SEC
w hofe Side is 5 Feet ; and, by the Line of Polygons, as already directed, make the Hbfceles Triangle CGD jo, as that C G being the Semi-diameter of a Circle, C D may be the Side of a regular Pentagon inferibed therein, and let fall the Perpendicular G E. Then con- ■ tinning the Lines E G and E C, make E F equal to the Side of the Square before made: And from the Point F, draw the right Line F H parallel to G C ; then a mean Proportional between GE and E F will be equal to half the Side of the Polygon (ought, which doubled, will give the whole Side. The Side of the Pentagon thus had, the Pentagon itfelf may be defcribed, as above dircfled.
2». A Circle being given, to find a Square equal thereto. Divide the Diameter into 14 equal Parrs, by the Line of Lines, as above directed: Then will 12. 4 of thofe Parts found by the fame Line, be the Side of the Square fought.
30, A Square being given, to find the Diameter of a Circle equal thereto. Divide the Side of the Square into 11 equal Parts, by means of the Line of Lines ; and con tinue that Side to 12. 4 Parts; this will be the Dia- meter of the Circle required.
4°. To find the Side of a Square equal to an Eliffis, Kbefe tranfverfe and conjugate Diameters are given. Find a mean Proportional between the tranfverfe and conjugate Diameters ; which, being divided into 14 equal Parts; u* v thereof, will be the Side of the Square re- quired.
U5 ]
SEC
Ufe of the Sector in Surveying.
ibe Searings of three Places, as A, B, C, (Fig. 5.) '« each other; i. e. -1 he Angles ABC, BCA and CAB, being given : And tie Diftance of each, from a founb ftandiig ameng them : as, D, /'. e. B D, D C, and A D being given ; To find the Difiances of the feveral 'Places A, B, C, from each other; i. e. The Lengths of the mes A B, B C, AC. Having drawn the Triangle IfG (Fig. 6 ) fimilar to ABC, divide the Side
- ■ G in H, fo as that E H may be to H G, as A D
'" D C, after the Manner already directed : And, after the like Manner mull E F be divided in I, fo as EI ""v be to I F, as A D to D B Then continuing the ""!« E G, E F, fay. As E H - H G is to H G, fo is
' H + HG to G H, and as E 1 — I F is to 1 F, fo let E I -f. I p be to F M ; which Proportions arc e.iiily ^tought by vour Line of Lilies on the SebJor. This done, Jfttfi H K 'and I M, in the Points L N ; and about the raid Points as Centres, with the Difiances L H, and I N, nelctibe two Circles interfering each other, in the Point 1, from the Angles EFG, draw the right F O, and O G, which will have the fame
Proportion to each other, as the Lines A D, B D, D C: £» "' r ' he V n r? g °. F O, and G O, be equal to the I d f% r^ n ?' ! D ' D G ' the Diita "«s * F, F G, But it ?'n W n P *V D I fla,,ces of the Places required J £ ?> P P '.OG, be leli than A D, D B, D C,
O G, be greater than AD, D B, D C, cut off from them Lines equal to AD, B D, DC, and join the Points of Sea,onby_ three right Lines; the Lengths of be the Lilfances of the
the laid thre
ight three Places fought. Note, If E H be equal to H G, or E I to IF the Centres L and N, will be infinitely diftant from Hand I; that is, in the Points H and I, there mull be Perpendiculars raifed to the Sides E E G, infiead of Circles, till the but if E H be leli than H G, on the other Side of the Bale 'continued, and is to be underliood of E I, I F.
Ufe of the Seflor in tbeProjellvn of the Sphen Orthcgrafhic and Siereigrafhic ; " and Stereographic.
mteriecl each other ; the Centre L will fall he fame
. both See Orthographic
\ j». To defenbe an Ellipfis in any given Ratio of its Vo ^Diameter; the Area whereof pall be equal to a given Square. Suppofe the Proportion of the tranfverle and conjugate Diameters be icquired, as 2 to 1; divide the Side ot the given Square into jj equal Parts: Then as 2 is to 1, to is n X 14 c ij4 to a 4th Number; the Square whereof is the conjugate Diameter fought. Then, as 1 to 2, fb is the conjugate Diameter to the tranfverfe. Now,
6". To defenh an Ellipfis, by having the tranfverfe end cenfigate 'Diameters given. Suppoie A B and E D (Fig. 4J io be the given Diameters ; take A C in your Compalfes, and to the Extent thereof open the Sector, till the Dilfance from 90 to 9.,, on the Lines of Sines, be equal thereto. Then may the Line A C be divided into a Line of Lines, by taking the parallel Extents of the Sine of each Degree, on the Legs of the Senior, in your Compalfes, and laying them off from the Centre C. The Line thus divided into Sines, (in the Figure 'tis only done into every 10th Sine) from each raiie Perpendicu- lars both Ways ; then, find Points in thofe Perpendicu- lars through which the Ellipfis mufl pals, thus : Take the Extent of the Semi-conjugate Diameter C E between your Compaffes, and open the Se&'or, till the Aperture of 90 and 90 on the Lines of Sines be equal thereto : Then rake the parallel Sines of each Degree of the Line of Sines of the Seblcr, and lay rhem ofF on thofe Perpendiculars drawn through their Complements in the Line of Sines A C; thus will you have two Points in each Perpendicular, through which the Ellipfis mufl pafs. E. gr. The Setter flill remaining the fame, take the Di- ilance from 80 to 80 on the Lines of Sines, in your Com- palfes, and letting one Foot in the Point 10, on the Line A C, with the other, make the Points a and b in the Per- pendiculars palling through that Point : Then will a and b be the two Points in the Perpendicular, through which the EHiplis mufl pafs. All the other Points, found after the fame Manner, being connecled, will give the Semi-Ellipfis DAE; and the other Half will be drawn after the fame Manner.
