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This digital edition by Joseph H. Peterson, Copyright © 2000. All rights reserved.

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Chapter xii. Of the Number Nine, and the Scale thereof.

The number nine is dedicated to the Muses, by the help of the order of the Celestiall Spheres, and divine spirits: Hence there are nine movable Spheres, and according to those there are nine Muses, viz. Calliope, Urania, Polymnia, Terpsichore, Clio, Melpomene, Erato, Euterpe, Thalia, which nine Muses indeed are appropriated to the nine Spheres, so that the first resembles the supreme Sphere, which they call Primum mobile, and so descending by degrees, according to the written order, unto the last, which resembles the Sphere of the Moon, so, viz. Calliope is appropriated to the Primum mobile; Urania to the Starry Heaven, Polymnia to Saturn, Terpsichore, to Jupiter, Cleo to Mars, Melpomene to the Sun, Erato to Venus, Euterpe to Mercury, Thalia to the Moon.

There are also nine orders of blessed Angels, viz. Seraphim, Cherubim, Thrones, Dominations, Powers, Vertues, Principallities, Archangels, Angels, which Ezekiel figures out of nine Stones, which are the Saphir, Emrald [sapphire, emerald], Carbuncle, Berill [beryl], Onyx, Chrysolite, Jasper, Topaze, Sardis: This number hath also a great, and Occult mysterie of the Cross: For the ninth hour our Lord Jesus Christ breathed out his Spirit. And in nine dayes the Ancients buryed [buried] their dead, and in so many yeers [years] they say Minea received Laws from Jupiter in a Cave; whence this number was most especially taken notice of by Homer, when Laws were to be given, or answers were to be given, or the sword was like to rage. The Astrologers also take notice of the number nine in the Ages of men, no otherwise then they do of seven, which they call Climactericall years, which are eminent for some remarkable change. Yet sometimes it signifies imperfectness, and incompleatness, because it doth not attain to the perfection of the number ten, but is less by one, without which it is deficient, as Austin [Augustine] interprets it out of the ten Leapers [leper]: Neither is the longitude of nine Cubits of Og King of Basan, who is a type of the divel [Devil], without a mysterie [mystery].

The Scale of the Number nine.

The names of God with nine letters.
Jehovah Sabaoth. úåàáö äåäé Jehovah Zidkenu. åð÷ãö äåäé Elohim Gibor. øáéâ íéäìà
In the originall world.
Nine Quires of Angels.
Nine Angels ruling the Heavens.
Seraphim.
Metattron [Metatron].
Cherubin.
Ophaniel.
Thrones.
Zaphkiel.
Dominations.
Zadkiel.
Powers.
Camael.
Vertue.
Raphael.
Principalities.
Haniel.
Archangels.
Michael.
Angels.
Gabriel.
In the intelligible world.
Nine moveable spheres.The primum mobile.The Starry Heaven. The sphere of Saturn.The sphere of Jupiter.The sphere of Mars. The sphere of the Sun.The sphere of Venus. The sphere of Mercury.The sphere of the Moon.In the Celestial world.
Nine stones representing the nine Quires of Angels.Saphir [saphire] Emrald [emerald].Carbuncle.Beril [beryl]Onyx. Chrysolite.Jasper. Topaze.Sardis.In the Elementary world.
Nine senses inward, and outward together. Memory.Cogitative.Imaginative.Common sense.Hearing. Seeing.Smelling. Tasting.Touching.In the lesser world.
Nine orders of divels [devils].False spirits.Spirits of lying. Vessels of iniquity.Avengers of wickedness. Juglers.Aiery powers.Furies, sowing mischief. Sisters or tryers.Tempters or insnarers.In the infernal world.

Chapter xiii. Of the Number Ten, and the Scale thereof.

