Auguste Comte
Know only facts: the positive age of science.
Misconceptions
Comte invented the word "sociology".
True on the whole, with a nuance. In the Course he first writes "social physics". It is in lesson 47 (volume 4, 1839), in a footnote, that he writes he thinks he must "venture, from now on, this new term", which he says is exactly equivalent to social physics. It is he who made the word known. Historians note however that the abbé Sieyès had already written it in manuscripts that remained unpublished, at the end of the 18th century: Comte could not have known them.
Comte rejects all religion: there is only science.
False. He rejects supernatural religion and thinks theology is outdated. But he holds that humanity needs a religion, whose function is to "regulate each individual nature" and to "rally all individuals". At the end of his life he founds one: the Religion of Humanity, with a cult, a calendar, a clergy. Many of his scientific disciples followed him as far as the Course, not further. It is one of the great disagreements between him and Mill.
Comte's positivism means "only what can be verified counts".
It is half of it. The formula resembles the logical positivism of the Vienna Circle (1920s), which is much later. For Comte, positivism is first a philosophy of history (the three states), a classification of the sciences and a project for society. He himself says the positive spirit is no less removed from empiricism, that is from the mere piling up of facts, than from mysticism.
The motto "Ordem e Progresso" on the flag of Brazil comes from Comte.
Yes, but shortened. His full formula is: "Love as principle, Order as basis, and Progress as goal". The pair "order and progress" is already central to lesson 46 of the Course (1839). The Brazilian republic of 1889, in which positivists were influential, kept these two terms on its flag.