vide the product by the number remaining after the Proportion middle or second is subtracted from double the first; the quotient is a third harmonical proportion; thus supposing the numbers 9, 12, 16, a fourth will be found by the rule to be 24. Proportion, tude of two things, which determines the quantity of Arithmetical and Geometrical PROPORTION. See Inordinate PROPORTION, is where the order of the terms compared is disturbed or irregular. As, for example, in two ranks of numbers, three in each rank, viz. in one rank, and in the other, 2, 3, 9, 8, 24, 36, 5. If there be four numbers disposed in order, whereof one extreme and the two middle terms are in arithmetical proportion; and the same middle terms with the other extreme are in harmonical proportion; the four are in geometrical proportion; as here 2: 3 :: 4: 6, which are geometrical; whereof 2, 3, 4, are arithmetical, and 3, 4, 6, are harmonical. 6. If betwixt any two numbers you put an arithmetical mean, and also an harmonical one, the four will be in geometrical proportion thus betwixt 2 and 6 an arithmetical mean is 4, and an harmonical one 3; and the four 2: 34: 6, are geometrical. We have this notable difference between the three kinds of proportion, arithmetical, harmonical, and geo which are proportional, the former to the latter, but in metrical; that from any given number we can raise a 2:3:24:36, 3:9:: 8:24, a different order, viz. and then; casting out the mean terms in each rank it is concluded that 2:9::8:36, that is, the first is to the third in the first rank, as the first is to the third in the second rank. : Harmonical or Musical PROPORTION, is a kind of numeral proportion formed thus of three numbers, if the first be to the third as the difference of the first and second to the difference of the second and third; the three numbers are in harmonical proportion. Thus 2, 3, 6, are harmonical, because 2: 6:13. So also four numbers are harmonical, when the first is to the fourth as the difference of the first and second to the difference of the third and fourth. Thus 24, 16, 12, 9, are harmonical, because 24: 9 83. By continuing the proportional terms in the first case, there arises an harmonical progression or se ries. 1. If three or four numbers in harmonical proportion be multiplied or divided by the same number; the products or quotients will also be in harmonical proportion thus, if 6, 8, 12, which are harmonical, be divided by 2, the quotients 3, 4, 6, are also harmonical; and reciprocally the products by 2, viz. 6, 8, 12. 2. To find an harmonical mean between two numbers given; divide double the product of the two numbers by their sum, the quotient is the mean required; thus suppose 3 and 6 the extremes, the product of these is 18, which doubled gives 36; this divided by 9 (the sum of 3 and 6) gives the quotient 4. Whence 3, 4, 6, are harmonical. 3. To find a third harmonical proportion to two numbers given. Call one of them the first term, and the other the second; multiply them together, and divide the product by the number remaining after the second is subtracted from double the first; the quotient is a third harmonical proportional: thus, suppose the given terms 3, 4, their product 12 divided by 2 (the remainder after 4 is taken from 6, the double of the first), the quotient is 6, the harmonical third sought. 4. To find a fourth harmonical proportion to three terms given; multiply the first into the third, and diVOL. XVII. Part II. t : continued arithmetical series increasing in infinitum, but not decreasing the harmonical is decreasable in infinitum, but not increasable; the geometrical is both. PROPORTION, or Rule of Three. See ARITHMETIC. Reciprocal PROPORTION. See RECIPROCAL. PROPORTION is also used for the relation between unequal things of the same kind, whereby their several parts correspond to each other with an equal augmentation or diminution. Thus, in reducing a figure into little, or in enlarging it, care is taken to observe an equal diminution or enlargement through all its parts; so that if one line, e. gr. be contracted by one-third of its length, all the rest shall be contracted in the same proportion. PROPORTION, in Architecture, denotes the just magnitude of the members of each part of a building, and the relation of the several parts of the whole; e. gr. of the dimensions of a column, &c. with regard to the ordonnance of the whole building. One of the greatest differences among architects, M. Perrault observes, is in the proportion of the heights of entablatures with respect to the thickness of the columns, to which they are always to be accommodated. In effect, there is scarcely any work, either of the ancients or moderns, wherein this proportion is not different; some entablatures are even near twice as high as others—yet it is certain this proportion ought of all others to be most regulated; none being of greater