Fig. Practical Geometry. T PROBLEM. I. O erect a Perpendicular, from the Point B on the Line KN. Open your Compaffes to any fmall diflance; fet one Foot in B, and with the other make the 2 Marks D, G. this done, open the Compaffes to any convenient diftance, then fet one Foot in D, and with the other draw the obfcure Arch GG. 20. Again, the Compaffes ftill keeping the fame diftance, fet one Foot in the Point G, and defcribe the Arch HH, croffing the former in the Point A, from which draw the Line AB, and it will be perpendicular to the given Line KN. PROBLEM. II. Fig.21. To raife a Perpendicular DB,upon the End of the Line AB. Open your Compaffes to any ordinary extent, and fetting. one Foot upon the point B, let the other fall at pleafure, as at the Point K, and without altering the Compaffes, fet one Foot in the Point K, and with the other crofs the Line AB, at D, alfo on the other Side defcribe the Arch EE, then, lay your Ruler to D, and K, draw the Line DKF: laftly, from the point B to the Interfection at g, draw the Line B g D, which is perpendicular to the Line AB PROBLEM III. Fig.22.To let fall aPerpendicular AE,to the given Line. RQ from the givenPoint A, which is out of the Line BC, having fet the foot of the Compaffes upon A, with any Interval, defcribe 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 fay the Line AE is perpendicular to RQ. PROBLEM IV. Fig. 23. From apoint C given; to draw a Line CD Parallel to the Line AB given. On the Point C as on a Center, ftrike anArch of a Circle cutting the Line AB given in the Point A: Then fet the Foot of the Compaffes any where (at a good diftance from A) in the given Line AB, as B, and with the fame Interval ftrike the Arch D: Then take in the Compaffes 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 PROBLEM V. Fig. 24. To divide the given right Line AB into two equal parts, and at Right Angles. Take in your Compaffes any diftance above half the length of the Line AB, and fetting one Foot in the end A, with the other draw the Arch CDE, then with the fame interval on the Center B,defcribe the Arch FGK, intercepting the former in F and G, from which Points draw the Line FGH, and it is done. PROBLEM VI. A fecond way to draw Lines Parallel to each other. Fig. 25. Let BD he a Line given; to make a Line Parallel unto it, fet one Foot of the Compaffes at G, and with the other defcribe an Arch as a e, and do the fame at the other end of the Line, and through the utmoft Convexity, and of thofe two Arches draw the Line IL. A third way how to draw Lines Parallel to another Line, which alfo paffes through a Point affigned, Fig. 26. Let BD be the given Line, E, the Point through which the Parallel muft pafs, Place one foot of your Compaffes in E, and open them till the other foot just touch the Line BC, and defcribe the Arch ae; with the fame extent in any part of the given Line, fet one foot of your Compaffes, 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. PROBLEM VIII. Fig. 27 To defcribe a Triangle, ACB, whofe fides, AC, CB, and AB, fhall 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 Compaffes the Line F, to which make AB equal: Then on the Center B with the diftance D defcribe the Arch zx. Again on A with the Line E defcribe an Arch cutting the former in C, thea draw AC, and CB, and it is done. PROBLEM IX. Note, The very fame way you may make a Triangle equal to another Triangle. given. PRO PROBLEM X. Fig. 28. To make an Angle BACequalto the Angle EDF at A the end of the Line ABgiven. Defcribe from the Points A and D as Centers two Arches BC, and EF, with the fame interval of the Compaffes; then take the diftance EF, and fet it from B to C, then draw the Line AC, I fay, the Angles BAC, and EDF, are equal. PROBLEM XI. Fig. 29. To make a Square BCDE, whose fides fhou'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 Perpendicular CD alfo equal to the Line A,then with the fame diftance, fet one foot in B, frike the Arch kl, and on D defcribe the Arch bb, crofling each other in the point M, which will conftitute the Square BCDE. PROBLEM XII. 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 them. Firft lay down your longeft fide |