2-' 



ABUTMENT. 



ABYSSINIAN CHRISTIANS. 



conclusive with direct demonstration. For this there is no foundation ; 

 though it must be admitted that direct demonstrations are more 

 pleasing and more elegant. But it is obvious that, if everything which 

 contradicts a proposition be false, the proposition itself must be true. 

 The student of logic must distinguish between that which is only 

 contradictory, and that which is contrary to a proposition. Thus, to 

 the proposition that " all squares are equal," it is contradictory that 

 " tome squares are not equal," and contrary, that " no squares are 

 equal." The contrary is the most complete contradictory, and affirms 

 that the proposition is true in no one instance. It is not correct to 

 say that, if a proposition be false, its contrary is true ; for example, it 

 is false that all squares are equal, and equally false that no squares are 

 equal. But of a proposition and its contradictory one must be true ; 

 thus cither all squares are equal or some squares are not equal. Hence, 

 whatever disproves a proposition proves something contradictory, and 

 whatever disproves everything contradictory proves the proposition. 

 The Reducti'j ad Alvrdv.m is, therefore, as conclusive as direct demon- 

 stration. 



The Riiliirt;,, ml. Abtnrtlum, in Euclid, is wholly unnecessary to all 



m Bee that contra-positive propositions are identically the same. 

 The following forms are contra-positive : 

 Every A is B 

 Every not-B is not- A. 



liii' lid I. 4) two sides equal to two sides understood, proves that 



equal angles give equal areas : that is, unequal areas give unequal 



II'' then has to prove I. 6, which he does by Reductio ad 



His to] m j.-. filial base angles give equal opposite sides: 



iM equivalent contra-positive is, unequal sides give unequal opposite 



From the unequal sides it may immediately be shown, as in 



I , that two triangles having two pairs of sides equal, each to each, 

 have unequal area', and therefore unequal angles. Thus it is shown 

 that the angles opposite unequal sides art' unequal : which is but 



j that the aides opposite equal angles are equal. Had logic been 

 cultivated concurrently with geometry, the Rednctiu ad Abntnlum 

 would long ago have disappeared, in nearly all the eases in which it is 



i seel. 



ABUTMENT, in building, is that which receives the end of , and 

 Drives supj>ort to, anything having a tendency to thrust outwards in a 

 \\ur\r.' :.- H. The piers against which an arch that is less than 



a semi ;re abutments ; while the supports of an arch of any 



ligure, which springs at right angles to the horizon, are imposts. 

 The piers of the arches of Southwark and Vauxhall bridges are abut- 

 ments or abutment-piers; whereas those of London, Blackfriars, and 



loo bridges, and of the old Westminster bridge, are imp" 

 inipiwl-pifrs. Nevertheless, the piers at the extremities of a brid^f. of 

 whatever form its arch or arches may be, are always termefl its abut- 



: that is, abutments of the bridge itself. 



M'.I'TMKNT, in machinery, is a term applied to a fixed point from 

 which resistance or re-action is obtained. In an ordinary steam-engine, 



i tuple, each end of the cylinder acts alternately as an abutment. 

 The rteain. bcinj,' unable to expand itself in the direction of the fixed 



If. that is. the end of the cylinder, expends the whole of its elastic 



in the opposite direction, against the movable obstacle or piston. 



In like manner the breech of a gun forms an abutment for the expansive 



f the ignited powder; although in this case, the abutment not 



lieing absolutely a fixed point, its recoil occasions some loss of power. 



Even a rotatory steam-engine, with a continuous circular action, must 



H :il>utment to render the force of the steam effective. Springs, 

 r used to impel machinery, a* in the case of a watch, or to 

 measure or control force, a- in the various contrivances noticed under 

 .SpRi.vii BAI.AM r, must have their abutments or points of resistance; 

 as also must all mechanical combinations in which power is trans- 

 mit tvd by means of screws, of which it is sufficient to cite as an example 

 the nut in the fixed head of an ordinary screw-press. In all these cases 

 an analogy may be traced with the use of the term abutment in archi- 

 tecture. With a similar meaning the name is applied in carpentry to a 

 joint in which two pieces of timber meet so that the fibres of one piece 

 rim in a direction oblique or perpendicular to the joint, and those of the 



[larallel with it. 



ABUTTALS, from the French alntlttr, to limit or bound, are the 

 luittings and bounding** of lands to. the east, west, north, and south, 



'if; by what other lands, highways, hedges, rivers, &c., such lands 

 are in those several directions bounded. 



boundaries and abuttals of corporation and church lands, and of 

 parities, are usually preserved by an annual procession. 



ABYSSINIAN CHRISTIANS. The discovery of abody of Christians 



in o remote a country excited, in no small degree, the attention of 



in tho 15th century, which was again revived by Salt's last 



n, in 1810. From the ' Tareek Negushti,' or ' Chronicle of the 



Abyssinian Kings,' combined with the evidence of the ecclesiastical 



learn that Christianity was introduced into Abyssinia in 



i if. by Frumentius, or Fremonatos, as the 



< hronicles call him. Frumentius, after residing some years in the 



ry, was raised by Athanasius the patriarch of Alexandria, to the 

 dignity of bishop. He arrived in Abyssinia, perhaps about the year 

 A.D. 830, and probably in tho reign of the King Aizarias, whose name 



;its In the inscription of Axuin. It is, however, not certain to 

 which king of tho A !' we ought t<> apply the 



names of Aizanas and his brother Saizanas, both of which occur in the 

 inscription, and also in a letter of the Emperor Coustantine, addressed 

 to them A.D. 356. When the Greek merchant Cosmas visited 

 Abyssinia, A.D. 525, it was completely a Christian country, and well 

 provided both with ministers and churches. Of the Abyssinian 

 churches, which probably belong to the earlier periods of their conver- 

 sion, or at least are eight or nine hundred years old, there are still 

 some remains. The most remarkable is Abuhasubha, hewn out of the 

 solid rock, which at this place is soft and easily worked. The Portu- 

 guese, Alvariz, describes ten such churches as these, of which he has 

 given a plan, and one of them is probably the same as that which Mr. 