importance, as there is none in which a defect is sooner seen, nor any in which it is more shocking. Compass of PROPORTION, a name by which the French, and after them some English, authors call the SECTOR. PROPORTIONAL, relating to proportion. Thus we say, proportional compasses, parts, scales, spirals, &c. PROPORTIONALS, in Geometry, are quantities, either linear or numeral, which bear the same ratio or relation to each other. PROPOSITION, in Logic, part of an argument, wherein some quality, either negative or positive, is attributed to a subject. PROPOSITION, in Mathematics, is either some truth advanced and shown to be such by demonstration, or some operation proposed and its solution shown. If the 3 M proposition Proposition. ted whether a poem can be written in prose. We enter not into that dispute, as we have said enough on the subject elsewhere. See Novel. I 24. PROPOSITION, in Poetry, the first part of a poem, wherein the author proposes briefly, and in general, what he is to say in the body of his work. It should comprehend only the matter of the poem, that is, the action and persons that act. Horace prescribes modesty and simplicity in the proposition, and would not have the poet promise too much, nor raise in the reader too great ideas of what he is going to relate. PROPREFECT, among the Romans, the prefect's fieutenant, or an officer whom the prefect of the pretorium commissioned to do part of his duty in his place. PROPRETOR, a Roman magistrate, who, having discharged the office of pretor at home, was sent into a province to command there with his former pretorial authority. It was also an appellation given to those who, without having been pretors at Rome, were sent extraordinarily into the provinces to administer justice with the authority of pretors. PROPRIETOR, or PROPRIETARY, is he who possesses any thing as his own in the utmost degree. Such monks were called proprietary as had reserved goods and effects to themselves, notwithstanding their formal renunciation of all at the time of their profession. They are frequently mentioned in the Monast. Anglic. &c. and were to be very severely dealt with; to be excommunicated, deprived of burial, &c. Monachi proprietarii excommunicentur ab abbatibus: et, si in morte proprietarius inventus fuerit, ecclesiastica careat sepultura, &c. Addit. ad Matt. Par. PRO RATA, in commerce, a term sometimes used by merchants for in proportion; as, each person must reap the profit or sustain the loss, pro rata to his interest, that is, in proportion to his stock. PROROGATION, the act of prolonging, adjourning, or putting off, to another time. The difference between a prorogation and an adjournment of parliament is, that by prorogation the session is ended, and such bills as passed in either house, or both houses, and had not the royal assent, must at the next assembly begin again. PROSCRIPTION, a publication made in the name of the chief or leader of a party, whereby he promises a reward to any one who shall bring him the head of one of his enemies. Sylla and Marius by turns proscribed each others adherents. Under the triumvirate great part of the best and bravest of the Romans fell by proscription. The term took its rise from the practice of writing down a list of the persons names, and posting it in public; from pro and scribo, "I write." PROSE, the natural language of mankind, loose and unconfined by poetical measures, rhymes, &c. In which sense it stands opposed to verse. There is, however, a species of prose which is measured, such as that in which epitaphs and other inscriptions are generally written; and indeed every man who has formed for himself a style writes in uniform periods regularly recurring. It has been much dispu The word prose comes from the Latin prosa, which some will have derived from the Hebrew poras, which signifies expendit: others deduce it from the Latin prorsa, of prorsus, " going forwards:" by way of op position to versa, or "turning backwards," as is necessary in writing. PROSECUTION, in the criminal law. The next step towards the punishment of offenders after COMMITMENT, is their prosecution, or the manner of their formal accusation. And this, in the English law, is either upon a previous finding of the fact by an inquest or grand jury; or without such previous finding. The former way is either by PRESENTMENT or INDICTMENT. See these articles. The remaining methods of prosecution are without any previous finding by a jury, to fix the authoritative stamp of verisimilitude upon the accusation. One of these, by the common law, was when a thief was taken with the mainour, that is, with the thing stolen upon him, in manu. For he might, when so detected, flagrante delicto, be brought into court, arraigned, and tried, without indictment: as by the Danish law he might be taken and hanged upon the spot without accusation or trial. But this proceeding was taken