A P O
A P P
APOTHERMUM, /ixA^m, in antient Writers, a lharp kind of fauce, like that prepared of muftard, oil, and vinegar, or of vinegar alone. Caji. Lex. Med. p. 68.
APOTOME (Cycl.)— Euclid makes fix forts of Apttomts.
Apotome Prima, is when the greater number is a rational number* and the difference of the fquares of both numbers is a Iquare number, e. gr. 3-^-/5, where the difference of the fquarcs 9 and 5 is the fquare number 4. The fame holds in 6 — 4/2C, for that the difference of the fquares 36 and 20, is the fquare number 16.
A pot OM E Sectaida,is where the leffer number isa rational number, and the fquare root of the difference of the fquares of both num- bers has a ratio exprefhble in numbers to the greater number, fuchis^/iS — 4,for that the difference of the fquares 18 and 16 is 2, and 4/2 is to 4/18 as 1 103, becaufev/18— 34/2. The fame holds of ^48 — 6, for that the difference of the fquares 48 and 36 is 12; and 4/12 is to ^48 as I to 2, for 4/12 = 2 4/3, and 4/48 = 44/3, or elfc 4/48 = 24/12.
Apotome Tertia, is when both the numbers which are fub- ftracted from each other are irrational numbers, and the fquare root of the difference of their fquares has a ratio in numbers to the greater. This holds in 4/24 — 4/18, for the difference of their fquares 24 and 18 is 6, and the fquare root thereof 4/ 6 is to 4/24 as 1 to 2, for 4/24 = 24/6.
Apotome Quarts, is when the greater number is a rational number, and the fquare root of the difference of the fquares of both numbers has no ratio to it in numbers. Such is 4 — 4/3, for that the difference of the fquares, r6. and 3, is 13, but the fquare root of 13, viz. 4/13 has no numerical ratio to 4.
Apotome Qitinta, is when the leffer number is a rational num- ber, and the fquare root of the difference of the fquarcs of both numbers has no ratio in numbers to the greater number. Such is 4/6 — 2, for that the difference of the fquares 6 and 4, is 2, and 4/2 has to 4/6 no ratio in numbers.
Apotome Sexta, is where both numbers are irrational, and the fquare root of the difference of their fquares has no ratio in numbers to the greater. Such is the cafe in 4/6 — 4/2, for the difference of the fquarcs 6 and 2 is 4, and the root thereof 2 has to the 4/6 no ratio in numbers.
Peter Ramus cenfurcs Euclid's doflrine of Apotomes, and even all the reft delivered in the tenth book concerning irrational lines in the following terms.
Materies decline libra propofita, eo modo ejl tradita, lit in huma- nis Uteris atque artibus Jimikm objeuritatem nufquam depreben- derim ; obfeuritatem dico uou ad intelligendum, quid prtecipiat Euclides, — -Jed ad perfpiciendum penitus et explorandum, quis finis et ufus fit operi propositus, quiz genera, /pedes, differentia; junt rerum fubjeelarum : nibil enim unquam tarn cmfufumvel imiolutum legi vel audivi. Schol. Mathem. 1. 21. p. 252. He adds that the inventors of thefe matters made but an ill ufe of their time. Kepler anfwers Ramus, and lhews, that on this doflrine is laid the foundation of the knowledge of the ftruflure of the world ; he does not hefitate to fay : veftrum ejio carpere qua: uon intelligitis, mibi, qui rerum eaufas indago, pr&terquam in decimo Euclidis femita: ad illas nulla; paiuerunt. The reafon is that Euclid makes ufe of the knowledge of ir- rational lines to prove the properties of the five regular bodies, out of which Kepler, in his myjierium cojmographicum, de- duces the number of the planets, and the magnitude of the world. Kepler alfo makes ufe of the fame doflrine in his Hannoniee mundi, where he fhews the reafons of the harmo- nical proportions. Harmon. Mund. 1. 1. in Pnef. p. 3. Oughtred has publiihed Declaratianem Elementi deeimi Euclidis, which has been reprinted with hisClavis atOxford 1693; but he fcems to have made the matter more obfeure, by an improper ufe of figns. Michael Slifelius has given a clear explanation of the whole tenth book of Euclid, and particularly of the doflrine of Apotomes, in his Aritbmetica Integra. Lib. I. c. 23. p. 187 feq. Wolf. Lex. Math. p. 128. feq.
Apotome, in mulic, is the difference of the tone major and Limma, cxpreucd by fjfj. There is a miftake in the Cy- clopedia, when it is faid, that the Apotome is the part re- maining of an entire tone when the greater femi- tone has been taken from it. V. JVallis Append, ad Ptolcm. Harm. p. 170. Oper. Tom. 3. See Tone and Limma. The Apotome is by fome authors, as Bcethius % called bemi- tonium majus ; and the limma, bemittmium minus. He alfo calls the difference of thefe two comma b .— p Ap. IVallis, loc. cit. » Wallis, ibid.]
APOTRAGOPOGON, in the materia medica, a name given by fome of the old authors to the labdav.um. Jt is mentioned in a pre- scription recorded inGalen from fome of theempiricks of his time, it being the cuftom of thofe people who were fond of fecrets, to tlifguife the names of the things they ufed, that no body might find out what they meant. Many have fuppofed that this word ifood for fome for t of the herb tragopogon, or goat's beard ; but the whole meaning of its being made a name of labdanum was that this gum, which is produced from the ciftus, is wiped off from the beards of the goats that feed on that fhrub in the dewy mornings. See Laddanum.
