(18) In hyperbolic geometry, if P is a point not lying on line l, then there are exactly two lines through P parallel to l. (19) In hyperbolic geometry, if P is a point not lying on line l, then there...


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(18) In hyperbolic geometry, if P is a point not lying on line l, then<br>there are exactly two lines through P parallel to l.<br>(19) In hyperbolic geometry, if P is a point not lying on line l, then<br>there are exactly two lines through P perpendicular to l.<br>(20) In hyperbolic geometry, if I || m and m || n, then 1 || n (transi-<br>tivity of parallelism).<br>(21) In hyperbolic geometry, if m contains a limiting parallel ray to<br>1, then I and m have a common perpendicular.<br>(22) In hyperbolic geometry, if l and m have a common perpendic-<br>ular, then there is one point on m that is closer to l than any<br>other point on m.<br>(23) In hyperbolic geometry, if m does not contain a limiting par-<br>allel ray to l and if m and l have no common perpendicular,<br>then m intersects l.<br>(24) In hyperbolic geometry, the summit of any Saccheri quadrilat-<br>eral is greater than the base.<br>

Extracted text: (18) In hyperbolic geometry, if P is a point not lying on line l, then there are exactly two lines through P parallel to l. (19) In hyperbolic geometry, if P is a point not lying on line l, then there are exactly two lines through P perpendicular to l. (20) In hyperbolic geometry, if I || m and m || n, then 1 || n (transi- tivity of parallelism). (21) In hyperbolic geometry, if m contains a limiting parallel ray to 1, then I and m have a common perpendicular. (22) In hyperbolic geometry, if l and m have a common perpendic- ular, then there is one point on m that is closer to l than any other point on m. (23) In hyperbolic geometry, if m does not contain a limiting par- allel ray to l and if m and l have no common perpendicular, then m intersects l. (24) In hyperbolic geometry, the summit of any Saccheri quadrilat- eral is greater than the base.

Jun 04, 2022
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