The number ten is called every number, or an universall number, compleat, signifying the full course of life: for beyond that we cannot number, but by replication; and it either implies all numbers within it self, or explains them by it self, and its own, by multiplying them: wherefore it is accounted to be of a manifold Religion, and power, and is applyed to the purging of souls. Hence the Ancients called Ceremonies Denary, because they that were to be expiated, and to offer sacrifices, were to abstain from some certain things for ten dayes. Whence amongst the Egyptians it was the custome for him that would sacrifice to Io, to fast ten dayes before, which Apuleius testifies of himself, saying, It was commanded that I should for the space of ten dayes refrain all meat, and be fasting. There are ten sanguine parts of man, the Menstrues, the Sperm, the Plasmatick spirit, the Mass, the Humours, the Organicall body, the vegetative part the sensitive part, reason, and the mind. There are also ten simple integrall parts constituting man, the bone, cartilage, nerve, fibre, ligament, artery, vein, membrane, flesh, skin. There are also ten parts of which a man consists intrinsecally; The spirit, the brain, the lungs, the heart, the liver, the gall, the spleen, the kidnies [kidneys], the testicles, the Matrix. There were ten Curtains in the Temple, ten strings in the Psaltery; ten musicall instruments with which Psalms were sang, the names whereof were, Neza, on which their Odes were sang, Nablum, the same as Organs, Mizmor, on which the Psalms, Sir, on which the Canticles; Tehila, on which Orations, Beracha, on which Benedictions, Halel, on which Praises: Hodaia, on which Thanks, Asre, on which the Felicity of any one, Hallelujah, on which the praises of God only, and Contemplations. There were also ten singers of Psalms, viz. Adam, Abraham, Melchisedech, Moses, Asaph, David, Solomon, and three sons of Chora, there are also ten commandments; And the tenth day after the ascension of Christ the Holy Ghost came down. This lastly is the number, in which Jacob wrestling with the Angel all night overcame, and at the rising of the Sun was blessed, and called by the name of Israel. In this number Joshua overcame thirty one Kings, and David overcame Goliath, and the Philistines, and Daniel escaped the danger of the Lions. This number also is as circular as unity, because being heaped together, returns into a unity, from whence it had its beginning, and it is the end, and perfection of all numbers, and the beginning of tens. As the number ten flows back into a unity, from whence it proceeded, so every thing that is flowing is returned back to that from which it had the beginning of its Flux. So water returns to the Sea, from whence it had its beginning, the body returns to the Earth, from whence it was taken; time returns into Eternity, from whence it flowed, the spirit shall return to God that gave it; and lastly, every creature returns to nothing, from whence it was created, neither is it supported but by the word of God, in whom all things are hid; and all things with the number ten, and by the number ten, make a round, as saith Proclus, taking their beginning from God, and ending in him. God therefore that first unity, or one thing, before he communicated himself to inferiours, diffused himself into the first of numbers, viz. The number three, then into the number ten, as into ten Ideas, and measures of making all numbers, and all things, which the Hebrews call ten Attributes, and account ten divine names; For which cause there cannot be a further number. Hence all tens have some divine thing in them, and in the Law are required of God as his own, together with the first fruits, as the originall of things, and beginning of numbers, and every tenth is as the end given to him, who is the beginning, and end of all things.

The Scale of the Number ten.



The Scale of the Number ten.

