Page:Cyclopaedia, Chambers - Volume 1.djvu/365

 C H O

(211 )

have invented

CHO

itrong, without altering the Tone. g L BOW '. n. !ls t0 th = Arrow : which occafion'd the

The fixth Chord of Bafs- Viols, and the tenth of large ant '= nt G ?T Ctr,c ' ans, to »". this %" ">= &rf of ,hc

Theories, confill of 50 Threads, or Guts : There are feme ~£S 5?-*? " h ",f he ^"/f • ° r Ar . row i <»= former of twilled and polifti'd with Equife-

- 07/y

of them 100 Foot Ion: turn, or Hotfe-Tai

For the "Divifion of Chords, fo as to confiitu. given Interval, the Rules are as follow. 1. To affign ftwb a Ttirt of a Chord A B, as Jhall con- ftitute any Concord, v.g. a Fifth, or any other Interval, with the whole.

Divide AB into as many Parts, as the greateft Number of the Interval has

which Names is (till continu'd,' tho the latter is difus'd. What the AnuenrsrallM Sagitta, is now term'd the Sine of

Units; v.g. the Fifth being 2:3, the Line is divided into 3. Of

-I-

1-

the Complement. See Sagitta.

Half the Chord of ike double Arch B 0, is what we now call the Sight Sine ; and the Excefs of the Radii b-yond the Sagitta E, the Verfcd Sine. See Sine.

The Chord of an Angle, and the Chord of its Comple- ment to a Semicircle, arc the fame thing. The Chord of 5oDegrees is alfo the Chord of 130.

'TIS demonftrated, in Geometry, that the Radius C E, biffefling the Chord B A in D, does alfo bif&a the Arch inE, and is perpendicular to the Chord AB; and wee vff"- AaA again, if the right Line NE biflefl the Chord A B, and be perpendicular thereto; that it piffes thro the Centre, and docs biffeft both the Arch AEB, and the Circle A N B.

Todi- .-. Parts. Dtaw a pendicular to the middle Point DE of the Chord ABt this biflbas the given Arch A B.

2. To defcribe a Circle, that mall pafs thro' any three

. AB, that front VS£g&^tt t Sft&fii? W^&'S

and B : draw the right Lines DE and H G. The Point of Interfeflion I, is the Centre of the Circle to be defcrib'd thro' A, B, and C.

JDsmmft. For the Points A C and C B are in the Peri- phery of fome Circle ; and therefore, the Lines A C and CB are Chords. But E D is perpendicular to AC, ancf GH to BC; ED biffefls AC, and GH biftefts EC; wherefore each paffes thro' the Centre. Now as D E and G H only interfeft in I ; I will be the Centre of a Circle,

feveral Numbers of the Series","^ ihT&mTc D* and V ^ g '^'^ P V °l ^T - A ' C ' ^ ?' • ,

E • fo as A C to AD is a TW An? a c ' SH Hence, affuming three Points in the Periphery or Arch

AB Octave ' ° '° AE * Flfth ' t0 °/. i^ Circ, le - ^Centre may be found, and the given

thefe I take as many as the Leffer Number, v.g. 2 = A C • A C is the Part fought : That is, two Lines, whofe Lengths are to each other as A B to A C, make a Fifth

I reduce the given Ratios 1 : 2, 2. 3, and 4 : J, to oneBuS pendicul"- - - -°- --- •■ " "3-"" Pa "-'

damcncal ; the Series becomes

24, 20=15. The Fun-

damental is 30 ; and the Seftions fought are 24; the Third • - 20, the Fifth ; and 15, the Octave. feci

, . f. ~ % ,,, ~" V " —"'"V JJ.JJ, it HUM I I Vl/b

the leafi, gradually to the whole, Jball contain a given Se- ries of Intervals Hi any given Order, viz. fo as the lead to the next greater contain a Third g; that to tho next greater, a Fifth ; and that to the whole an Octave. Reduce the three Ratios 4:5,2:

ries ; hence we ^ _ R _

have 8 : 10 : 15 J


 * 3 °- q D i! ide the Line int ° tlle Number of Parts of the

greateft Extreme of the. Series, vis,. 30 \ we have the Sections fought at. the Points of Divifion, anfwering the

, C, D, and Fifth, to

1 : 2, to one Se-

3. To divide a Line A B into two Tarts, to contain be- twixt them any Interval, v. g. a Fourth.

Add together the Numbers containing the Ratio of the Interval, v.g. 3:4; and the

Line into as many Parts as the a ....*_ 7. Sum,

AH-l-M-l-i-iB

v.g. 7 ; the Point of Di- vifion anfwering to any of the given Numbers, v.g. 4orC, gives the thing fought.

4. For the harmonical {Divifion of Chords To And Z'tr „ 1 two SeBions of a Line, which with the whZjlMll be L &' r ? . fr ° m ,™ hlch ,<*eraft the fquare Root =DC: harmonical Proportion, with regard to their Quantity.

