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A.N Q
ANGERONALIA, in Antiquity, folemn Feafts, held by the Remans, on the 21$ of December, in honour of Ange- rona, or Angeronia, the Gcddeis of Patience and Silence. See Feast.
"Psfius and Julius Modeftm, quoted by Macrobius, Sa- turn. 1.1. c.io. derive the Name from Angina, Squinancy ; and fuppofe the Gcddefs to have been thus denominated, by reafon file prefided over that Difeafe.- Others fup- pofe it fcrnfd from Angor, Grief, Pain- to intimate that Jhe gave Relief to thofe afflicted therewith. Others de- duce it from Angio I prefs, I clofe ; as being reputed the Goddefsof Silence, &c. See God and Goddess.
ANGINA, in Medicine, a Difeafe, popularly calPd the ghiincy, Squinancy, or Efyuinancy. See Sqjii nancy.
Angina is a Difficulty of Refpiration and Deglutition, from a Difeafe in the Mufclesand Glands about the Throat and Larynx. See Larynx, &c.
The Word is formed from the Greek &fyj' v -> ftrangulare to ftrangle, fuffocate.
If any Symptoms appear on the outfide of the Throat, the Angina is Paid to be external ; if none appear, inter- nal. It is fometimes fuppofed to be epidemical.
In the external Angina, before any Suppuration appears,
recourfe is had to repeated Venjefeclion in the Jugulars.
Yeficatories, and Cupping are alfo ufed 5 with Purgatives, emollient Gargles, &c.
ANGLE, Angulus, in Geometry, the Aperture or mu- tual Inclination of two Lines, which meet, and form an Angle in their Point of Interferon. SeeLiNE.
Such \st\\Q Angle ABC, (Tab. Geometry, Fig. pi.) form'd by the Lines AB, and AC, meeting in the Point A — The Lines A B and A C, are called the Legs of the An- gles ; and the Point of Interferon, the Vertex. See Leg and Vertex.
Angles are fometimes denoted by a ilngle Letter amVd to the Vertex, or angular Point, as A ; and fometimes by three Letters, that of the Vertex being in the middle, as BAG
The Meafure of an Angle, whereby its Quantity is ex- preffed, is an Arch, DE, defcribed from its Vertex A, with any Radius at pleafure, between its Legs, AC and BC. See Arch.
Hence Angles are diftinguifhed by the Ratio of the Arches which they thus fubtend, to the Circumference of the whole Circle. See Circle andCiRCuMFERENCE.— And thus, an Angle is {aid to be of fo many Degrees, as are the Degrees of the Arch DE. See Degree.
Hence alfo, fince fimilar Arches, AB and DE, fig. 87. nave the fame Ratio to their respective Circumferences; and the Circumferences contain each the fame Number of Degrees ; the Arches AB, and D E, which are the Mea- fures of the two Angles ACB, and ADE, are equal j and therefore the Angles themfelves are fo too. ■ Hence, again, as the Quantity of an Angle is ellimated by the Ra- tio of the Arch, fubtended by it, to the Periphery ; it does not matter what Radius that Arch is defcribed with- al : But the Meafures of equal Angles are always either equal Arches or fimiJar ones $ and contrarily.
It follows, therefore, that the Quantity of the Angle re- mains ftill the fame, tho' the Legs be either produced or diminifhed And thus fimilar Angles, and in fimilar Fi- gures, the Homologous or Correfponding Angles are alfo equal. See Similar, Ficure, i$c.
To meafure, or find the Quantity of an Angle.'
i°. On Paper Apply the Centre of a Protractor on the
Vertex of the Angle Oj (Tab. Surveying, fig. 29.) fo as the Radius Op lie on one of the Legs : The Degree /hewn in the Arch, by the other Leg of the Angle, will give the
Angle required. See Protractor. To dothefame
with a Line of Chords, fee Chord.
z°. On the Ground — Place a furveying Internment, E.gr. a Semi-circle, fig. 16. in fuch manner as that a Radius thereof CG may lie over oneLegofthe^//gA>,and the Center Cover
the Vertex. The firii is obtain'd by looking thro' the
Sights F and G, towards a Mark fixed at the End of the Leg ; and the latter, by letting fall a Plummet from the
Centre of the Instrument -Then, the moveable Index
HI being turn'd this way and that, till thro' its Sights, you difcovcr a Mark placed at the extreme of the other Leg of the Angle • The Degree it cuts in the Limb of the Inilru- ment, ftiews the Quantity of the Angle. See Semi- circle.
To take an Angle with a £>nadrant, theodolite, plain Table, Circumferentor, Compafs,Sic. fee Quadrant,The- odolite, Plain Table, Circumferentor, Com- pass, Z$c.