In the originall åäéåçéäåäé
The name Jehova of ten letters collected.
àä åàå àä ãåé
The Name Jehovah of ten letters Extended.
úåàáö íéäìà
The name Elohim Sabaoth.
The name of God with ten letters.
 äéäà
Eheie.
øúë
Kether.
äåäé é
Iod Jehovah.
äîëç
Hochmah.
íéäìà äåäé
Jehova Elohim.
äðéá
Binah.
ìà
El.
ãñä
Hesed.
øáéâ íéäìà
Elohim gibor.
äøåáâ
Geburah.
äåìà
Eloha.
úøàôú
Tiphereth.
úåàáö äåäé
Jehovah Sabaoth
äöð
Nezah.
úåàáö íéäìà
Elohim Sabaoth.
ãåä
Hod.
éãù
Sadai.
ãåñé
Iesod.
éðãà
Adonai melech.
úåëìî
Malchuth.
Ten names of God.
Ten Sephiroth.
In the intelligible world.Seraphim.
Haioth ha-kados.
Metattron.
Cherubim.
Ophanim.
Jophiel.
Thrones.
Aralim.
Zaphkiel.
Dominations.
Hasmallim.
Zadkiel.
Powers.
Seraphim.
Camael.
Vertues.
Malachim.
Raphel [Raphael].
Principalities.
Elohim.
Haniel.
Archangels.
Ben Elohim.
Michael.
Angels.
Cherubim.
Gabriel.
Blessed souls.
Issim.
The soul of Messiah.
Ten orders of the blessed according to Dionysius.
Ten orders of the blessed according to the traditions of men.
Ten Angels ruling.
In the Celestiall world. Reschith ha-gallalim.
The Primum Mobile.
Masloth.
The sphere of the Zodiake [zodiac].
Sabbathi.
The Sphere of Saturn.
Zedeck.
The sphere of Jupiter.
Madim.
The Sphere of Mars.
Schemes.
The sphere of the Sun.
Noga.
The sphere of Venus.
Cochab.
The sphere of Mercury.
Levanah.
The sphere of the Moon.
Holom. Jesodoth.
The sphere of the Elements.
Ten spheres of the world.
In the Elementary world.A Dove.A Lizard.A Dragon.An Eagle. A Horse.Lion.Man.Genitals [sic. Serpent]Bull.Lamb. Ten Animals consecrated to the Gods.
In the lesser world.Spirit.Brain.Spleen.Liver.Gall. Heart.Kidneys.Lungs.Genitals.Matrix. Ten parts intrinsecall of man.
In the infernall world.False Gods.Lying spirits. Vessels of iniquity.Revengers of wickedness. Juglers.Aery powers.Furies the seminaries of evil. Sifters or tryers.Tempters or ensnarers.Wicked souls bear rule. Ten orders of the damned.


Chapter xiiii. Of the Number eleven, and the number twelve; with a double Scale of the Number twelve Cabalisticall, and Orphicall.

The number eleven as it exceeds the number ten, which is the number of the commandements [commandments], so it fals short of the number twelve, which is of grace and perfection, therefore it is called the number of sins, and the penitent. Hence in the tabernacle there were commanded to be made eleven Coats of hair which is the habit of those that are penitent, and lament for their sins, whence this number hath no Communion with Divine or Celestiall things, nor any attraction, or scale tending to things above: neither hath it any reward; but yet sometimes it receives a gratuitous favor from God, as he which was called the eleventh hour to the vineyard of the Lord, received the sanne reward as those who had born the burden, and heat of the day. Now the number twelve is divine, and that whereby the Celestials are measured; it is also the number of the Signs in the Zodiack over which there are twelve angeis as chief, supported by the irrigation of the great name of God. In twelve yeers [years] also Jupiter perfects his course, and the Moon daily runs through twelve degrees. There are also twelve chief joynts [joints] in the body of man, viz. in hands, elbones [elbows], shoulders, thighs, knees, and vertebrae of the feet. There is also a great power of the number twelve in divine mysteries. God chose twelve families of Israel, and set over them twelve Princes; so many stones were placed in the midst of Jordan, and God commanded that so many should be set on the breast of the Priest; twelve Lyons [lions] did bear the brazen Sea that was made by Solomon: there were so many fountains in Helim, and so many spies sent to the land of promise, and so many Apostles of Christ set over the twelve tribes, and twelve thousand people were set apart and chosen; the queen of Heaven crowned with twelve Stars, and in the Gospel twelve baskets of the fragments were taken up, and twelve Angels are set over the twelve gates of the City, and twelve stones of the heavenly Jerusalem. In inferior things many breeding things proceed after this number; so the Hare and Coney being most fruitfull, bring forth twelve times in the yeer [year], and the Cammel [camel] is so many moneths in breeding, and the Pea-cock [peacock] brings forth twelve Eggs.