 Pearce visited at Jummada Mariam. (Salt, p. 302.) The great church 

 at Axum is comparatively modem, though parts of it, such as the 

 steps, clearly belong to a prior edifice. Mr. Salt describes the well- 

 built remains of a church or monastery near Yahee, which \a assigns to 

 the 6th century of the Christian era. 



The monastic, and also the solitary life, spread into Abyssinia from 

 the deserts of the Thebais, and when the Portuguese Jesuits entered 

 the country they found it full of such devotees ; many of them seemed, 

 however, to be monks only as far as celibacy was concerned, for they 

 cultivated the ground and lived in villages. 



With the Christian religion, the Abyssiniaus received the Holy 

 Scriptures, which they now possess in the ancient Ethiopia version, 

 made, according to Ludolf, from the Greek Septuagint, though nothing 

 is known of the date of this version. As to the New Testament (says 

 Ludolf), no entire copy has been yet brought to Europe. Mr. Brucn 

 brought with him from Abyssinia a complete copy of the Scriptures in 

 the Ethiopic language, and also a set of the Abyssinian Chronicles. 

 The Abyssinians divide the Scriptures, which they have entire, differ- 

 ently from what we do, making four principal parts of the Old Testa- 

 ment, and mixing what we call the Canonical with the Apocryphal 

 books. The New Testament is also divided into four parts, to which 

 they add the Book of Revelation as a supplement. The old written 

 language is of the Semitic stock, and is written from left to right, but 

 the language is not now spoken ; there are two languages now in use, 

 the TigriS and the Amharic. For other information respecting the 

 Abyssinian liturgies, and the religioxis opinions of the Abyssinians, we 

 refer to Ludolf, Book iii. chaps. 4, 5. Ludolf denies the existence of 

 the Book of Enoch, because he had only seen a spurious copy. A 

 knave who got possession of an Ethiopic book, wrote the name of Enoch 

 upon it, and sold it to Peiresc for a considerable sum of money, and 

 this was the book that Ludolf saw. Bruce brought home three copies 

 of the book of Enoch ; one of which he gave to the Bodleian Library 

 at Oxford. This book was originally written in Greek, but the original 

 is lost all but one large fragment. In the epistle of Jude reference 

 is made to the prophecies of Enoch ; and Mr. Bruce says, " the quota- 

 tion is word for word the same in the second chapter of the book." 

 This, however, will not prove the genuineness of the prophecies of 

 Enoch, ns Mr. Bruce has very well argued. An English translation of 

 the book of Enoch was published by Dr. Lawrence, Oxford, 8vo. 1822. 



The High Priest (or sole bishop) of Abyssinia is called Abuna, which 

 signifies Our Father ; and as Frumentius, the first bishop, received his 

 appointment from the Patriarch of Alexandria, this dignitary has, pro- 

 bably, always been a foreigner. The king is the head of the Church. 

 Polygamy, though not allowed by the ecclesiastical canon, is common 

 enough in practice ; and Mr. Salt mentions an instance of one gentle- 

 man who had five wives at once. The king, of course, marries as many 

 as he pleases : the clergy, also, who are not monks, may marry, but 

 only once. A second marriage renders them unworthy of their sacred 

 office, according to the ancient canons. Circumcision, according to 

 Bruce, is practised in Abyssinia, and baptism of infants and agapa) or 

 love-feasts have been in use ever since the introduction of Christianity. 

 The creed of the Abyssinian Church is what is called the Monophyiste ; 

 i. e., admitting the divinity of our Saviour, but acknowledging in him 

 only one nature. 



It would appear, from what we know of the Abyssinian Church, 

 that its priests, at present, are not well informed, nor are the people in 

 general well acquainted with the principles of the Christian religion, 

 though they may be Christians in name ; yet some of their ceremonies 

 are conducted with great decency, and very much resemble those of 

 the Church of England. When Salt was at Chelicut, Lent was strictly 

 observed for fifty-two days, and no fleah was eaten during this period, 

 though fish and various dishes were always plentiful on the table : the 

 people always fasted till sunset. A feast followed this severe and 

 protracted fast, in which they all seemed anxious to make up for lost 

 time, by over eating and drinking. The Sacrament is also administered 

 in Abyssinia,, in a very decorous manner ; and red wine made of ;i 

 grape which is common in some parts of the country, is used on tho 

 occasion. Formerly (says Mr. Salt) if a man married more than one 

 wife, he was excluded from participating in this rite, but wealth and 

 power have induced the Church to relax its severity in this respect. 

 Marriage itself in Tigr<5, appears a mere civil institution : the woman 

 keeps her name, and the parties can separate whenever they agree to 

 do so. In this case the woman has her dowry back, which is not 

 forfeited unless she is manifestly guilty of adultery. The higher classes 

 are subject to no rule, but what may be considered as imposed by the 

 relatives of the male and female. The priests are forbidden to marry 

 : ,ft,.r ordination. The Abyssinians bury their dead immediately after 



