First book of Mathematics Being An Easy And Practical Introduction to the Study

Cover First book of Mathematics Being An Easy And Practical Introduction to the Study
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To make a triangle equal in area to a given quadrilateral.
Let ABCD be the given quadrilateral.
Draw CA, joining the ends of any two adjoining EQUIVALENT FIGURES. 41 sides, BC, BA. Through B draw BE, parallel to CA, meeting DA produced in E. Join EC.
Fie. 36 The triangle ECD is equal to the quadrilateral ABCD.
Bote. This depends on the geometrical truth, that Two triangles (ABC, AEC), on the same base (AC) and between the same parallels (AC, EB), are equal.
These two triangles being equal, add
...the triangle ACD to each then, the whole triangle ECD is equal to the figure ABCD.
148. Cor. 1. To reduce a given rectilineal figure to another, equal in area, but with one side less.
This is done in the present problem. The same con- struction will apply, however many sides there may be from C by D to A. Let any two adjacent sides be treated as AB and BC in this problem.
149. Cor. 2. To reduce any polygon to an equal triangle.
By the preceding corollary reduce it to an equal polygon with one side less ; do the same with the poly- gon thus obtained, and so on.


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