PROVING PERPENDICULARS.

16

lessons, and care will be taken to make the principles ofthem plain and comprehensible.

Having drawn DB, fig. 21, pi. 1, perpendicular to AC, letus suppose that BA is equal to BC; then the oblique linesdrawn from D to A, and from D to C, are equal. In fact,if we fold the part BDC on BDA, the perpendicular BD,serving as the hinge, the two right angles ABD, CBD,being equal, BC will fall on BA, and C on A, and DCwill be equal to DA. Consequently, two oblique linesequally distant from the perpendicular are equal.

Application of this principle to verify perpendicularlines. —Draftsmen, ship-builders, house-carpenters, masons,&c. frequently make use of this property of geometry,when they wish to ascertain if one line is perpendicular toanother, and they cannot have recourse to the bevel orsquare. They measure very exactly two portions, BA,BC, fig. 21, equal to each other, setting out from theline BD, the position of which they desire to ascertain.They then measure with a rule, or some other instrument,the distance between the points A and D, or the length ofthe oblique line AD; they transfer this measure to DC,setting out from D; if it terminate exactly in C, the twooblique lines AD, DC, are equal, and BD is perpendicularto AC.

When it is required to verify the position of a perpen-dicular, DB or ABC, care must be taken not to draw theoblique line Da too near the perpendicular; for if it isvery near to B, a considerable deviation in B from theperpendicular would only produce a slight alteration inthe length of the oblique line D b, and a mistake mighteasily be committed. It would also be inconvenient tomake the oblique lines at too great a distance, the bestpositions for them being those in which AB, BC, are inlength equal to BD.

By precautions of this nature, conducted on such prin-ciples in each particular case, we can give to plans, build-ings and machines, that degree of precision and correct-