away by several statutes in the reign of Edward III. though in Scotland a similar process remains to this day. So that the only species of proceeding at the suit of the king, without a previous indictment or presentment by a grand jury, now seems to be that of INFORMATION; which see. These are all the methods of prosecution at the suit of the king. There yet remains another, which is merely at the suit of the subject, and is called an ArPEAL. See that article. But of all the methods of prosecution, that by indictment is the most general. See INDICTMENT. PROSECUTOR, in Law, he that pursues a cause in another's name. PROSELYTE, a new convert to some religion or religious sect. PROSERPINACA, a genus of plants belonging to the triandria class, and in the natural method ranking under the 15th order, Inundata. See BOTANY Index. Ceres, PROSERPINE, in fabulous history, the daughter of Jupiter and Ceres, was carried off by Pluto as she was gathering flowers with her companions. disconsolate for the loss of her daughter, after having long sought her, heard where she was, and intreated Jupiter to let her return from hell. This request Jupiter granted, on condition she had tasted nothing in Pluto's dominions. Ceres therefore went to fetch her; but when her daughter was preparing to return, Ascalaphus gave information that he had seen Proserpine eat some grains of a pomegranate she had gathered in Pluto's garden; on which she was sentenced to continue in Tartarus in quality of Pluto's spouse, and the queen of those gloomy regions: but to mitigate the grief of Ceres for her disappointment, Jupiter granted that her daughter should only spend six months together in hell with her husband, and the other six on earth with her mother. Some mythologists imagine that the latter part of the fable Prose Proserpine. Proserpine fable alludes to the corn, which must remain all the ned more closely the structure of the load, and found that Protagoras winter hid in the earth, in order to sprout forth in the it was put together with mathematical exactness; upon Protagora spring, and produce the harvest. which he asked the youth whether he himself had made Protest. PROSEUCHE, in antiquity, properly signifies pray- it up. Protagoras assured him that he had; and immeer; but it is taken for the places of prayer of the Jews, diately taking it to pieces, with great ease replaced and was pretty near the same as their synagogues. But every log in the same exact order as before. Democrithe synagogues were originally in the cities, and were tus expressed much admiration of his ingenuity; and covered places: whereas, for the most part, the pro- said to him, "Young man, follow me, and your talents, seuches were out of the cities, and on the banks of ri- shall be employed upon greater and better things." The vers; having no covering except perhaps the shade of youth consented, and Democritus took him hoare, mainsome trees or covered galleries. The word is Greek, tained him at his own expence, and taught him philo gooux, prayer. sophy, which qualified him for the office of legislator of the Thurians. He was more subtle than solid in his reasonings; however, he taught at Athens with great reputation, but was at length banished from thence for the impiety of his doctrines. He then travelled, and visited the islands in the Mediterranean, where it is said that he was the first philosopher who taught for money. He died in a voyage to Sicily, in a very advanced age, He commonly reasoned by dilemmas, and left the mind in suspense with respect to all the questions he proposed. His moral principles were adopted by Hobbes. (Sea MORAL PHILOSOPHY). Plato wrote a dialogue against him. He flourished 400 years B. C. PROSLAMBANOMENE, the name of a musical note in the Greek system. As the two tetrachords of the Greeks were conjunctive, or, in other words, as the highest note of the first served likewise for the lowest note of the second, it is plain that a complete octave could not be formed. To remedy this deficiency, therefore, one note beneath the lowest tetrachord was added, as an octave to the highest of the last tetrachord. Thus, if we suppose the first to have begun on B, the last must have ended upon A, to which one note subjoined immediately beneath the lowest B in the diatonic order must have formed an octave. This note was called proslambanomene. But it appears from authors who have scrutinized antiquity urney's with some diligence, and perhaps with as much success istory of as the data upon which they proceeded could produce, usic, that the names of the notes in the Greek system, which essert. originally signified their natural station in the scale of ascending or descending sounds, were afterwards applied to their positions in the lyre. Higher or lower, then, according to this application, did not signify their degrees of acuteness or gravity, but their higher or lower