DOI Page / Citation link:
https://doi.org/10.11588/diglit.62828#0156
( 100 )
of courfe produces a furface or fuperficies confonant to the
nature of the fecftion, and agreeable to the fhape of the folid
which is cut.
Hence, if a cylinder be cut oblique to its bafe, this fedion
will produce a furface perfectly elliptic ; and if a cone, Fig. 12,
Plate VI. have a fedion parallel to its axis, the curved boun-
daries of the fuperficies will be hyperbolic. See page 52.
“ If a fphere be cut in any manner, the plane of the fac-
tion will be a circle, whofe center is in the diameter of the
fphere.”
But if two plains, or ftraight furfaces, cut each other, their
common faction is a right line.
I mention thefe particulars, that the reader may more
readily and clearly underftand the following Problems.
Prob. XXIX. Fig. 32. Plate VI.
Let Fig. 32, Plate VI. be confidered a folid, of the fhape
of a vafe, whofe covering and fedtion are to be found; or, in
other words, if a vafe is required to be veneered, how to cut
the veneer fo as each joint ihall appear ftraight when the veneer
is laid.
Operation.
of courfe produces a furface or fuperficies confonant to the
nature of the fecftion, and agreeable to the fhape of the folid
which is cut.
Hence, if a cylinder be cut oblique to its bafe, this fedion
will produce a furface perfectly elliptic ; and if a cone, Fig. 12,
Plate VI. have a fedion parallel to its axis, the curved boun-
daries of the fuperficies will be hyperbolic. See page 52.
“ If a fphere be cut in any manner, the plane of the fac-
tion will be a circle, whofe center is in the diameter of the
fphere.”
But if two plains, or ftraight furfaces, cut each other, their
common faction is a right line.
I mention thefe particulars, that the reader may more
readily and clearly underftand the following Problems.
Prob. XXIX. Fig. 32. Plate VI.
Let Fig. 32, Plate VI. be confidered a folid, of the fhape
of a vafe, whofe covering and fedtion are to be found; or, in
other words, if a vafe is required to be veneered, how to cut
the veneer fo as each joint ihall appear ftraight when the veneer
is laid.
Operation.