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What were the fundamental principles and ideas of projective geometry that made people consider it groundbreaking and separates it from the rest of the geometry? I would love to learn about a good book on projective geometry I could read.

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While the wiki article mentions Desargues, it is inaccurate in that it implies that Desargues only had the notion of a point at infinity, whereas he went much further, including the line at infinity. A series of recent papers (not mentioned in the wiki articles) tries to give Desargues the proper credit, as he went amazingly far:

Anglade, Marie; Briend, Jean-Yves Nombrils, bruslans, autrement foyerz: la géométrie projective en action dans le Brouillon Project de Girard Desargues. Arch. Hist. Exact Sci. 76 (2022), no. 2, 173–206.

Briend, Jean-Yves Mathématiques en perspective: Desargues, la Hire, le Poîvre. Arch. Hist. Exact Sci. 75 (2021), no. 6, 699–736.

Anglade, Marie; Briend, Jean-Yves Le diamètre et la traversale: dans l'atelier de Girard Desargues. Arch. Hist. Exact Sci. 73 (2019), no. 4, 385–426.

Anglade, Marie; Briend, Jean-Yves La notion d'involution dans le Brouillon project de Girard Desargues. Arch. Hist. Exact Sci. 71 (2017), no. 6, 543–588.

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