This historic book may have numerous typos and missing text.
Purchasers can download a free scanned copy of the original book
(without typos) from the publisher. Not indexed. Not illustrated.
1821. Excerpt: ... PROP. VII. PROB. To bisect a given triangle, by
a straight line drawn from a given point in one of its sides. Let
it be required, from the point D, to draw DF, bisecting the
triangle ABC. ANALYSIS. If D be the middle of AC, the line DB drawn
to the vertex will obviously (II. 2. El.) divide the triangle into
two equal portions. But, if not, bisect (I. 7. EI.) the side AC in
E, and join EB, EF and BD. The triangle ABE is equal to EBC, and is
consequently the half of ABC, wherefore ABE is equal to AFD, and,
taking AFE from both, the remaining triangle EFB is equal to EFD;
and since these triangles stand on the same base, they must (U.S.
El.) have the same altitude, or EF is parallel to BD. But the
points B and v D C J) being given, the straight line BD is given in
position, and consequently EF is also given in position.
COMPOSITION. Having bisected AC in E and joined BD, draw EF
parallel to it, meeting AB in F; the straight line DF divides the
triangle ABC into two equal portions. For join BE. Because BD is
parallel to EF, the triangle EFB (II. 1. El.) is equal to EFD; and,
adding AFE to each, the triangle AFD is equal to ABE, that is, to
the half of the triangle ABC. PROP. VIII. PItOB. To find a point
within a given triangle, from which straight lines drawn to the
several corners will divide the triangle into three equal portions.
Let F be the required point, from which the lines FA, FB, and FC
trisect the triangle ABC. ANALYSIS. Draw FD, FE parallel to the
sides BA, BC, and join BD, BE. Since FD is parallel to AB, the
triangle ABF (II. 1. El.) is equal to ABD, which is hence the third
part of ABC; and, for the same reason, the triangle BFC is equal to
BEC, which is also the third part of ABC. Wherefore the bases AD
and EC are each the third part of ...
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|Country of origin:
||246 x 189 x 5mm (L x W x T)
||Paperback - Trade
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