Take any three Numbers in harmonical Proportion, as 3 — 4 — *5 and divide the whole Lines into as many Parts as the greater! of thefe three Numbers, v.g, 6 ; and at the Points of Divifion anfwering the other two Numbers, v. g. 3 and 4, you have the Sections fought.

5. To find two Settions of a Line, which together with the whole -Jball he harmonical, with refpecJ to gtiantity or Tune.

Take any three Numbers concord with each other, v.g. 2. 3. and 8, and divide the Line by the greateft • the Points of Divifion aniwering the other two give the Sec- tions fought.

6. To divide a Chord A B, in the mofi Jimple manner, fo as to exhibit all the original Concords.

Divide the Line into two equal Parts at C, and fubdi-

vide the Part C B into equal „ „ .,

Parts at D ; and again, the

Part CD into two equal Parts

at E. Here AC to AB is

Fifth ; AD to A B a Fourth

A-

-i-(_|-

B

n Octave ; A C to A D a, ACtoAEa Third; AE to AD a Third; D C AE to EB a Sixth 9; AE toAB a Sixth C. See Monociiord; fee alfo Tune, Concord, Harmony, t£c.

Chord is alfo us'd in Mufick for the Note, or Tone to JTthtte oT^TomI be touch d, or (ounded : m which a. n ft ;» i« ,„„i;„ki„ .„ ,.,, j«jui»,

Arch compleated.

Hence alio, if three Points of one Periphery do agree or coincide with three Points of ano'her ; the whole Periphe- ries agree, and therefore the Circles are equal.

Hence, laftly, every Triangle maybe inferib'd in a Circle.

The Chord of an Arch AB, (Fig. 7.) and the Radius CE being given ; to' find the Chord V the half Arch AE. From the Square of the Radius C E, fubtracf the Square of half the given Chord AT), the Remainder is the Square of C ; from which extract the fquare Root = D This fubtraaed from the Radius E C, leaves E. Add the Squares of AE and Eo; the Sum is the Square of A E : whence, the reft being extraaed, we have the Chord of half the Arch A E.

Line of Chords, is one of the Lines of the Seaor and Plain Scale. See its Defcription and Ule under the Words Sector, and Plain Scale.

Chord, Chorda, in Anatomy, a little Nerve extend- ed over the Membrana Tymfani, or Drum of the Ear. See Tympanum.

Anatomifts are nor agreed about the life of the Cbordit Tympani : Some fay, it ferves to. vary and modify the Sound of the Tympanum, in the fame manner as the Strings, or Braces, ftretch'd over the War-Drum. Others will have it to be no more than a Branch of the fifth Pair. See Ear.

CHORDAPSUS, in Medicine, a Difeafe of the Intef tines, otherwife call'd Mifcrere mei : Tho Tome fay 'tis on- ly a Species of the Miferere. See Miserere.

Galen defines it, a Humour or Inflation of the fmall In- terlines, which makes them appear fill'd, and ftretch'd like a Chord. Archigenes makes it a kind of Miferere ; con- fiding in a Tumor in a certain Place of the fmall Intcftines, which finks in, and gives way to the Hand when prefs'd .- He adds, that it's exceeding dangerous, and ordinarily kills unlcfs it come to Suppuration j

, . - — . — — 1,1 "ii". u, luur jnou


 * ufick. tee Conco'rd. " ^^ '" ^ ^^ docs ™

In this Scni'e, the Fifth is faid to confift of five Chords, orTones. See Fifth, &c.

Chord, Chorda, in Geometry, a right Line connea- ing the two Extremes of an Arch. See Arch.

Or, it is a right Line, terminated at each Extreme in the Circumference of a Circle, without paflingthro' the Cen- tre ; and dividing the Circle into two unequal Parts, call'd Segments : fuch is the Line A B, Plate Geometry, Fig. 6.

The Chord of an Arch, is a right Line drawn from one Extremity of a* Arch to the other; call'd alfo the Snbtenfe.

The Chord of the Complement of an Arch, is the Chord that lubtends the reft of the Arch ; or fo much as makes up the Arch a Semicircle. See Complement.

<i is perpendicular to a Line drawn from the

—-•■■- jtara ; by which it is, as it were, ty'd or held forcibly Centro ot the Circle to tho Middle of the Arch, as C E ; downwai .J in Erection, efpecially its Premm. "

Tis probable, however, that the'Chorda/ifits is in reality nothing elfe but the Miferere. Celfus informs us, that iri his Time they were the fame thing.

The Word comes from the Greek x°f^ a * Chord, and tvirliirQcti, to touch.

CHORDEE, in Medicine, an Inflammation and Con- traaion of the Fr<gmim, and under Part of the Trail; foas to render Ereaion painful. See Erection.

It happens in Gonorrhreas, and is generally proportional to the Degree of the Virus receiv'd ; fo that in vitulent Gonorrhoeas, it is ufually a very troublefome Symptom. See Gonorrhjea.

It proceeds from the Acrimony oi the Matter which runs from the Urethra, irritating the under Part of the Yard :,

When the Acri^