ent points. No two of them are conjugate points. Any two figures have in common four points which lie on one line, or to each line corresponds one of the possible combinations two by two of the six figures and the four lines common to any two figures pass through an point.
The connecting link between the system and the system is formed by the lines which fact is indicated by the suffix We have already seen that the lines which pass through are
Now three lines which pass through one point are (Veronese, p. 35)
That is, given three pairs of lines such that one member of each pair passes through a common point, the remaining members pass through a common point. This correspondence between points and points I shall indicate by giving two such points the same notation. It will then be observed that the three lines of one point are obtained by taking its opposite pairs of letters in the order in which they stand; but the three lines of one point by taking opposite pairs of letters with an inversion of one pair. On a line, lie two points, and two points,
The three points which have the same notation as the three lines of an point lie on an line (Veronese, p. 39). Through each point pass three There are points and
Two lines of the same notation as the two points of one line meet in a point through which pass two lines of the third system These lines, in number, determine by their intersections in threes the points, which lie in threes on the lines. There are pairs of points answering to the pairs of the system that is to say, after the first system the intrinsic difference between points and drops out, or lines no longer meet by fours in points, but by twos in points.
In general, from the system the system is derived by means of lines the connectors of pairs of points and also of pairs of points. From the system we pass to the system by means of points the intersections of pairs of lines and also pairs of lines.
All the pairs of lines of same notation but from different systems,
![{\displaystyle [H_{1}h_{1}],}](https://wikimedia.org/api/rest_v1/media/math/render/svg/421c5f82887e0a2e18ef537148c8916c8ca2ef5d)
![{\displaystyle [H_{2}h_{2}],}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb43feaeeae241b44fd7c1ebb671636340ca93ea)
![{\displaystyle [H_{3}h_{3}].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5a9f4865cae3c340445369cb98e0ea9e175ba954)
![{\displaystyle [H_{1}h_{1}];}](https://wikimedia.org/api/rest_v1/media/math/render/svg/513754b02cec4719eb3f94e28f6e45267ee48d9f)
![{\displaystyle [H_{2n-1}h_{2n-1}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/74be95c3b96ee3de296ef81ee6ee57f0ff8d543d)
![{\displaystyle [H_{2n}h_{2n}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d812a291efb312faa5962e0cc364e20035b8a864)
![{\displaystyle [H_{2n+1}h_{2n+1}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf6816a727008848628714c958cd008f342da442)
