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O erect a Perpendicular, from 20.
the Point B. on the Line KN. Open your compasses to any small diftance ; let one Foot in B, and with the other make the 2 Marks D, G. this done, open the Compasses to any convenient distance, then set one Foot in D, and with the other draw the obscure Arch GG.
Again, the Compasses ftill keeping the same distance, fet one Foot in the Point G, and describe the Arch HH, crossing the former in the Point A, from which draw the Line AB, and it will be perpendicular to the given Line KN.
PROBLE M. II.
Fig.21. To raife a Perpendicular DB,upon the End of the Line AB. Open your Com. passes to any ordinary extent, and serting one Foot upon the point B, let the other fall at pleasure, as at the Point K, and without altering the Compaffes, set one Foot in the Point K, and with the other cross the Line AB, at D, also on the other
Side describe the Arch EE, then, lay your Ruler to D, and K, draw the Line DKF: lastly, from the point B to the Intersection at g, draw the Line B g D, which is perpendicular to the Line AB.
Fig.22. To let fall a Perpendicular. E, to the given Line. RQ,from the given Point, which is out of the Line BC; having set the foot of the Compasses upon A, with any Interval, describe the Arch BC, which will cut the Line RQ at the points Band C: Then divide the Line BC into two equal parts at the point E. I say the Line AE is perpendicular to RQ.
Fig. 23. From apoint Cgiven; to draw a Line CD Parallel to the Line AB given. On the Point C as on a Center, strike an Arch of a Circle cutting the Line AB given in the Point A: Then set the Foot of the Compasses any where (at a good distance from A) in the given Line AB, as B, and with the same Interval strike the Arch D: Then take in the Compaffts the Length AB, and, puting one Foot in C, draw an Arch cutting the other in the Point D, through C and D, draw the Line CD, and it will be parallel to AB. PROB
Fig. 24. To divide the given right Line AB into two equal paris, and at Righe Angles. Take in your compasses any distance above half the length of the Line AB, and setting one Foot in the end A, with the other draw the Arch CDE, then with the same interval on the Center B, describe the Arch FGK, intercepting the former in F and G, from which Points draw the Line FGH, and it is done.
A second way to draw Lines Parallel to each other.
Fig. 25. Let BD he a Line given ; to make a Line Parallel unto it, set one Foot of the Compasses at G, and with the other defcribe an Arch as a e, and do the same at the other end of the Line, and through the utmost Convexity, and of those iwo Arches diaw the Line JL.
A third way how to draw Lines Porallel to another Line, which also passes
Fig.26. Let BD be the given Line, E, the Point through which the Parallel muft pass; Place one foot of your compasses in E, and open them till the other foot juft touch the Line BC, and describe the Arch a e; with the same extent in any part of the given Line, set one foct of your compasses, and ftrike the Arch D, then through the point E and the utmoft Convexity of the last Arch draw the line CK, which is parallel to BD and through the point E.
Fig.27. To defcribe a Triangle. ACB, whose sides, AC, CB, and AB, shall be equal to the three fides, E, D, and F given, provided that any two of them be greater than the third. Take with your Compasses the Line F, to which make AB equal : Then on the Center B with the diftance D describe the Arch z. X. Again on A with the Line E dercribe an Arch cutting the former in C, then draw AC, and CB, and it is done.
Note, The very fame way you may make a Triangle equal to another Triangle given.
Fig. 28. To make an AngleBAСequalto the Angle EDFat A the end of the Line ABgiven. Describe from the Points A and D as Centers two Arches BC, and EF, with the saine interval of the Compasses; then take the distance EF, and set it from B to C, then draw the Line AC, I lay, the Angles BAC, and EDF, are equal.
Fig. 29. To make a Square BCDE, whose sides shou'd be equal to the given Line A : Firft, make the Line BC, equal to the Line A, and on the end thereof at C, erect the PerpendicularCD also equal to the Line A, then with the same distance, set one foot in B, firike the Arch kl, and on D describe the Arch bb, crolling each other in the point M, which will constitute the Square BCDE.
Fig. 30 To make a ParallelogramABCDor long Square, having one fide equal to A and the other to B. This is like the former; let two Lines be given you, AB and BC, and let it be required to make a Parallelogram of thein. First lay down your longest lide