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Fifth head. This relates to geometrical forms; and again ithas to be premi sed that the spiritual mean ing of Scripture is notio be grasped, uni ess the literat mean ing be firSt understood. The preci se form of the ark the tabernacle, the temple Should be presented to us with mathematical accuracy ; it will then be possibi e to interpret their mystical signification. A rem arkable case in po intis the rainbow, of which we are told that it is a symbol of God's promi Se as to the Deluge. The mean ing of this i S mi sun derstood for want of understanding the geometry of the rainbow, whicli is produced by the solar rays stri hing on the raindrops and beingrestacted or reflected then e. Only by geometry Can Such a textas that of the threesold burning of mountains by the sun be under- StoOd. The mountains receive direct rays. The rays reflected by them are focussed in the air and contribute to warm them. LaStly, there are the doubly refracted rays passing frona the sun into the Clouds and froin the clouds into the air. Again, the rays may fallei ther vertical ly, or obliquely, or horizontally, producing differentei Cis in eaCh Case. The laws as to the passage of light throughSpace apply equalty to the paSSage of ali other forces. Os ali thesethings there is a Spiritual interpretation. Direct verti Cal rays maybe compared to the action os grace ora the righteous ; they nei ther reflect nor refraci it. In the wi Cked we see the light dri ven away, refected: in the imperfeci it is bent aside, refracted. It is to benoted here that the geometrical sorm of the triangle is speciallyadapted to symbolire the Trinity. Each angle is distinct yet eachembraces the whole Space. Again, Our geometri Cal principies a S to the action os forces may be applied to the estimation of the forces of temptation, whi Ch aci in proportion to their proximi ty. Hence theneed of hee ping the tempted as far removed as possibi e froni theobjectS Whi Cli tempt . . 210 219 Sixth head . This relates to number. saὶ As With geometri CalfOrm S, So with number there is a spiritual mean ing bellind the liter linean ing. θ) For the understanding of Chronicies it is necessary toknow the different systems of numeration, and to be able to Convertone into another. ci There are variotis arithmetical operations in
the Je isti laru requiring a knowledge of the subjeci. sae) There are
many corruptions in the text whi Ch Only an arithmetici an Can uni avel . ei The perfections in herent in the number three Can only bo Under-stood by arithmetici an s. Arithmetic is neceSSary in astronomy, which we have seen to be needful to the theologian . Some instances Os iis value in astronomy are here given. we have to define thelen gili os a line on the earlli 's furface Corresponding to a degrOct. V e must talae a mile aS 4,Ooo cubiis : a cubit as Il feet. HOW many miles must we Walla northward frona a gi ven poliat to find the pole-
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cxii A LYSIS OF THE OPUS MAJUS
fisty-six miles, 2,984 1 Cubit S. Froin the diameter of the earth weobtain iis circumferenCe and iis sui face. The distance of the heavenlyhodies may be meas ured in SemidiameterS of the earth - 3 23O miles. Alfraganus estimates the di Stance of the Starry sphere to be 2o II Osemidiameters ; which gives the diameter of this sphere asI3O, IIS OOO mileS. From thi S we Can Calculate the circumferen Ceand sursace. The longest distance of Saturn is the Semidiameter of
distance of the su Ceed ing. As to the ninth and the tentii heaven we have no scientific knowledge. Ag to the height of the atmosphere thereis great unCertnin ty. For mensuring the apparent diameters of the Stin and the Moon reCOurSe has been to water-clOCES; the number
