SEC 



SEC 



CD, bifett each other at right angles in E (Plate XIU. 

 Geometry, Jig. 9.) Make A E a tranfverfe diameter to 90 

 and 90 on the fines ; and take the tranfverfe diftances of 10°, 

 20°, 30°, 40°, jo^, 60°, 70°, 80°, fucceflively, and apply 

 thofe diftances to A E from E towards A, as at the points 

 I, 2, 3, 4, 5, 6, 7, 8 ; and through thofe points draw lines 

 parallel to E C ; make E C a tranfverfe diftance to 90 and 

 90 on the fines ; take the tranfverfe diftances of 80°, 70°, 

 60°, 50°, 40°, 30°, 20°, 10°, fucceffively, and apply thofe 

 diftances to the parallel lines from I to i, 2 to 2, 3 to 3, 

 4 to 4, 5 to 5, 6 to 6, 7 to 7, 8 to 8, and fo many points 

 will be obtained, through which the curve of the ellipfis is to 

 pafs. The fame work being done in all the four quadrants, 

 the eUiptical curve may be completed. In the conftruftion 

 of folar eclipfes, inftead of ufing the fines to every ten de- 

 grees, the fines belonging to the degrees and minutes cor- 

 refponding to the hours and quarter hours, are to be ufed. 



7. To defcribe a parabola whofe parameter (hall be equal 

 to a given fine. Draw a line to reprefent the axis, in which 

 make AB (_/^. 10.) equal to half the given parameter; 

 divide A B, like a line of fines, into every ten degrees, as at 

 the points 10, 20, 30,40, 50, &c. and through thefe points 

 draw lines at right angles to the axis A B. Make the lines 

 A a, lob, 20c, ^od, 40f, &c. refpeftively equal to the 

 chords of 90°, 80°, 70°, 60°, 50°, &c. to the radius A B, 

 and the points a, b, c, d, e, &c. will be in the curve of a para- 

 bola ; and a fmooth curve line drawn through thofe points, 

 and the vertex B, will reprefent the parabolic curve re- 

 quired. 



N. B. As the chords on the feftor run no farther than 60, 

 thofe of 70, 80, and 90, may be found by taking the tranf- 

 verfe diltance of the fines of 35°, 40°, 45°, to the radius 

 A B, and applying thofe diftances twice along the lines 20 c, 

 10 b, See. 



8. To defcribe an hyperbola, the vertex A, and afymp- 

 totes B H, B I, being given (Jig. 11.) The afymptotes 

 B H, B I, being drawn, the line B A bifefting the angle 

 I B H, and the vertex A taken, draw A I, AC, parallel 

 to B H, B I. Make A C a tranfverfe diftance to 45 and 4J, 

 on the upper tangents, and apply to the afymptotes from B 

 fo many of the upper tangents taken tranfverfely as may be 

 thought convenient, as BD 50°, BE 55°, B F 6o^ BG 

 65^ B H 70°, &c. and draw D d, E e, &c. parallel to 

 A C. Make A C a tranfverfe diftance to 45 and 45, on 

 the lower tangents ; take the tranfverfe diftances of the co- 

 tangents before ufed, and lay them on thofe parallel lines : 

 thus, make T) d - 40°, E e = 35% F/ = 30°, G^ = 25°, 

 ah ^ 20°, &c. and through the points A, d, e,f, g, h, &c. 

 draw a curve line, which will be the hyperbola required. 



Sector, in Surveying, U/e of the. The bearings of 

 three places, as A, B, C {Plate VII. Surveying, Jig. i.) 

 to each other, i. e. the angles A B C, B C A, and C A B, 

 being given ; and the diftance of each, from a fourth ftand- 

 ing among them, as D, i. e. B D, D C, and A D, being 

 given ; to find the diftances of the feveral places A, B, C, 

 from each other, i. e. to find the lengths of the fides A B, 

 BC, AC. Having drawn the triangle EFG ijg. 2 ) 

