Clinching the Democratic Party nomination, former secretary of state Hillary Clinton greets supporters at her primary night victory party on Tuesday in Brooklyn. (Melina Mara/The Washington Post)

Hillary Clinton began her telling of American history Tuesday night by recounting Seneca Falls, a July 1848 gathering in Upstate New York of women and a smattering of men committed to examining and improving the social and legal conditions of women.

At the time, the most radical of the ideas ultimately included in the list of declarations and demands produced at that convention -- the thing that caused early disagreements, departures and splits -- was the idea that women should demand the right to vote. In the end, amid heated discussion, the Seneca Falls Convention concluded that the franchise was, in fact, fundamental to the ability of women to live full and influential lives.

The following week, the New York Reformer published an account of the proceedings that was equal parts factual and declaratory.

It being the first convention of the kind ever held, and one whose influence shall not cease until woman is guaranteed all the rights now enjoyed by the other half of creation -- Social, Civil and Political.

In Brooklyn on Tuesday night, Clinton became the first woman in American history to claim the mantle of a major party's presumptive presidential nominee. That was the history -- the legacy Clinton claimed for herself and members of every other group legally and assertively left out, locked out and barred from the promises of freedom and equality for all that was delineated but not delivered by the founders.

And, lest those who have no affection for the bits of American history where the plot and hero worship veers away from wealthy, white men miss the point -- or those who have no recall of Elizabeth Cady Stanton and her bold assertions about the political rights of women fail to make the connection between Seneca Falls 1848 and Brooklyn 2016 -- Clinton spoke of June 4, 1919. That was the day Congress passed the 19th Amendment, initiating the process that would give American women the right to vote. And that was the day Clinton's mother came into the world.

This moment, Clinton all but said, was fated.

Clinton's speech Tuesday night was full of soaring rhetoric and historical references to big, long-fought and ultimately successful reaches for the full measure of what it means to be American. Those sections mentioned above will almost certainly be excerpted and clips pulled and played on repeat today, as the candidate hopes, as well as in future campaign ads.

But buried within this tale of transgressive and radical patriotism, one that aimed to fully include women, was something incredibly pragmatic -- something that will ultimately determine whether Clinton becomes the next president.

That's why Clinton spent much of her time on stage Tuesday night speaking not just to and about women, but also people of color, the disabled, people who were not the beneficiaries of promised equality or even open opportunity in the once-great nation about which Donald Trump, the presumptive Republican nominee, often speaks. In repeating the words "all of us" and "together" over and over, Clinton was proposing an alternative vision. She played up gender, but as a way to appeal to more than just women.

Put another way -- a more overtly political and eyebrow-raising way -- Clinton was saying that Trump and his campaign promises are best for white men and anyone who takes comfort in returning to a time when their health, safety, economic and social conditions really were all that mattered.

And there is plenty of data underpinning Clinton's appeal. In every presidential election since 1996, women have voted at greater rates than men. In 2012, the last presidential election, women of all races cast a slight majority -- 53 percent -- of the nation's votes. They went mostly to Democrats. Black women voted in greater numbers than any other group. And, lest anyone take comfort in the idea that other groups of voters -- perhaps the white working-class voters Trump is so focused on -- simply were not motivated the last time around but will be this time, it's worth reinforcing: Mathematically, there aren't nearly enough white men in the right states with big Electoral College prizes to elect Trump alone.

To win, Trump has to convince a substantial portion of white women that that he shares their political interests and goals, as well as peel off more than the 18 percent of Latino voters that the most sunny polls indicate are with him right now. He'll have to grow his personal collection of black Americans -- women in particular -- beyond the point where he feels the need to point one out in a rally crowd. And he'll also want to make inroads with the nation's fastest-growing but still relatively small demographic group, Asian Americans.

Clinton needs to add more white women and some white young men (many of which support Sanders) to the coalition she has already built.

That's the hard, cold electoral truth about a changing nation. And it's why the first female major-party nominee alluded to the history that is her gender but then used that to expand outward.

Now, Clinton could have avoided speaking of Seneca Falls and the slow expansion of rights to successive groups of Americans on Tuesday night. She could have found some other way to claim her moment in American history. Like every campaign, Clinton's includes entire teams of researchers and speech writers. But by linking a white-woman-dominated struggle for the franchise with the longer-running fights of other groups for full inclusion, Clinton was saying: "Look here, America. Here is a path that can be carved and followed if taken in unison." She was speaking about and to the coalition that has the numbers to decide the outcome of the 2016 election if it shows up and votes.

Clinton, notably, opted not to mention the fact that after the Civil War, when Congress gave black men the franchise, some white suffragists argued that white women should gain the vote, too, to balance out or negate the impact of black men voting. Clinton did not mention that Susan B. Anthony declared herself willing to "cut off her right arm" before she would insist on the ballot for "the Negro and not the woman." And Clinton certainly did not mention that in the runup to a major 1913 suffrage parade, black women were told to march in a segregated unit, not along the white women organized by state.

The arc of American history may bend toward inclusion and expanded equality, but getting there has been slow, messy, not always consistent and quite long.