they happen to wander into the wrong district. Extreme loyalists are still active, mindlessly petrol-bombing Catholic homes in the night.
Observers often ask how such opposing aspirations can be reconciled. The answer is: with the utmost difficulty. Everything in this peace process takes ages to get done. Everything is miles behind schedule, with the increments of progress coming only after the most laborious and exhausting efforts.
A lot of people think all this is a year and a half late, and regret all the slippage there has been in the peace process timetable. The delay bred frustration but it did not kill the hope.
There is a yearning for peace in the hearts of most, though the pursuit of it is complicated by the basic instinct not to let the other side away with anything. But then that self-interest has its effect, for most can appreciate that the present much-improved security situation is not enough.
A political underpinning of the republican and loyalist ceasefires is also essential, for it cannot be assumed they will last for ever in a continuing political vacuum. The local politicians have to get down to working together to provide the wider population with a new template for political cooperation that will hopefully give rise eventually to better community relations.
More than 18 months have passed since the Good Friday Agreement was signed by most of the parties, and then put to a referendum in which it received 71 per cent endorsement. The spirit of the accord was often obscured in all those months of stasis, but yesterday it reasserted itself.
And something new was added. Mr Trimble and Mr Adams both subscribed to the Good Friday Agreement, but it was put together for them by officials: the two never met until months after it had been signed.
This time the words were worked out by the two men themselves with help from George Mitchell, whose contribution is described by all involved as magnificent. The two men may continue to differ over decommissioning, but they have found common ground in the agreement.
Gerry Adams has had more than one relative murdered by loyalists; David Trimble had one of his closest friends killed by the IRA. Both these politicians emerged first as tribal champions but both now seem to be going beyond that, and developing into something more complex.
They have no illusions about each other but all the signs are that they have lately developed a new capacity to see the other side's point of view. There may never be friendship or liking there, but mutual respect is becoming discernible.
The politics are going to remain difficult. David Trimble looks intent on forming the new executive without first witnessing the actual destruction of IRA weaponry, and after that there is much uncertainty about whether and when the IRA might decommission. Gerry Adams is the most pragmatic republican leader there has ever been, and the first to lead his people in such a direction.
David Trimble is not the first Unionist leader to urge his people towards accommodation: his challenge is to be the first to do so successfully, for the various others failed and lost their jobs.
His problem is that while most Protestants want accommodation some want it only on very tough terms, and many do not want it at all. Those who do not believe in reconciliation are not all bigots, though many undoubtedly are.
Some of them, having lived through a generation of paramilitary and political trench warfare, simply cannot conceive that other form of politics might be possible. Mr Trimble well knows that these people are going to give him a great deal of trouble, and may even split his party.
A split, though messy and dangerous, might in fact be the logical thing, for the party is already divided down the middle into those prepared to contemplate a deal and those who are not.
Mr Trimble will have to go to the party on a "back me or sack me" basis: the chances are he will win, but there will be much drama and many tense moments before he does so. This uncertainty within the party, with the uncertainty over de-commissioning, means that yesterday's developments represent both the culmination of a highly important negotiation and the opening of a turbulent new phase.
Once again the peace process moves on; once again new hurdles and challenges appear.
But yesterday may go down as the day when the beginnings of a shared vocabulary appeared, and when two previously warring blocs signified that they have more of a common purpose than the world had thought possible.Reuse content