liave been compared with the number issuing during a revolutionof the heavens. But there are more accurate methods by astrolabesor quadranis. From theSe, and shom observations of eclipses, themoon's diameter is estimated at of the Earth's diameter. The Earili is therefore abo ut 3Il as large as the moon. Similarly the Sun will be Mund to be 17O times as large as the Earth. Mercury is si si dod of the Earth. In a Similar way the relative magnitude of the other planet S as compared with the Earth may be determined. The fixed stars are I,O22 in number, and a re divided into si X grolapsaccording to this magnitude. Those of the first magnitude are Ioptimes as large as the Eurth; of the second, ninely times the Earthys magnitude of the third, Seventy- two times, of the Murth, fisty- urtimes, of the fifth, thirty-Six times, of the fixili, eighteen times. Buthesides these there are infinite numbers of other StarS WhOSemagnitude Cannot be determined ...... 219-236 Seventi, hea d. Music. The theologian Should be acquainted withthe theory, is not with the practice, of vocat and instrumental muSi C. Music Covers the whole ground of reCitation, punCtuation, ACCent, things neCesSary for Prose aS weli as poetry. of in Struments again many are Spolien Of in Scripture, and each has a spiritual as weli astiterat mean ing. NOr must dancing, whi Ch may be calleu visibi e
we have no in to Consider Certa in objections that have been rat sed with rogard to mathematical science. Mathematic has been conso unded with magic, and put on the Same level as fortune-telling, witCh-Crast, and the preparation os Charins and incantations. It hasbeen credi ted with the doctrine that human actions are absolutely
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determined by stellar insuen es. Aut this doctrine is explicit lycondemned by ali philosophers, both of Greece, Rome, and Arabia. They maintain Dee-will against any su Ch supposed physical necessity ;
and they reprobate ulteri y the use of Charins and incantations. The Prejudice against mathemati s was strengthened by the Stri se of heathenis in against Christiani ty, in whicli magi C was used by the former, and in whi Cli Christian mira les Were accounted for by magi C. The reproach of de nying Dee-Will rema ined, when the Suspicion Os magic had passed away. But examination of Ptolemy's Works showsclearly that he never feli in to this error. He, and his principat Arabian commentators, held that the fore asis of the future revealed by aStronomy indicated generat tendeta Cies ora ly, and diu not impose any Specific Compulsion on individual actions. But this distinctionlias not been always perceived in the attacks made by Christianwriters on mathematical Science. They have Con unded true scien Ce
with lal Se ........... 238-249
What is true is that the influen Ces of the stars implant certaintendencies to good or evit action, always at the sanae time leaving Dee scope to human will. It i S evident that physi Cal temperament is oneof the factorS in human aption. Temperament is it Self a result of the innuence of the stars. That climate affecis Character is obvious toe very one. And this influence is to be traced in minimis. Frome very part of the shy to every potnt of the earthys Suriace a Cone offorCes proCeed S, affecting more or less e Very Communi ty and e very individual, though not in su Ch a way as to overri de Dee-uill . Thesethings would be studi ed by physicians it they were better aCqua intecl
We now arrive at the practical applications of mathematical scienceto Church government. The first of these is the proos offered by astrology of the superiori ty of Christiani ty to other religionS, and the insight given into the nature of Antichrist. It must be under-stood that the heaven is to be divi ded into twelve Houses; that is,lahing the quadranis formed by the intersection of the meridianand horigon, ea si may be divi ted into three. To sive of the Seven planet S two HOuses are nil otted ; to Mercury and the Moonone eaCh. The asSociation of J upiter With each of the other planeis has a spe Cial mean ing. lf with Saturn, the referen e is to Judaism. With Mars, to Chaldaeisin. With the Sun, to Egypti an religion. Willi Venus, to the Saracen worship. With MerCury,
