Page:Cyclopaedia, Chambers - Volume 2.djvu/737

 S I N

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S I N

■j«2^eSiNE AD of the Arch kY. being given; to find the Sine c/ffe Half Arch, or Half of AE.

Find the Chord of the Arch A E (See Chord) : for Half of this is its Sine. Thus, iuppofing D G and A D, as in the preceding Problem ; we ihall find the Sine of the Arch Half A E, or the Sim of 15. = 2588 190.

than J,« e -Csm, and it will be proper for the newlncum bent to read the 30 Articles, and the Liturgy in the Church

ya ButfRea d I0 d0 w P hat ■ Mhe ! ; ,ncu " lb " 'y d°

But a Rettery, or a Portion of it, may properly be a j,V«..

Since the Angles at E and G are right Angles ; and the Angle B is common to each Triangle B C G and DEB $ we ihall have BC:CG::BD:DE: wherefore CG being found by the Second Problem, and B D being double of DGj D E is found by the Rule of Proportion.

4 The Sines F G md D E {Fig. 8.) of the Arches F A and D A,tv/.-oJe Pitfcreuce D F is greater than 45 Minutes \bcivg given 5 to fad any intermediate Sine, as 1L.

To theDifference FD of theArches,whofe<5/H«aregiven 5 the Difference of the Arch I F, whofe Sine is required, and the Difference of the given S'meS D H ; find a fourth Propor- tional : This added to the lefs given Sine F G 5 the Aggre- gate will be the Sine required.

5° lo.findthe Sine 0/45 degrees. Let H I (Fig. 6. ) be a Quadrant of the Circle ; then will H C I be a right Angle : coniequentlv the Triangle, rectangu- lar 5 therefore H I* — H C z -f C V = 2 H G% wherefore, fince HC the whole Sine, is 100000005 if from iHCTquared, 200000000000000, be extracted the fcjuare Root 14142136$ we fhall have the Chord H I, whofe Half 7671068 is the Sine of 45 required.

6° The Sine of a Minute or 60" F G, (Fig. %.) being given ^ to find the Sine of one or more Seconds MN.

Since the Arches A M and A F are very fmall ; A M F may be taken for a right Line, without any fenfible Error in the Decimal Fractions of the Radius wherein the Sine is cxprefs'd ; that is, the Arches A M and A F may be taken proportional to their Chords. Wherefore, fince M N is pa- rallel to F G 5 we fhall have A F : F G : : A M : MN : Therefore AF, FG and A M being given, M N is eafily had.

To Confiruft a Canon of Sines.

The Sines of 30 15 45° and 36 (which we have al- ready fhewn how to find,) being had; we can thence con- flruft a Canon of all the Sines to every Minute, or even Second. For from the Sine of 36 we find thole of 18 9° 4 30' and 2 15', by the Second Problem: The Sines of 54 72 8 1° 85° 30' and 870 45', &c. by the firft Problem. Again, for the Sine of 45°, find the Sine of22° 30' no 15', i$c. From the Sines of 30 and the Sines of 54°, find the Sine of 12. From the Sine of 12, find the Sines of 6° 3° 1 3o' 35' 78°, f§C, From the Sine of 15°, find the Sine of 7° 30', 30 4$', l$c. 'till you have 120 Sines fuc- ceedihg each other orderly, at an Interval of 45: Minutes. Between thefe, find the intermediate Shies by the Fifth ' Problem : Thus will the Canon be compleat.

From the Sine of an Arch given j to find the Tangent and Secant. See Tangent and Secant.

To find the Logarithm of a given Sine ; See Logarithm. Note, the Logarithm of a Sine, is call'd an Artificial Sine.

In every Triangle, the Sides are a« the Sines of the op- polite Angled. See Triangle,

The Sine B C (Fig. 9.) and the Verfe.i Sine AB, being given in common Meafure, not in Warts of the Radius $ to find the Arch E F C in ^Degrees. Find the Semi-diameter A D, (See Semi-diameter.) Then in the Triangle D B C, betides the Right Angle B, by the Sides A C and D C, we find the Angle ADC, which ihews the Number of Degrees in the Arch, the Double whereof is the Arch FC; the ufe of which Problem is in finding the Segment of a Circle. See Segment.

Line of Sines, a Line on the Se&or, Gtlntefs Scale, £-?c. the Defcription and Ufe whereof fee under the Articles Sector and Gunter's Scale.

SINECURES are Ecclefiaftical Benefices without Cure of Souls. See Benefice, and Cure.

No Church, where there is but one Incumbent, can pro- perly be a Sine-Cure; And though the Church being down, or the Parifh being become deftitute of Pariihioners, the Incumbent may be thereby neceffarily acquitted from the actual Performance of publick Duty, yet he is Hill under an Obligation to do if, whenever a Church fhall be built, and there are a competent Number of Inhabitants : And in the mean while, if the Church be Preftntative, as mod fuch Churches are, the Incumbent is inftituted into the Cure

,- .- zj— c — --™*m»j (j.-(/. j.u mac acre no JJ11-

penfation is neceflary to hold this. Sine-Cure with a former Living: Nor need he read the Articles or Divine Service, as required by, J &IZ. c. ,2. which extends only to a Be!

