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12. A Pair of Lines, which have two common points, have identical directions. |
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∗13. (a) A Pair of Lines, which have different directions, have not two common points. (b) A Pair of Lines, which have a common point and different directions, are intersectional. |
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∗14. A Pair of intersectional Lines have different directions. |
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∗15. A Pair of Lines, which have a common point and identical directions, are coincidental. |
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∗16. If there be given a Line and a point without it: it is possible to draw a Line, through the given point, having a direction different from that of the given Line. |
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17. A Line, which has a point in common with one of two coincidental Lines has a point in common with the other also. |
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18. A Line, which has a point in common with one of two separational Lines, has a point separate from the other. |
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∗19. A Line, which has a point in common with one of two separational Lines and also a point in common with the other, is intersectional with both. |
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∗20. If there be three Lines; the first a right Line; the second, not assumed to be right, having a point separate from the first and being equidistantial from it; the third a right Line intersecting the first and diverging from it without limit on the side next to the second: the third is intersectional with the second. |
