Sinossi
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1867 edition. Excerpt: ...138 in Euclid) will be adopted, but in the very great majority of instances, the triangles will be on the same base. (141.) To divide a triangle into any number of equivalent parts in the most simjrfe manner, fig. 117. Divide the base into the required number of equal parts, and from the points marking those parts draw lines to the apex of the triangle. Although the ultimate triangles will only be equivalent, or equal in a partial sense only, the parts of the line will be equal, as being only the subjects of comparison as regards length, and being in that respect equal. G r. Example:--To divide the triangle abe into three equivalent parts, (fig. 117.) 1. Divide the base ac into three equal parts at d and/. 2. Draw the lines db and fb. The triangle abe will then be divided into the three equivalent parts abd, dbf, and fbe, as required. In this example the triangles are on equal bases by construction, and between the same parallels, or of the same perpendicular height, as they all terminate at the point b; they are therefore equivalent. (142.) To divide a triangle into any number of equivalent parts, (say 3,) the lines of division between which shall terminate at fixed points, fig. 118. It must be obvious that practically the dividing a piece of land of a triangular form into several parts, all starting from the apex, would be attended with great inconvenience; and it must often happen that such a division would prevent the retention of the use of roadways, or otherwise operate injuriously for the enjoyment of some of the shares. Suppose therefore that it was desired, instead of having the division at d and at /, to have the points of division at m and at n. The following example will shew how the division may be effected; and such division...
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