“There are two equal and opposite errors into which our race can fall about the devils.”

As quoted in His Brother's Blood: Speeches and Writings, 1838–64 https://web.archive.org/web/20160319090912/https://books.google.com/books?id=qMEv8DNXVbIC&pg=PA333#v=onepage&q&f=false (2004), edited by William Frederick Moore and Jane Ann Moore, p. 333
1860s, Speech (June 1862)

This is from a fictional speech by Lincoln which occurs in The Clansman : An Historical Romance of the Ku Klux Klan (1905) by Thomas Dixon, Jr.. On some sites this has been declared to be something Lincoln said "soon after signing" the Emancipation Proclamation, but without any date or other indications of to whom it was stated, and there are no actual historical records of Lincoln ever saying this.
Misattributed

Source: Speech (June 1853), p. 79

Report on Manufactures (1791)
Context: It is not uncommon to meet with an opinion that though the promoting of manufactures may be the interest of a part of the Union, it is contrary to that of another part. The Northern & Southern regions are sometimes represented as having adverse interests in this respect. Those are called Manufacturing, these Agricultural states; and a species of opposition is imagined to subsist between the Manufacturing and Agricultural interests. This idea of an opposition between those two interests is the common error of the early periods of every country, but experience gradually dissipates it. Indeed they are perceived so often to succour and to befriend each other, that they come at length to be considered as one. (...) Perhaps the superior steadiness of the demand of a domestic market for the surplus produce of the soil, is alone a convincing argument of its truth.

La science, mon garçon, est faite d’erreurs, mais d’erreurs qu’il est bon de commettre, car elles mènent peu à peu à la vérité.
Source: Journey to the Center of the Earth (1864), Ch. XXXI: Preparations for a voyage of discovery

Fourth Lincoln-Douglas Debate (Charleston, 18 September 1858)
1850s, Lincoln–Douglas debates (1858)
Context: While I was at the hotel to-day, an elderly gentleman called upon me to know whether I was really in favor of producing perfect equality between the negroes and white people. While I had not proposed to myself on this occasion to say much on that subject, yet as the question was asked me, I thought I would occupy perhaps five minutes in saying something in regard to it. I will say then that I am not, nor ever have been, in favor of bringing about in any way the social and political equality of the white and black races, that I am not, nor ever have been, in favor of making voters or jurors of negroes, nor of qualifying them to hold office, nor to intermarry with white people; and I will say in addition to this that there is a physical difference between the white and black races which I believe will forever forbid the two races living together on terms of social and political equality. And inasmuch as they cannot so live, while they do remain together there must be the position of superior and inferior, and I as much as any other man am in favor of having the superior position assigned to the white race. I say upon this occasion I do not perceive that because the white man is to have the superior position the negro should be denied every thing. I do not understand that because I do not want a negro woman for a slave I must necessarily want her for a wife. My understanding is that I can just let her alone. I am now in my fiftieth year, and I certainly never had a black woman for either a slave or a wife. So it seems to me quite possible for us to get along without making either slaves or wives of negroes. I will add to this that I have never seen, to my knowledge, a man, woman, or child who was in favor of producing a perfect equality, social and political, between negroes and white men... I have never had the least apprehension that I or my friends would marry negroes if there was no law to keep them from it, but as Judge Douglas and his friends seem to be in great apprehension that they might, if there were no law to keep them from it, I give him the most solemn pledge that I will to the very last stand by the law of this State, which forbids the marrying of white people with negroes.

Source: 1930s, The conflict between Aristotelian and Galileian modes of thought in contemporary psychology, 1931, p. 109 as cited in: Man Cheung Chung, Michael E. Hyland (2012) History and Philosophy of Psychology. p. 107.

Book I, Chapter VII
Nicomachus of Gerasa: Introduction to Arithmetic (1926)