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But there is an other and more essentiat mean ing of the wordHouse. Is we divide the ecliptic into tWelve paris, and through the divisions Conduci Circles intersecting at the potes of the ecliptic, the regions belween any two of these Cir les is in the true Sensea HouSe; bearing the nam e of iis rodiacat sign. The principalHouse of each planet is that in which it was created. Leo is the Hota se of the Sun, Capricorn of Saturn, Sagittarius of Jupiter, Virgo of Mercury. There are certain signs for eaCh planet whicli are called iis Exaltation; for the Suia Aries, for Saturn Libra, for Jupiter Cancer, for Mars Capricorn, sor Venus Pisces, for Mercury Uirgo. The signs are divided into Mur groups : three, Aries, Leo, SagittariuS,are hol and dry: three, TauruS, Virgo, and Capri Corn, are Coldand dry : three, Gemini, Libra, Aquariu S, are hol and moisi: three, CanCer, Scorpio, and Pi Sces, are Cold and moist. A planet be ingin any of the groups to whicli iis House belongs is sald to be in iis Triplici ty. We have further to Consider Boundaries and AspectS. With regard to Boundaries, they vary for each planet and for eaChsign. With regard to Aspecis, ea li sigia is divideo into three equalportions of ten degreeS, and a portion is assigned to each planet in SequeNCO 258 26 lIt will appear in the result that Mercury has manisold and strongconnexions with the Sigia of Virgo. As Mercury is connected with Christi an faith, so is the Moon, with iis irregular motions, Connected with the corruption of that faith. The conjunctions of the planetS, and especialty those of Jupiter and Saturn, throw light ora importantepoclis of history. TheSe are of three hinds, occurring respectivelyin periods of 2O, of 24O, and of 96o years. Jud ging Dom What took place at previous period S, it may be inferreo that the Mahometanfaith will not be of much longer duration. There yet rρmainS theperiod of Antichrist, on the date of whicli study of these astronomicalperiods may throw light ........ 261 - 269 A seconci application os mathemati s to the service of the Churchis the correction of the Calendar. The Julian Calendar fixed thelength of the year at 363l dayS. Hen e the arrangement of an additional day every fourth year. But this estimate is known to betoo great by the do part of a day. Therefore in every I3O years
there is an accumulated error of One Jay ..... 269-27l Again, it has been assumed that the equinoxes and solstices occurred on fixed clays. These days in the beginning of the Clitarchwere fixed thus : the winter Solstice on December 25, the vernalequi nox on March 25, the summer Sol Stice On June 24, the Rutumnalequi nox on September 24. SubSequently the Vernat equi nox was transposed to Marcii 2I. Hence the earli est Easter, being the first Sunday after the fuit inoon succeed ing to the vernat equi nox, was
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Marcii 22. But the winter solstice and the vernat equi nox are nolonger on these days. At the present time the winter solstice is On December I 3, the vernat equi nox On March I3, the summerso istice on June I S, the autumnal equi nox on September I 6. IneVery I 23 years the error of another Jay aCCumulates. The Consequence of this error is that Easter is observed at the wrongii me, in the third and in the Murteenth years of the lunar CyCle. The error will be sar more serious in future Centuries, So that ultimately the period when Lent should be observed will he at a time When every one is eat ing meat 271 274 Further, there i S a serious error in the Computation of the lunarcycle. Successive periods of nineleen years differ in tength, Sonae containing Mur, others five leap-years. The only satisfactory periodwould he thirty Arah years of twelve lunations, making IO,63I dayS.It is true that the Councit os Nice adopted the lunar Cycle; and I 2O years after ards it was Confirmed by Pope Leo. The error at this laiter period was not more than a Jay. Since that time a Stronomy has been in digrepute, sor reasons at ready mentioned, and noone has been Mund who could clearly indicate the error, with sufficient authori ty; although in the time of Pope Hilary gome consideration was gi ven to the subjeci. At the present time the erroris so great as to attraci the ridicule of Jewi Sh and Arab astronomers, and deServes the serious attention of the ruter of the Church . 275 285GEOGRAPHY.We now pass to the insuence of the heavens upon things terrestriat. In ali things that are brought sortii on earth, whether for good or ovit, the sun and the heavens are thct m OVing CauSe. we have there reto consider the different ways in Whicli disserent paris of the ea risi 'ssursace are affected by theSe agenCies. Imagining that Suriace divided by the equator and the equinoctial colure into Mur equalportion S, we have specialty to Consider the portion contained he tweenthe equator and the potes, boundeo ea Si and west by the colure. What proportion does land bear to watery Ptolemy thought one- si xth, but other aut horities think the proportion muCh greater. Seneca and Pli ny look on the space of ocean dividing the west of Spatia from the east os India as inconsiderabie. Under the word Spain we must include a vast traci extending west ward S aCrOSS the Stratis of Gibraltar, in the direction Of Atlas. On the whole, it Seems probable that the land known to us hom east to weSt extendS OVermore than half the earlli 's circumferenCe. Further, it Seem S probabie
