SEC 



.SEC 



Sections, Similar. See Similar. 



Section of a Building denotes its profile, or a delinea- 

 tion of its heights and depths raifed on the plan ; as if the 

 fabric was cut afinidcr, to difcovcr the infide. 



Section, Hoi-i-^onial. Sec Ichnoguaphy. 



SECTIS non Facicndisi in Law, a writ brought by a 

 woman, who for her dower, &c. ought not to perform fuit 

 of court. 



SECTOR, in AJlrnnomy, the name of two different aftro- 

 nomical inftriiments, for mcafuring fmall angular diftancea in 

 the heavenly regions ; one of which has a motion in or pa- 

 rallel to the equator, and the other is direfted to the zenith. 

 The conftruftion and ufe of each of thcfe inftruments may 

 be feen under the refpeftive titles of Equatorial SeBor, 

 and Zenith Scilor. 



Sector, in Geometry, a part of a circle comprehended 

 between the radii and the arc. 



Thus the mixed triangle A C D (.Plate XIII. Geometry, 

 fg. 5.) comprehended between the radii A C and C D, and 

 the arc AD, is a feBor of the circle. 



It is demon llrated ijy geometricians, that the feftor of a 

 circle, as A C D, is equal to a triangle, whofe bafe is the 

 arc A D, and its altitude the radius A C. 



If from the common centre of two concentric circles be 

 drawn two radii to the periphery of the outer, the two arcs 

 included between the radii will have the fame ratio to their 

 peripheries ; and the two feftors, the fame ratio to the areas 

 of their circles. 



To find the area of a feftor D C E ; the radius of the 

 circle C D, and the arc D E, being given. To 100,314, 

 and the radius D C, find a fourth proportional number ; 

 this will be the femiperiphery : then to 180 degrees, the 

 given arc D E, and the femiperiphery jiilt found, find 

 another fourth proportional ; this will give the arc D E in 

 the fame meafure in which the radius D C is given : lailly, 

 multiply the arc D E into the femiradius, and the produA 

 is the area of the feftor. 



In order to find the area of any feclor of a circle. Dr. 

 Hutton, in his " Menfuration," has given the two fol- 

 lowing rules. 



Rule I. — Multiply the radius by half the arc of the feftor, 

 and the produft will be the area, as in the whole circle. 

 For the demonftration of this, fee the article Circm:. 

 Putting r = the radius of a circle, (/=^ the diameter, A = 

 the area of a feftor of it, a = the length of the arc of the 

 feftor, b = the degrees in ~ a, s :^ half the chord of the 

 arc a, or the fine of - a, and v — the verfod fine of i a : 

 then, by multiplying the radius by half the arc, by a va- 

 riety of rules which Dr. Hutton has dated, wc (hall have, 



I. A ~ ^ a r = . 1745329 brr, 2. A = r \^ J-y X 



2 . 3 rf 2 .4. 5 rf' 2 .4. 6. 7/i 



A: 



/ 3 ■" 

 \ / — ", ) nearly. 6. A 



V 3 rf — Tl ' 



X isd 



"I 4 \/ -- , nearly. It appears thxt the area of the 



feftor might be exprctled in feveral other ways ; fuch as bj 

 the tangent, cofine, &c. of its femi-arc ; but the formt 

 above given arc thofe that are the mod ufeful. 



Rule 1 1. — As 360 is to the degrees in the arc of the feAor, 

 fo is the whole area of the circle to the area of the feftor. 



Sector alfo denotes a mathematical inllrument, of grest 

 ufe in finding the proportion between quantities of the fame 

 kind ; as between lines and lines, furfaces and furfaces, &c. : 

 whence the French call it the compafs of proportion. 



Tlie great advantage of the lector above the common 

 fcalcs, &c. is, that it is made fo as to fit all radiufcs, and 

 all fcales. By the lines of chords, fines, &c. on the feftor, 

 we have lines ol chords, fines, &c. to any radiu« betwixt 

 the length and breadth of the feftor when open. 



The feftor is founded on the fourth propofition of the 

 fixth book of Euclid ; where it is demonltrated, that fimilar 

 triangles have their homoloprous fides proportional. An 

 idea of the theory of its conftrnftion may be conceived tims. 

 Let the lines A B, AC (PlaleXWl. Geometry, fg. b.) 

 reprcfcnt the legs of the feftor ; and AD, A E, two equal 

 feftions from the centre : if, now, the points C B and D E 

 be conncfted, the lines C B and D E will be parallel : 

 therefore the triangles A D E, A C B, will be fimilar; 

 and, confequently, the fides A D, D E, A B, and B C, 

 proportional; tliat is, as AD : DE :: AB : BC; 

 whence, if A D be the half, third, or fourth part of A B, 

 D E will be a half, third, or fourth part of C B ; and the 

 fame holds of all the rcll. 



If, therefore, A D be the cliord, fine, or tangent, of 

 any number of degrees to the radius A B ; D E will be the 

 fame to the radius B C. 



Sector, Defcription of the. The inllrument confifti of 

 two rulers, or legs, of hrafs or ivory, or any other matter, 

 reprefenting the radii, moveable round .in axis or joint, the 

 middle of which expredcs the centre ; whence feveral fcalcs 

 arc drawn on the faces of the rulers. See P/a/cXIII. Geo- 

 vtetry. Jig. 7. 



The icalcs generally put on fcftors may be diftinguifticd 

 into finglc and double. The fingle fcales arc fuch as arc 

 commonly put upon plain fcales ; the double (eales arc thofc 

 which proceed from the centre : each fcale is laid twice on 

 the fame face of the iiidrmnent, i-iz. once on each leg : from 

 thefe fcales, dimenfiuns or dillances are to be taken, when 

 the legs of the inllrument are in an angular pofition. 



The fcales commonly put upon the bed fcftors are 



" i") (Tnches, each inch divided into 8 and 10 parti- 

 2 Decimals, containing 100 parts. 



'1 



.1 



4 



5 

 6 



7 

 8 



9 

 10 

 1 1 

 12 



'3 



L14J 



o 



^ 5''-3'" g 



chords. 



Sines, 



Tangents, 



Khumbi, 

 ^ J Latitude, 

 ;= "j Hours, 



I^ongitudc, 



liiclin. Merid. 



Numbers, 

 Siuci, 



Vcrfed fines. 

 Tangents, 



' Linen, or of equal parts. 



Chords, 



Sines, 



Tangents to 45°, 



Secants, 



Tangents to above 45°, 

 i. Polygon;., 



fCho. 



Sin. 



Tang. 



Rum. 



Lat. 



Hou. 



Lon. 



111. Mer. 



Num. 



Sill. 



V. Sin. 

 (.Tan. 



■» Lin. 

 Cho. 

 Sim. 

 Tan. 

 Sec. 

 Tan. 

 Pol. 



The 