To plot or lay down any given Angle ; i.e. the Quantity of the Angle being given, to defcribe it on Paper, fee Plotting and Protracting.
To biffsH a given Angle, as HIK, fig. 92. from the Centre L, with any Radius at pleafure, defcribe an Arch
L M. From L and M, with an Aperture greater than LM, ftnkc two Arches, mutually interfeaing each otheV in N. Then, drawing the right Line IN, we have HIN ess N I K..
To trijfeLl an Angle, fee Trissection.
Angles arc of various Rinds, and Denominations. ~*
With regard to the Form of their Legs, they are di- vided into Retlilinear , Curvilinear, and Mix'd.
Retlilinear, or right -listed Angle, is that whofe Legs are both right Lines 5 as ABC (Tab. Geometry, fig. yi.) See Rectilinear.
Curvilinear Ancle, is that whofe Legs are both of* 'cm Curves. Sec Curve and Cur vilinear.
Mix'd, or Mixtilinear Angle, is that, one of whofe Sides is a right Line, and the other a Curve. SecMix'n.
With regard to their Quantity, Angles are again divided into Right, Acute, Obtufe, and Oblique.
Right Angle, is that form'd by a Line falling perpen- dicularly on another ; or that which fubtends an Arch of
90 Degrees Such is the Angle K.LM, Fig. 95. See
Perpendicular, i£c.
The Meafure of a right Ancle, therefore, is a Qua- drant of a Circle; and confequently all right Angles are equal to each other. See Quadrant.
Acute Angle is that which is lefs than a right Angle, or
than 90°- as A EC, fig.Sfi. See Acute.
Obtufe Angle, is that greater than a right Angle, or
whofe Meafure exceeds 9 c as A ED. See Oct use.
Oblique Angle, is a common Name both for Acute and Obtufe Angles. See Oeliqjje.
With regard to their Situation in refpeel of each other, Ancles are divided into Contiguous, Adjacent, Ver- tical, Alternate, and Oppoflte.
Contiguous Angles, are fuch as have the fame Vertex,
and one Leg common to both Such are FGH, and
H G I, fig- 94. See Contiguous. Adjacent Angle, is that made by producing one of the
Legs of another Angle Such is the Angle A E C, fig. 8t5.
made by producing a Leg E D, of the Angle A E D, to C. See Adj agent.
Two adjacent Angles, x and y 5 or any other Number of Angles made on the fame Point E, over the fame right Line CD, arc together equal to two right ones 5 and confe-
quently, to 1S0 And hence, one of two contiguous
Angles being given, the other is likewife given : as being the Complement of the former to 180 . See Complement. Hence, alfo, to meafure an inacceffible Angle in the Field ; taking an adjacent accefiiblc Angle, and fubftracl:- ing the Quantity thereof from 180 , the Remainder is the Angle required.
Again, all the Angles x^yjJiL, &c. made a-round a given Point E, are equal to four right ones ; and therefore all make 36b .
Vertical Anclep, are thofe whofe Legs are Continua- tions of each other -Such are the Angles and x, fig. %6.
See Vertical.
If a right Line AB, cut another, CD, in E, the verti- cal Angles x and 0, as alfo y, and E, are equal.' And
hence, if it be required to meafure in a Field, or any other Place, an inacceffible Angle, #; and the other ver- tical Angle, 0, be acceffible : This latter may be taken in lieu of the former. See Surveying.
Alternate Angles. See Alternate. Such are
the Angles xan&y ; fig. 36".
The alternate Angles y and x, are equal. Sec Oppo- site Angles.
Oppoflte Angles. See Opposite. Such are u and y t
and alfo 2 and y.
External Angles, are- the Angles of any right-lined Figure made without it, by producing all the Sides feve- rally.
All the external Angles of any Figure taken together, ara equal to four right angles: And the external Angle of a Triangle is equal to both the internal and oppoflte ones, as is demonflrated by Euclid, Lib. 1. Prop. 32.
Internal Angles, are the Angles made by the Sides of any right-lined Figure within.
The Sum of all the internal Angles of any right-lined Fi- gure, is equal to twice as many right Angles as the Figure hath Sides, excepting four. This is eafily demonflrated from Euclid, Prop. 32. Lib. 1.
The external Angle is demonflrated to be equal to tho internal oppoflte one ; and the two internal oppofite ones, are equal to two right ones.
Homologous Angles, arefuch Angles in two Figures, as retain the fame Order from the firft, in both Figures. See
F] GURE.
Angle at the Periphery, is an Angle whofe Vertex and l Legs do all terminate in the Periphery^of a Circle-
Such is the Angle E F G, fig.
Angle in the Segment, is Periphery. See Segment. r Cc
See Periphery the fame with that at the
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