test2

$$(ct')^2 + (vt)^2 = (ct)^2$$ $$c^2t'^2 + v^2t^2 = c^2t^2$$ $$c^2t'^2 = c^2t^2-v^2t^2$$ $$t'^2={c^2t^2-v^2t^2\over c^2}$$ $$t'^2= （1-{v^2\over c^2}）t^2$$ $$t'= t\sqrt{1-{v^2\over c^2}}$$