APOTROP^iA, A?ro1 ? os*,a, in the antient poetry, verfes, compofed for averting the wrath of incenfed deities. Seal. Poet. J. 3. c. 102.
Thefe amounted to much the fame with Apeuclic verfes. See the article Apeuctic.
APOZEM, (Cycl.) Apozema, is fometimes alfo corruptly written Apoxim. Du Cange, Glofli Lat. T. 1. p. 264. in voc. Abo- zimare.
In writers of the barbarous age we meet with Apozimare, to infufe, to make an Apozem. Du Gauge, loc cit. Apezem differs from infuffon on account of the greater degree of heat made ufe of in preparing the former, whcrcby D the Apozem becomes more fitly impregnated with thofe parts of the fubjefl which are readily foluble in boiling water. Apozems are medicines of the extemporaneous kind, and there- fore the lefs ufed, by reafon what is once made up will not keep. What is direfled in this form, is generally fent to the patient in the quantity of a quart at a time, to be'drank off plentifully as common drink. Shtinc. Pharm. Left. 12. p. 132. Apozems are frequently made of infufions, that is, by firff di- gefting and drawing the infufion of plants, then boiling the lubjefl over again in the fame liquor for an Apozem. Vid. Beerb. New Mcth. of Chem. P. 3. Proc. 2. p. 20. feq.
APPANAGE (Cycl.)-Um, cited by Menage, chutes to de- duce this word from the French Appcnner, to feather, q. d. dormer dis Pennes, to give a young prince, turned out of his father's houfe feathers or means tu fly and fhift for him- felf. V. Menag. Orig. Franc.
St. Julien ffarts another etymon, vix. from the old French word Apaner, which fignifies to cut and deal every one his fhare of bread.
The Appanage is unalienable ; collateral branches do not in- herit it. The cldeft fon alone is heir to the whole Appanage ; but is to allow the younger an honourable maintenance. Vid. Chopin. Tract du Domaine, 1. 2. and 3. In France Appanages are of two kinds, royal and cuftomary ; the firft only granted to males the kings brothers, exclufi've of the females. Thefe arc not fo properly alienations of the kings demefnes as difmembring of them. Atibcrt, Ap. Richcl. Diet. T. 1. p. 96.
Cuftomary Appanages are thofe granted to women, the kino 's filters. °
Hoft'meifter, Lvferus, Schiltcr, Mullcr, Bcrger, lie. have difcourfes exprefs concerning the laws and rights of Appanage. V Bibl, Jur. Imper. c. 4. Lipen.Bibl Jur. p. 21. Bibl. Germ. T. 9. p. 226.
Hertius, Thomafius and Lombardus have treated exprefsly on the difference between Appanage and Parage. — The fecond afferts the difference to be real, the firff fiflitious. Bibl. Jur. Imper. loc. cit.
Joach. Meierus has publifhcd a body of all the writers on Appa- nage^ and Parage, in one volume in folio. Corpus juris Appa- nagii, &c. continens fcriptorcs quotquot inveniri potuerunt, qui de Appanagio et Paragio ex inftituto egerunt— Lemgov. 1727. An account of which is given in Aft. Enid. Lipf. 1728^ p. 49. feq.
APPARATOR Comitatus (Cycl.)— There was formerly an of- ficer called by this name, for which the fheriffs of Bucking- hamfhire had a confiderable yearly allowance; and in the reign of queen Elizabeth, there was an order of court for mak- ing that allowance. But the cuftom and reafon of it arc now altered. Hales, Sher. Acco. [04.
APPARATUS Chemical. See Vessels.
APPARENT (Cycl.)— AvrAREKT-Di/lance, in optics, that diftance which we judge an objefl to be from us when feen afar off, being commonly very different from the true diftance ; becaufe we are apt to think that all very remote objefls, whole parts cannot well be diftinguifhed, and which have no other objefl in view near them, to be at the fame diftance from us, though perhaps the one is thoufands of miles nearer than the other, as is the cafe with regard to the fun and moon. Stone, Mathem. Diet in voc. Apparent. SeeDiSTANCE.
Apparent Figure, in optics, that figure or fhape, which an objefl appears under when viewed at a diftance, being often very different from the true figure, for a ftreight line viewed at a dif- tance may appear but as a point ; a furface, as a line ; and a folid, as a furface ; and each of thefe of different magnitudes, and the two laft of different figures, according to their fituation with re- gard to the eye. Thus an arch of a circle may appear a ftreight line ; a fquare or oblong, a trapezium, or even a triangle; a circle, anellipfis; angular magnitudes, round; a fphere, a circle, &V.
Alfo any fmall light, as a candle, feen at a diftance in the dark, will appear magnified, and farther off than really it is. Add to this, that feveral objefls feen at a diftance, under angles that are fo fmall as to be infenfible, as well as each of the angles fubtended by any one of them and that next to it ; then all thefe objefls will appear not only to be contiguous' but to conftitute, and feem but one continued magnitude.^ Id. Ibid.
APPARITION, (Cycl.) in a general fenfe, the appearance or femblance of a thing.
Apparition is alfo ufed to denote a fpeflre, or preternatural appearance of fome fpirit, or the like.
We read of Apparitions of angels, genii, daanons, fairies, witches, departed fouls, EJV. Apparitions ol God, of Chrift, the Virgin, faints, prophets, and of the devil himfelf.
Se-