situation upon this instrument. Feld's i. PROSODY, that part of grammar which treats of the quantities and accents of syllables, and the manner of making verses. The English prosody turns chiefly on two things, numbers and rhyme. See POETRY, N° 66-76. and Part III. PROSOPIS, in Botany, a genus of the monogynia order, belonging to the dodecandria class of plants. The calyx is hemispherical and quadridentate; the stigma is simple; the legumen inflated and monospermous. See BOTANY Index. PROSOPOPOEIA, a figure in oratory, whereby we raise qualities of things inanimate into persons. See ORATORY. PROSTATÆ, in Anatomy, a gland, generally supposed to be two separate bodies, though in reality but one, situated just before the neck of the bladder, and surrounding the beginning of the urethra. See ANATOMY Index. PROSTYLE, in Architecture, a range of columns in the front of a temple. PROTAGORAS, a famous Greek philosopher, was born at Abdera. In his youth, his poverty obliged ory of him to submit to the servile office of frequently carosophy, rying logs of wood from the neighbouring fields to Abdera. It happened that as he was one day going on briskly towards the city under one of these loads, he was met by Democritus, who was particularly struck with the neatness and regularity of the bundle. Desiring him to stop and rest himself, Democritus exami PROTASIS, in the ancient drama, the first part of a comic or tragic piece, wherein the several persons are shown, their characters intimated, and the subject of the piece proposed and entered upon. It might reach as far as our two first acts; and where it ended the epitasis commenced. See the article EF1 TASIS. PROTEA, the SILVER-TREE, a genus of plants, belonging to the tetrandria class; and in the natural method ranking under the 47th order, Stellatæ. See BOTANY Index. PROTECTOR, a person who undertakes to shelter and defend the weak, helpless and distressed. Every Catholic nation, and every religious order, has a protector residing at the court of Rome, who is a cardinal, and is called the cardinal protector. Protector is also sometimes used for a regent of a kingdom, made choice of to govern it during the minority of a prince. Cromwell assumed the title and quality of lord protector of the commonwealth of England. PROTESILAI TURRIS, the sepulchre of Protesilaus, with a temple, at which Alexander sacrificed, (Arian); situated at the south extremity of the Helle spont, near the Chersonesus Thracia. Protesilaus was the first Greek who landed on the coast of Troy, and the first Greek slain by the Trojans, (Homer, Ovid). His wife Laodamia, to assuage her grief, begged the gods for a sight of his shade; and obtaining her request, she expired in his embraces, (Hyginus). Protesilaus was also called Phylacides, from Phylace, a town of Thessaly. PROTEST, in Law, is a call of witness, or an open affirmation that a person does, either not at all, or but conditionally, yield his consent to any act, or to the proceeding of any judge in a court in which his jurisdiction is doubtful, or to answer upon his oath farther than he is bound by law. Any of the lords in parliament have a right to protest their dissent to any bill passed by a majority: which protest is entered in form. This is said to be a very 3 M 2 ancient Protest ancient privilege. The commons have no right to proU test. See PARLIAMENT. Protogenes. PROTEST, in Commerce, a summons written by a notary-public to a merchant, banker, or the like to accept or discharge a bill of exchange drawn on him, after his having refused either to accept or pay it. See BILL of Exchange. PROTESTANT, a name first given in Germany to those who adhered to the doctrine of Luther; because in 1529 they protested against a decree of the emperor Charles V. and the diet of Spires; declaring that they appealed to a general council. The same name has also been given to those of the sentiments of Calvin; and is now become a common denomination for all those of the reformed churches. PROTEUS, in Heathen Mythology. See EGYPT, N° 6. PROTHONOTARY, a term which properly signifies first notary, and which was anciently the title of the principal notaries of the emperors of Constantinople. Prothonotary, with us, is used for an officer in the court of king's bench and common pleas; the former of which courts has one, and the latter three. The prothonotary of the king's bench records all civil actions sued in that court, as the clerk of the crown-office does all criminal causes. The prothonotaries of the common pleas enter and enrol all declarations, plead ings, assizes, judgments, and actions: they also make out all judicial writs, except writs of habeas corpus, and distringas jurator, for which there is a particular office, called the habeas corpora office; they likewise enter recognizances acknowledged, and all common recoveries; make exemplifications of records, &c. In the