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that the disposition of land and water may be similar on the otherside of the northern hemisphere to that of this fide ; and the fame may be argued of the two divisions of the solitherii hemisphere especialty as the Sun in itS annuat course Comes nearer to it . 286-294Speaking of the paris known to us, Ptolemy and others have distinguis hed Seven climata-marhing them by the in creasing tengthos the longe Si da y. The position of each place referred to is define clby the intersection of the line of latitude and longitude belongingio it. The goneS, or climam, of Ptolemy are marked according to the increase of a quarter os an hour in the tength of the longest day upto the fixty-frst degree of latitude ; then e to the Sixty-Murth degree, hy half an hour's increase ; then e to the Sixty- si xth by one hour' SincreaSe. Leyond this potnt we Come to the region where in the Summer SenSOn the Sun i S at nyS above the horigon, in Winter alwaysheneath it. Here the divisions must be marhed a cord ing as thelongest day is One monili, Or two or three, up to Six. As to longitude, it Sliould be mensured not Dom any arbitrary potnt, but fromthe true east and west On the equator. The neglect of this pre- caution has led to much confusion in the tables os Toledo; and generalty a far more acCurate determination of the latitude and longitude of towns and StateR is needed, such as cara Only be instituted by apostolicat, imperiat, or at least regat authority .... 294-301 A right understanding of locali ty and climate Concertas alike the interpretation os Scripture, the propagation of the faith, and the wellare os commonwealth S. Mission aries in particular should know the distribution of the various religions of the worid ; where the lost tribes of Judea are to be looked for, where the incursions of Antichrist are most to be drended. Our knowledge of these matters,
derived Dona Pliny, Ptolemy and other writers of antiqui ty, has been recently enlarged by the traveis of William Rubruquis in Central
At the tropic of Cancer we begin to find regions where the sun atthe Summer Sol Stice CastS no Ahado v. Solithwards to the tropic os Capricorn the fame phenomenon occurs for each place twice in theyear. And we have knowledge of regions fouth of the tropic ofCapri Corn Where the noonclay shaclow is always to the solith. Andthough in these last the sun approacheS So nearly at our Winter time, and recedes So sar at Our Summer time, as to involve great extremitte Sof heat and Cold, 3 et these eviis may be lessened by the configurationos mountain and plain, so that the region is habitabie, as we knowin the Case of the istand of Taprobane ..... 305-309we may begin our description of the habitable world with India Iis fouthern Coasis are Washed by a branch of the Atlantic Oceani sovast that stoin the mouth of the Red Sea to the fouili os India is
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South-west, passing the opening of the Red Sea, and bound ing Solath Ethiopia illi the Indian Sea joins the Atlanti c. On the Nile, at thelatitude os si xteen cleg rees, we find the is and of Saba, the royal cityos Aethiopia called also Meroe, about 7OO miles froni the Coast. At the fame latitude, on the Red Sea, is the City Os Ptolemais. BetweentheSe two, or more probably to the west of Meroe, is Herenice the Cityos the Troglodytes, who are identi fied with the Garamantes. West of these are the Hesperi 310 3la Egypt is the region includet be tween Syene and the Mediterranean divided into tapper Egypt or the Thebais, and the Delta. The Delta extends from Heliopolis on the Arabian fronti er toAlexandria on the confines of Africa. Africa received iis nam esrom Asser, a descendant of Abraham. Defore this it had been called Libya. Much of the northern Coast was o Cupied by Medes, Perstans, and Armenians brought by Hercules. The interior was occupied by Gaetulians, aster ards Called NumidianS, amongst whomthe Carthaginians estahli Shed their empire. Bet Neen Carthage and Egypt are Tripolis and Cyrene ....... 