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Euler in Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie, 17-24 feb 1761, writes about objects he calls spaces (my emphasis):

As a general notion encompasses an infinity of individual objects, one regards it as a space within which all these individuals are enclosed: thus, for the notion of man, one makes a space (fig. 39) in which one conceives that all men are comprised. For the notion of mortal, one also makes a space (fig. 40), where one conceives that everything mortal is comprised. Then, when I say that all men are mortal, that comes down to the former figure being contained in the latter.

 

(...)

 

These round figures or rather these spaces (for it doesn't matter what shape we give them) are very well-suited to facilitating our reflections (...)

etc., and illustrates this with what we would call ensemblist diagrams (fig. 39 to 89), famously reproduced on Swiss banknotes. The applications he gives here are to everyday logic, so perhaps less mathematical than intended by the question. (I don't know if he ever wrote again on the subject.)

Edit: Something I didn't know is that these diagrams were themselves anticipated by Leibniz, as can be seen in his undated manuscript De formæ logicæ comprobatione per linearum ductus ($\simeq$ "Testing logical forms through line drawings") published in "Opuscules et fragments inédits de Leibniz: Extraits des manuscrits de la Bibliothèque royale de Hanovre", Alcan, Paris (1903), pp. 292-321.

Further edit: This was mentioned at an earlier question, pointing indirectly to Margaret E. Baron, A Note on the Historical Development of Logic Diagrams: Leibniz, Euler and Venn (1969).

Euler in Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie, 17-24 feb 1761, writes about objects he calls spaces (my emphasis):

As a general notion encompasses an infinity of individual objects, one regards it as a space within which all these individuals are enclosed: thus, for the notion of man, one makes a space (fig. 39) in which one conceives that all men are comprised. For the notion of mortal, one also makes a space (fig. 40), where one conceives that everything mortal is comprised. Then, when I say that all men are mortal, that comes down to the former figure being contained in the latter.

(...)

These round figures or rather these spaces (for it doesn't matter what shape we give them) are very well-suited to facilitating our reflections (...)

etc., and illustrates this with what we would call ensemblist diagrams (fig. 39 to 89), famously reproduced on Swiss banknotes. The applications he gives here are to everyday logic, so perhaps less mathematical than intended by the question. (I don't know if he ever wrote again on the subject.)

Edit: Something I didn't know is that these diagrams were themselves anticipated by Leibniz, as can be seen in his undated manuscript De formæ logicæ comprobatione per linearum ductus ($\simeq$ "Testing logical forms through line drawings") published in "Opuscules et fragments inédits de Leibniz: Extraits des manuscrits de la Bibliothèque royale de Hanovre", Alcan, Paris (1903), pp. 292-321.

Further edit: This was mentioned at an earlier question, pointing indirectly to Margaret E. Baron, A Note on the Historical Development of Logic Diagrams: Leibniz, Euler and Venn (1969).

Euler in Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie, 17-24 feb 1761, writes about objects he calls spaces (my emphasis):

As a general notion encompasses an infinity of individual objects, one regards it as a space within which all these individuals are enclosed: thus, for the notion of man, one makes a space (fig. 39) in which one conceives that all men are comprised. For the notion of mortal, one also makes a space (fig. 40), where one conceives that everything mortal is comprised. Then, when I say that all men are mortal, that comes down to the former figure being contained in the latter.

(...)

These round figures or rather these spaces (for it doesn't matter what shape we give them) are very well-suited to facilitating our reflections (...)

etc., and illustrates this with what we would call ensemblist diagrams (fig. 39 to 89), famously reproduced on Swiss banknotes. The applications he gives here are to everyday logic, so perhaps less mathematical than intended by the question. (I don't know if he ever wrote again on the subject.)

Edit: Something I didn't know is that these diagrams were themselves anticipated by Leibniz, as can be seen in his undated manuscript De formæ logicæ comprobatione per linearum ductus ($\simeq$ "Testing logical forms through line drawings") published in "Opuscules et fragments inédits de Leibniz: Extraits des manuscrits de la Bibliothèque royale de Hanovre", Alcan, Paris (1903), pp. 292-321. (Further edit: This was mentioned at an earlier question pointing indirectly to Margaret E. Baron, A Note on the Historical Development of Logic Diagrams: Leibniz, Euler and Venn (1969).)