££".3h? ?"£ *~k S '" e - C T Donat,ve w « Sta- tion and Induction: but one Prefentative mud have both, efpec.ally ,t it conhft in Glebe and Tythes, and not in a Por- tion of Money : But the Inflation muft not run in Oral Anmamm, but >n ReBonani, five fivrtionem ReBori* de

i i ' T, C \, y the, ab °™:-mention'd Statute 2 1 H. VIII not only Prebends and Retteries, with Vicarages endowed, but Deaneries and Archdeaconries, are declared to be Bene! rices without Cure.

SINE-DIE, in Law, when Judgment is given againft the Plaintiff ; he is then laid to be in mifencordia pro fallo clamorefuo: But when for the Defendant, then if is laid, hat Hide fine d/e t i. e. he is difmifted the Court —The Phnle is alio ufed in Parliament, for the Adjournment of any De- bate, without fixing the Day when it fhall come on Lain, and is looked upon as a genteeler Diiiniflion of the Thin" required. &

SINEW, in Anatomy, {&, is w h at „e otherwife call a Nerve. See Nerve.

SINGING, the ASion of making divers Inflexions of the Voice, agreeable to the Ear, and even sneering to tho Notes of a Song or Piece of Melody. See Song

The firli thing done in learning to/,. s> is to raife a Seal, of Notes by Tones and Semi-tones, to an Oc'ive and de fcend again by the fame Notes ; and then to rife' and fall by greater Intervals as a 3d, 4 ,h, and 5 th ; and to do all thirty Notes of different Pitch. Then thefe Notes are re, prefented by Lines and Spaces, to which the Syllables fa,fd, la, mi, are applied, and the Pupil taught to name each Line and Space thereby ; whence this Pradice is ulu- ally caUd .Sd-fa-im The Nature, Reafon, Defefls £*; whereof, iee under me Article Sol-fa-ing '

SINGULAR Number, in Grammar, the firft manner of declining Nouns, and conjugating Verbs ; ufed when we onlyipeakorafinglePerion or Thing. See Number.

The Latins, French, Engbjb, &c. have of, Numbers but the SnigfarMi Plural i the Greeks and Hebrews have like- wife 3,'Dual. See Plural, Dual, £& m^ IN o? ULTUS ,' '".M^'^ a convu'lfive Motion of the

o d I r ^ C °r nmonl >' caU ' d K < c «-»t- See Hiccoup.

SIMCAL ^ua.,ranr, a Kind of Quadrant furniih-J

with an Index, and two Sights, to take Altitudes, !$ c

by; and, befides, its Side, or Face, covered over with

Sincst drawn from each Side, intetfeSing each other,

. wh " cb y' h, ; Scatn! :, n "« ^«. by Irrfpeftion, any Problem in Plain Sailing, see Sailing.

i'l SS? r and U ' C ' '" UndCr ,hC A " ide Q_«BR AN T.

SINlSiLK, fomeming on, or towards the left Hand Hence Swifter. is ordinarily ufed among us for unlucky = rho"' in the Holy R,tes of Divining, the Remans tried it i„ an oppofite Senfe. Thus Avis Simjira, or a Bird on the left Hand, was etteem d a happy Omen : Whence in the Law of the Twelve Tables, Ave Sinifira MuR magifter eft. And hence the Greeks, according to Liffiiis, call the left Hand a.e/.viey- v i beI '- *

Somederive :the Word Snifter, a Sme>.idoi becaufe the Gods by iuch Auguries, permit us to proceed in our Defigns

Si N ,ster in Heraldry. The Swifter Side of an Ef- cutcheon is the left Side. Snifter chief Point, is the next middle Chief, on the left Side. Swifter bafe Point, is next the bale Point, at the bottom of the Elcutcheon. See Point Escutcheon, Sjfc. "ini,

„f 8 f ™ M™ Jft f' am ° ng A(lroIo S ers . " an Appearance, of two llanets, happening according to the Succeffi™ of the Signs; as Saturn m Aries, and Mars in the lame Degree of Gemini. See Aspect.

SINISTRI a Seel of ancient Hereticks, thus call'd ; be- caufe they held the left Hand, Siniftram maimrn, in Abhor- rence, and made it a Point of Religion, not to receive any thing therewith, \yhat in us, is a Piece of Civility ; in than was a Superftition. Salfainau obferves, that they were like- wiie a,\cd SabbatJiiaus and Novatians. SeeNovATiANs.Sfc

SI nan omnes, a Writ of Aflociation, whereby, if all in Commiffion cannot meet at the Day affign'd, it is per- mitted, that two or more of them may finiih the Buiinels" See Association.

SINOPER, in Natural Hiftory. See Ruddle

SINOPLE or SENOPLE, in Heraldry, the Gr-en Co lour ,n Armories ; thus called by the ancient Heralds, tho' Pliny and Jftdore, by Color Prafmus, or Simple, mean * ■"■ browTiifh