313-3l8Sonething must be said of the Nile. Iis origin is in Aethiopia, probably in the region hordering on the Red Sea. Ιts Course is fora long time west wards as far as Meroe. Bel een Meroe and Syene it is northward. and so onward to the Delta. Iis inundation is in summer. hen e the difficulty of explaining it. The opinion of Thales that it was due to northern Wincis preventing the out flow, is dispro vel by the faci that the inundation begins in the uuper part of the river. A more probabie vi eiu is that of Anaxagoras. that it is due to the melling of snow in the mountains of Aethiopia. Aristolle rejecis this vlew, but gives reaSonS for SuppoSing a great ra infati to occurn Summer time in the marshy regions frona whicli the Nile
The region frona the eastern bank of the Nile is to be regardeclas part of Arabia, which also includes the vast space east ard astar as the Persi an gulf and northward through solith and east Palesti ne as far as the Euphrates. We can now tra e the principalpositions os the Hebrews in the Deseri, and also of Edom, of Moab and of other ne igh bouring tribes mentione d in the Scriptures . 325-332 The region belween the Tigris and the Euphrates is Assyria OrMesopotamia, in Which were the cities of Nineveli, Aram, an d
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Babylon. In Babylonia dweli Noah and his sons after the deluge. Loth the Tigris and the Euphrates rise in Armenia. The Tigris flows for Some space underground before reaching Ninevel, and joining the EuphrateS. The Euphrates s elis in summer AS cloeSthe Nilo. To the east of the Euphrates lie Nortii Arabia and Syria, the fouthern part of whicli is the Holy Land. Here a more de talleo
Beginning with the coasi, we find Gaga ora the Confines of Egyptand Palestine, then proceecling northWard ASCalon. Joppa, AzotuS,CaeSarea, Acon, Tyre, Sarepta, Sidon, Barui, Gibeleth, Tortosa, Laodicea. From this last to Antioch is two dayS' journey. Frona Antioch to Tarsus in Cilicia three days' journey . . . 335 33 6 Passing to the interior, We find Beer-Sheba at the Southernhoundary. Tu enly miles to the norit, is Hebron, the place of sepulture of the patriarch S. Near Hebron is Carmel, and a litileto the east, the town and mounta in of Ziph : Murteen miles to then orth is Bethlehem, Whicli is si x miles to the South of Jerusalem. This city is twelve leagues s rom Joppa, and ni ne leagueS to the eastos it is Jericho. Tehoa, the count of Amos, is t etve miles to the South-eaSt, and here We come to Pentapolis, the region of the Dead Sea, Where nothing lives, where hodies that usualty Sink in wateriloat, tum pS of bitumen are Mund on the sursace ; here too are found
The Jordan flows into the Dead Sea. Iis origin is by two branches frona Lebanon, and it passes through the Iahes of Gennesareth and Tiberias. North of Jericho is Scythopolis orllethsan. west ard and to the north of Jerusalem is Anathoth the birthplace of Jeremiali. Thence northward, twelve leagueS DomJerusalem, i S Samaria, now Called Sebaste. North- eastward is theplain os Megiddo; norit, of this and east of ACOn, at Seven leagueS'di Stance, is Nagareth. Two leagues further east is Mount Tabor, and the city of Tiberias, and the lal e of that name, containing the Purest Walers of Judaea ; it is near but distin t froni the lake of Gennesareth. To the north, separated by a desert region, are Bethsaida and Capernaum. East of Acon, and two leagueS northos Nagareth, is Cana os Galilee. Stili further north is Coragatio. e are thus brought in to the region of Lebanon, whence sertiligingwaters descend to the neighbourhood of Tyre and Sidon . . 339-348 Beyond Jordan, norit, of the Dead Sea, is the Citadet os Macheron. Here was the tribe of Reuben. North is Pella, at the boundary of Palestine on that si de of Jordan. East ward were the kingdomSof Og and of Sihon. On their boundaries is Ramoth-Gilead, notiar fro in the range of Anti-Lebanon. In this neighbourhood is theci ty os Damascus, sit ualed Mur days' bourney Dom Ierusalem . 343-344