Euler in Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie, 17-24 feb 1761, writes about objects he calls spaces (my emphasis):

As a general notion encompasses an infinity of individual objects, one regards it as a space within which all these individuals are enclosed: thus, for the notion of man, one makes a space (fig. 39) in which one conceives that all men are comprised. For the notion of mortal, one also makes a space (fig. 40), where one conceives that everything mortal is comprised. Then, when I say that all men are mortal, that comes down to the former figure being contained in the latter.

(...)

These round figures or rather these spaces (for it doesn't matter what shape we give them) are very well-suited to facilitating our reflections (...)

etc., and illustrates this with what we would call ensemblist diagrams (fig. 39 to 89), famously reproduced on Swiss banknotes. The applications he gives here are to everyday logic, so perhaps less mathematical than intended by the question. (I don't know if he ever wrote again on the subject.)

Edit: Something I didn't know is that these diagrams were themselves anticipated by Leibniz, as can be seen in his undated manuscript De formæ logicæ comprobatione per linearum ductus ($\simeq$ "Testing logical forms through line drawings") published in "Opuscules et fragments inédits de Leibniz: Extraits des manuscrits de la Bibliothèque royale de Hanovre", Alcan, Paris (1903), pp. 292-321. 

Further edit: This was mentioned at an earlier question, pointing indirectly to Margaret E. Baron, A Note on the Historical Development of Logic Diagrams: Leibniz, Euler and Venn (1969).

Euler in Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie, 17-24 feb 1761, writes about objects he calls spaces (my emphasis):

As a general notion encompasses an infinity of individual objects, one regards it as a space within which all these individuals are enclosed: thus, for the notion of man, one makes a space (fig. 39) in which one conceives that all men are comprised. For the notion of mortal, one also makes a space (fig. 40), where one conceives that everything mortal is comprised. Then, when I say that all men are mortal, that comes down to the former figure being contained in the latter.

(...)

These round figures or rather these spaces (for it doesn't matter what shape we give them) are very well-suited to facilitating our reflections (...)

etc., and illustrates this with what we would call ensemblist diagrams (fig. 39 to 89), famously reproduced on Swiss banknotes. The applications he gives here are to everyday logic, so perhaps less mathematical than intended by the question. (I don't know if he ever wrote again on the subject.)

Edit: Something I didn't know is that these diagrams were themselves anticipated by Leibniz, as can be seen in his undated manuscript De formæ logicæ comprobatione per linearum ductus ($\simeq$ "Testing logical forms through line drawings") published in "Opuscules et fragments inédits de Leibniz: Extraits des manuscrits de la Bibliothèque royale de Hanovre", Alcan, Paris (1903), pp. 292-321.

Euler in Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie, 17-24 feb 1761, writes about objects he calls spaces (my emphasis):

As a general notion encompasses an infinity of individual objects, one regards it as a space within which all these individuals are enclosed: thus, for the notion of man, one makes a space (fig. 39) in which one conceives that all men are comprised. For the notion of mortal, one also makes a space (fig. 40), where one conceives that everything mortal is comprised. Then, when I say that all men are mortal, that comes down to the former figure being contained in the latter.

(...)

These round figures or rather these spaces (for it doesn't matter what shape we give them) are very well-suited to facilitating our reflections (...)

etc., and illustrates this with what we would call ensemblist diagrams (fig. 39 to 89), famously reproduced on Swiss banknotes. The applications he gives here are to everyday logic, so perhaps less mathematical than intended by the question. (I don't know if he ever wrote again on the subject.)

Edit: Something I didn't know is that these diagrams were themselves anticipated by Leibniz, as can be seen in his undated manuscript De formæ logicæ comprobatione per linearum ductus ($\simeq$ "Testing logical forms through line drawings") published in "Opuscules et fragments inédits de Leibniz: Extraits des manuscrits de la Bibliothèque royale de Hanovre", Alcan, Paris (1903), pp. 292-321. (Further edit: This was mentioned at an earlier question pointing indirectly to Margaret E. Baron, A Note on the Historical Development of Logic Diagrams: Leibniz, Euler and Venn (1969).)