26(14)
SUPPLEMENT.
PROBLEM I.
HAVING two points given A and B, to determine the Locus of the cen-
ters of all ſuch circles as may be drawn through A and B.
ters of all ſuch circles as may be drawn through A and B.
Join AB and biſect it in the point C, and through C, draw a perpendicular
to it CE, and continue it both ways in infinitum, and it is evident that this line
CE will be the Locus required.
to it CE, and continue it both ways in infinitum, and it is evident that this line
CE will be the Locus required.
PROBLEM II.
Having two right lines given AB and CD, to determine the Locus of the
centers of all ſuch circles as may be drawn touching both the ſaid lines.
centers of all ſuch circles as may be drawn touching both the ſaid lines.
Case 1ft.
Suppoſe AB and CD to be parallel;
then drawing GI perpendicu-
lar to them both; biſect it in H, and through H draw EHF parallel to the two
given lines, and it will be the Locus required.
lar to them both; biſect it in H, and through H draw EHF parallel to the two
given lines, and it will be the Locus required.
Case 2d.
Suppoſe the given lines being produced meet each other in E,
then biſecting the angle BED by the line EHF, this line EHF will be the Locus
required.
then biſecting the angle BED by the line EHF, this line EHF will be the Locus
required.
PROBLEM III.
Having two circles given whoſe centers are A and B;
to determine the Locus
of the centers of all ſuch circles as ſhall touch the two given ones.
of the centers of all ſuch circles as ſhall touch the two given ones.
Cases 1ſt and 2d.
Suppoſe it be required that the circles be touched outwardly
by both the given ones; or that they be touched inwardly by both the given
ones.
by both the given ones; or that they be touched inwardly by both the given
ones.
Then joining the centers A and B, let AB cut the circumferences in C and
D and produced in P and O: let CD which is intercepted between the convex
circumſerences be biſected in E: ſet off from E towards B the center of
D and produced in P and O: let CD which is intercepted between the convex
circumſerences be biſected in E: ſet off from E towards B the center of