13
PROBLEMS
CONCERNING
TANGENCIES.
CONCERNING
TANGENCIES.
PROBLEM I.
THROUGH two given points A and B to deſcribe a circle whoſe radius
ſhall be equal to a given line Z.
ſhall be equal to a given line Z.
Limitation.
2 Z muſt not be leſs than the diſtance of the points A and B.
Construction.
With the centers A and B, and diſtance Z, deſcribe two
arcs cutting or touching one another in the point E, ( which they will neceſſarily
do by the Limitation ) and E will be the center of the circle required.
arcs cutting or touching one another in the point E, ( which they will neceſſarily
do by the Limitation ) and E will be the center of the circle required.
PROBLEM II.
Having two right lines AB CD given in poſition, it is required to draw 2
circle, whoſe Radius ſhall be equal to the given line Z, which ſhall alſo touch
both the given lines.
circle, whoſe Radius ſhall be equal to the given line Z, which ſhall alſo touch
both the given lines.
Case 1ſt.
Suppoſe AB and CD to be parallel.
Limitation.
2Z muſt be equal to the diſtance of the parallels, and the
conſtruction is evident.
conſtruction is evident.
Case 2d.
Suppoſe AB and CD to be inclined to each other, let them be
produced till they meet in E, and let the angle BED be biſected by EH, and
through E draw EF perpendicular to ED, and equal to the given line Z; through
F draw FG parallel to EH, meeting ED in G, and through G draw GH paral-
lel to EF. I ſay that the circle deſcribed with H center, and HG radius,
touches the two given lines: it touches CD, becauſe EFGH is a
produced till they meet in E, and let the angle BED be biſected by EH, and
through E draw EF perpendicular to ED, and equal to the given line Z; through
F draw FG parallel to EH, meeting ED in G, and through G draw GH paral-
lel to EF. I ſay that the circle deſcribed with H center, and HG radius,
touches the two given lines: it touches CD, becauſe EFGH is a
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