 fimilar to ABC, divide the fide E G in H, fo that E H 

 may be to H G, as A D to D C, after the manner already 

 direfted ; and after the hke manner muft E F be divided 

 in I, fo that E I may be to I F as A D to D B. Then 

 continuing the fides EG, E F, fay, as E H — H G is to 

 H G, fo is E H + H G to G K ; and as E I - I F is to 

 IF, fo let EI + I F be to F M ; which proportions are 

 eafily wrought by the fcales of lines on the feftor. This 

 done, bifeft H K and I M in the points L, N ; and about 

 the faid points as centres, with the diftances L H and I N, 



defcribe two circles, interfefting each other in the point O ; 

 to which, from the angles E, F, G, draw the right lines 

 E O, F O, and O G, which will have the fame proportion 

 to each other, as the lines AD, B D, DC. Now, if the 

 lines E O, F O, and G O, be equal to the given lines 

 AD, B D, DC, the diftances E F, F G, and E G, wiU 

 be the diftances of the places required. But if E O, O F, 

 O G, be lefs than AD, D B, DC, continue them till 

 P O, OR, and O Q, be equal to them ; then the pointt 

 P, Q, R, being joined, the diftances PR, R Q, and P Q, 

 will be the diftances of the places fought. Laftly, if the 

 lines E O, OF, O G, be greater than AD, D B, DC, 

 cut off from them lines equal to A D, B D, D C, and join 

 the points of feAion by three right lines ; the lengths of 

 the faid three right lines will be the diftances of the three 

 places fought. 



Note, if E H be equal to H G, or E I to I F, the 

 centres L and N will be infinitely diftant from H and I ; 

 that is, in the points H and I there muft be perpendiculars 

 raifed to the fides E F, EG, inftead of circles, till they in- 

 terfeft each other ; but if E H be lefs than H G, the centre 

 L will fall on the other fide of the bafe continued ; and the 

 fame is to be underftood of E I, IF. 



The feftor is of efpecial ufe for facilitating the projeAion 

 of the fphere, both orthographic and ftereographic. 



See on the conftruAion and ufe of the feftor, Bion's 

 Conilruftion, &c. of Mathematical Inttruments, by Stone, 

 p. 54, &c. edit. I. and Robcrtfon's Treatife of Mathe- 

 matical Inftruments, &c. p. 30, &c. edit. 2. 



Sector 0/ a Sphere, is compofed of a fegment lefs than 

 a hemifphere, and of a cone having the fame bafe with the 

 fegment, and its vertex in the centre of the fphere. The 

 feftor of a fphere, generated by the revolution of the feftor 

 of a circle CAE {Plate III. Geometry, Jig. 12.) about 

 the radius A C, is equal to a cone, whofe bafe is equal to 

 the portion of the fpherical furface generated by the arc 

 A E, or to the circle defcribed with the radius A E, and 

 whofe height is equal to C A the radius of the fphere. 

 Arch, de Sphaer. et Cyl. Maclaurin's Fluxions, Introd, 

 p. 15. See Sphere. 



SECUL, m Geography, a town of European Turkey, 

 in the province of Moldavia ; 5 miles S.W. of Niemecz. 



SECULAR, fomething that is temporal; in which fenfe 

 the word ftandsoppofite to ecclefmjlical. 



Thus we fay, fecular power, fecular arm, fecular jurif. 

 diftion, &c. 



Secular is more peculiarly ufed for a perfon who lives at 

 liberty in the world ; not fhut up in a monaftery, nor bound 

 by vows, nor fubjefted to the particular rules of any reli« 

 gious community. 



In which fenfe the word ftands oppofed to regular. 



The Romifh clergy is divided into regular znd fecular. 



The regulars pretend, that their itate is much more perfeA 

 than that of the feculars. Secular priells may hold abbeys 

 and priories both fimple and conventual, though not re- 

 gularly, but only in commendam. 



It is a maxim, in their canon \-ayi, fecularia fecularibus, i.e. 

 fecular benefices are only to be given to fecular perfons ; re- 

 gular only to regular. 



Secular Corporation. See Corporation. 



Secular Games, Ludi Seculares, in Antiquity, were 

 folemn games held among the Romans, once in an age ; or, 

 in a period deemed the extent of the longoft life of man, called 

 by the Greeks ziiv, a id by the l^aXiu^, fculum. 



The fecular games were alfo called Terentine games, ludi 

 Terentini, either becaufe Maiiius Valerius Tcrentinus pave 

 occafion to their inftitution ; for having been warned, in a 



dream, yti 



I 