court of Rome there is a college of 12 prelates, called apostolical prothonotaries, empowered to receive the last wills of cardinals, to make all informations and proceedings necessary for the canonization of saints; and all such acts as are of great consequence to the Papacy for which purpose they have the right of admission into all consistories, whether public or half public. They also attend on the pope whenever he performs any extraordinary ceremony out of Rome. PROTO, a Greek term, frequently used in composition of priority thus proto-collum, in the ancient jurisprudence, signifies the first leaf of a book; protomartyr, the first martyr; proto-plast, the first man formed, &c. PROTOGENES, a celebrated ancient painter, was born at Caunas, a city of Caria, subject to the Rhodians, and flourished 300 years before the birth of our Saviour. He was first obliged to paint ships for his livelihood; but afterwards acquired the highest repu tation for history-painting; though Apelles blamed him for finishing his pieces too highly, and not knowing when to have done. The finest of his pictures was that of Jalisus, which is mentioned by several ancient authors, though none of them give any description of it. He worked seven years on this picture; during which time he lived entirely upon lupines and water, being of opinion that this light and simple nourish ment left him greater freedom of fancy. Apelles, on seeing this picture, was struck with such admiration, that he was unable to speak, or to find words sufficient to express his idea of its beauty. It was this picture that saved the city of Rhodes when besieged by De- Protogenes metrius king of Macedon; for being able to attack it only on that side where Protogenes worked, which he Protracte intended to burn, he chose rather to abandon his design than to destroy so fine a piece. Pliny says, that Apelles asking him what price he had for his pictures, and Protogenes naming an inconsiderable sum, Apelles concerned at the injustice done to the beauty of his productions, gave him 50 talents, about 10,cool, for one picture only, declaring publicly, that he would sell it for his own. This generosity made the Rhodians sensible of the merit of Protogenes; and they were so eager to purchase the picture Apelles had bought, that they paid him a much greater price for it than he had given. PROTOTYPE, is the original or model after which a thing was formed; but chiefly used for the patterns of things to be engraved, cast, &c. PROTRACTOR, an instrument for laying down and measuring angles upon paper with accuracy and dispatch; and by which the use of the line of chords is superseded. This instrument is variously formed, as semicircular, rectangular, or circular; and constructed of different materials, as brass, ivory, &c. It is necessary in laying down those surveys or other plans where angles are concerned. The rectangular protractor is constructed in form of a right-angled parallelogram, which, when applied to a case of mathematical instruments, is substituted in place of the semicircular protractor and scale of equal parts. Fig. 1. is a representation of it: the manner of using it is exactly similar to that of the semicircular one. The circular protractor, as its name implies, is a complete circle, and is superior by far to either of the former, both in point of accuracy and dispatch, espe cially when several angles are to be formed at the same point. The limb of this instrument is divided into 360 degrees, and each degree in some protractors is halved: it has a subdividing scale or vernier, by which an angle may be laid down or measured to a single minute. In the centre of the protractor is a fine mark, which, when an angle is to be protracted or measured, is to be laid upon the angular point, and o, or zero on the limb, upon the given line forming one side of the angle. Plate ccccxlviä fig, 1. Fig. 2. represents a circular protractor whose limb is rig, 2. divided as above described, and the dividing scale on the index, which moves round the limb of the protractor on a conical centre, gives every minute of a degree. That part of the index beyond the limb has a steel point fixed at the end, in a direct line with the centre of the protractor, and whose use is to prick off the proposed angles. Fig. 3. is another circular protractor, a little differ- Fig. 3. ently constructed from the former. The central point is formed by the intersection of two lines crossing each other at right angles, which are cut on a piece of glass. The limb is divided into degrees and half degrees, baving an index with a vernier graduated to count to a single minute, and is furnished with a tooth and pinion, by means of which the index is moved round by turning a small nut. It has two pointers, one at each end of the index, furnished with springs for keeping them suspended while they are bringing to any angle; and |