SECULAR, fomerhmg Temporal, in which Senfe th« "Word is ufed in Oppofition to Ecclejiallical. Thus we lay. Secular 'Power, Secular Arm,&.c.
Secular is alio uied for a Perfon who lives at liberty
- - the World, not Ifiut up in a Monattcry, not bound by
nor fubjected to the particular Rules of any Reli- gious Community : In which Senfe the Word ttands in Oppofition to Rigular. The Romifij Clergy is divided into Regular and Secular. The Regulars pretend their State is much more perfeel than that of the Seculars. Secular Priells may hoid Abbies and Priories both fiinpl; and Conventual, though not regularly but only in Com- mendam. "Pis a Maxim, in their Canon Law, Secularia Seculanbus, and Secular Benefices are
nly 10 be ;
me E O
to Secular Perfons ; Regular to .Regular. See Regular.
SLOULARE CARMEN, Secular 'Room; A Poem lung, or re-hearied, at the Secular Games. Of this Kind we have a very fine Piece among the Works of Horace : 'Tis a Saphic Ode, which ulually comes at the End of his Epodes. In fbme Editions, the Twenty-firll Ode of the firft Book, is called Carmen SecuLre.
- , SECULAR GAMES, Secuhvres Ludi
- In Antiquity,
folemn Games, l.cld among the Romans, once in an Age ; or, in a Period, deemed the Extent of the longell Life of Man, called by the Greeks mil, and the Latins, Seadumi They laited three Days, „nd as many Nights, during which, Sacrifices were performed, Theatrical Shews ex- hibited, with Combats, Games, ££?<;. in the Circus. Their Origine, and Inflitution, is delivered at Length by Val. Maximus : The Occafion thereof was, to flop the Progrefs of a Plague. The firll who had them celebrated, at Kane, was Valerius Publicola, the firll Conful created after the Expulfion of the Kings, in the Year of Rome 245. The Ceremonies to be obferved therein were found in one of the Books of the Sibyls. At the Time of their Celebration, Heralds were lent to invite all the World to a Feafl no body had ever yet feen, nor was ever to fee again.
Authors are not agreed of the Number of Years where- in thefe Games returned ; partly, becaufe the Quantity of an Age or Sectllltm among the Antients is not known; and partly on other Accounts : Some will have it, that they were held once every hundred Years, and that the Seculum, or Age, was our Century. This Varro and Livy feem to exprefs in very plain Terms ; yet others will have it, that Seculum comprehended no Years, and that the Secular Games only returned in that Period, that is, at the Beginning of every iiirh Year; which Opinion is countenanced by Horace, in his Secular 'Poem, v. 2 1. Be this as it will, it is certain they fometimes did not flay for the mth, nor even for the 100th Year, for the Celebration of thefe Games. Augufttis, fo£.In- flance, held them in the Year of Rsme 736; and Caligulu again in the Year of Romegiq, and of Chrill 38, »j«. 64 Years after the former ; and 1)omitian, again, in Hill lei's Time, viz. in the Year of Chrift 87, at which Tacitus affifled in Quality of Decemvir, as he himfelf tells us, Annul. Lib. xi. c. ii. This was the Seventh Time that Rome had feen them from their firll Inflitution. The Emperor Sevens exhibited them the Eighth Time: 1 10 Years after thofe of Domitian : Zozimus (ays, thefe were the lall ; but he is miflaken, for in the Year of Rome 1000, Fifty Years after thofe of Severus, the Em- peror Philip had them celebrated with greater Magnifi- cence than had ever been known. We find them repre- fented On Medals.
The L.ndi Seculares were alfo called Ludi Tarentini,
from Maaitis Valerius Tarentinus, who gave Occafion
[M] t»