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Summing up these delatis, we may Speak of Syria as including the Space Dom the Euphrates to the Mediterranean, and Dona Cilicia toEgypt. It is divided in to the provinces of Syria Comagena, Syria Caele, Phoenici an Syria, and the three divisions of Palestine, Galilaea, , amaria and Judaea. Comage i S the Capital City of the fit st. Antioch of the second. Phoenician Syria extends Dona the fouili os Lebanon to the north of Palestine. It contains the Cities of Damascus, Tripolis, Tyre and Sidon ; and beyond the Iordan Pella and Mount Hermon and Mount Gilead .... 344 347 The three regi Ons of Galilaea, Samaria, and Judaea belonged tot he Hebreius, who held the region beyond the Jordan frona the Dead Sea to Mount Hermon. In the norit, part of Galilee is Decapolis. Solath of this Ithuraea or the tetrarchy of Trachonitis. The northern part of Galilee contained a mixed race of Jews and hea then. Lower Galilee begitis With the lahe of Tiberias. Sout hos Galilee is the district of Samaria, and South of Samaria is
we see then that the amo unt of territory possessed by the Jews vas but smali. Frona Dan to Beer-sheba is but I7O miles, DomJoppa to the Jordan, not severa ty. To this, their POSSeSSion S east of the Jordan are to be ad deo 348 350 Passing to other regionS of the worid, we find the range of Mount TauruS extending froin the Indian Ocean, Separat ing Parthia, Mesopotamia, and Syria, Dona the Scythian regionS, and DomArmenia and Cappadocia, and finalty reaching Cilicia. In iis
Hyrcani an and many others. Media, Persia, Parthia, lie belweenthe Indus and the Tigris east and west, having the Caspian Sea and Caucasian motanta in s to the north, and the Pei Sian guis to theso ut h. The Parthian empire coincides with what was Once the
India lies east of the Indus; bo unded On the noriti by the Sericsea and by the motantains whicli extend east frona the Caucasiani ange. Vast as the Indus is, the Ganges flowing Dona the Caucasus in to the Eastern Ocean is yet greater. On the Ganges live the Brahmin s. living a life of extreme temperance and Cha Stity, and attaining great longevi ty. North of India is the Scythian OCeun and the Caucasian range a tready spolien of .... 352 353West ward Dona India, at the confines of India and Parthia, we. tind the Caspian gales on the fouth Shores of the Caspian OrHyrcani an Sea. This sea is entiret γ' in landi formed by great riversnowing froin the north. V est os Parthia is Hyrcania, and then thegi eater Armenia divided by the Euphrates frona Cappadocia. Thelesser Armenia is identi fled is illi Cilicia. This region from South to
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itiem I reland .......... 356-358
At the norit, of the Ballic Sea is Esthonia, east ward is Livonia, and fouth of it Courlandia, then Prussia and Pomerania. On the Confines of Dacia and Saxonia is the pori of Lube . In the Ballicli es the istand of Gothland. Solith of Prussia is Polano; south of this Bohemia, then Austria ; west of Austria is Alemannia, France and Spain ; east ard is Hungary bounded to the north-east by Albania,
whicli extendΗ as far as the river Don, having Bulgaria, and Constantinople, and the province of Cassaria to the South, and Russiato the noriti. North again os Russia are the Hyperboreans, a PeaCefullong-lived race, with a Climate far more equable than might be expected hom iis position. Among these northeria nations i S a great variety of religions. The Livonians, CuriandianS, Prussian S, Esthonian S ure pagan S. The Ru Scenes are Greela Christians, though incommon with the Poles, Bohemians and many others, their languageis Selavonian. The Tartars, who have subjugaled almost ali nationsi rom the Danube to the extreme east, lead a wandering pastoral liis. Some of the tribes subject to them are pagans, others follow the
on the north- easteria border of the Pontic Sea is the land of the Georgian S, and Corasi minians, where of old Amaetons used to live. South of these are Cappadocia and Armenia. Frona the mountain Sof Armenia flow the Euphrates and Tigris. Here Noah 'S ark rested. SS. Bartholome , Judas, and Thaddeus suffered martyrdom here ;and at one time there were Zoo Christian churches ; though Rubruquis mund but two, and these s mali. The city of Naxuana, the principallown of Armenia, noru destroyed by the Tartars, was visited by him, aS he paSSed up the river AraxeS. In the mountains to the east he