The Scale of the Number twelve.

The names of God with twelve letters   àåä
Holy
(ê)åøá
Blessed
ùã÷ä
He [Ipse]
  ùã÷ä çåøå ïá áà
Father, Son, Holy Ghost.
 In the originall world.
The great name returned back into twelve banners. äåäé åääé ääåé éäåä äéåä åéää äéäå ääåé éääå åäéä äåéä éåää  
Twelve orders of the blessed Spirits. Seraphim.Cherubim.Thrones.Dominations.Powers. Vertues.Principalities.Archangels.Angels.Innocents. Martyrs.Confessors.In the Intelligible world.
Twelve Angels ruling over the signs. Malchidiel.Asmodel.Ambriel.Muriel.Verchiel. Hamaliel.Zuriel.Barbiel.Adnachiel.Hanael. Gabriel.Barchiel. 
Twelve Tribes:Dan.Ruben.Judah.Manasseh. Asher.Simeon.Issachar.Benjamin.Napthalin. Gad.Zabulon.Ephraim. 
Twelve Prophets.Malachi.Haggai.Zachary.Amos. Hosea.Micha.Jonah.Obadiah.ZephaniahNahum. HabakukJoel. 
Twelve Apostles.Mathias.Thadeus.Simon.John. Peters.Andrew.Bartholemew.Philip. James the elderThomas.Matthew.James the yonger. 
Twelve signs of the Zodiack.Aries.Taurus.Gemini. Cancer.Leo.Virgo.Libra.Scorpio.Sagittarius. Capricorn.Aquarius.Pisces.In the Celestiall world.
Twelve Moneths [months].March.April.May.June. July.August.September.October.Novemb.December. January.February.In the Elementall world.
Twelve Plants.SSang.Upright Vervain.Bending Vervain. Comfrey.Lady's Seal.Calamint.Scorpion-grass.Mugwort. Pimpernel.Dock.Dragon-wort.Aristolochy. 
Twelve stones.Sardonius.A Carneol.Topaze Calcedony.Jasper.Emrald [emerald].Berill.Amethyst. Hyacinth.Chrysoprasus.Crystall.Saphir. 
Twelve principall members.The head.The neck.The arms. The brest [breast].The heart.The belly.The kidnies [kidneys]. Genitals.The hams.Knees.Legs.Feet. In the Elementary world.
Twelve degrees of the damned, and of Divels [devils]. False godsLying spirits.Vessels of iniquity. Revengers of wickedness.Juglers.Aery powers. Furies the sowers of evils.Sifters or Tryers. Tempters or ensnarers.Witches.Apostates. Infidels.In the infernall world.


The Orphical Scale of the Number twelve.

Twelve Deities.Pallas.Venus.Phoebus.Mercury. Jupiter.Ceres.Vulcan.Mars.Diana.Vesta. Juno.Neptune.In the intelligible world.
Twelve signs of the Zodiake.Aries.Taurus.Gemini. Cancer.Leo.Virgo.Libra.Scorpio.Sagittarius. Capricorn.Aquarius.Pisces.In the Celestiall world.
Twelve Moneths [months].March.April.May.June. July.August.September.October.Novemb.December. January.February.In the Elementall world.
Twelve consecrated birds.The Owle.Dove.Cock. Ibis.Eagle.Sparrow.Goose.Pie.Daw.Heron. Peacock.Swan. 
Twelve consecrated beasts.Shee Goat.He Goat.Bull. Dog.Hart.Sow. Asse.Wolf.Hind.Lyon [lion].Sheep.Horse. 
Twelve consecrated trees.Olive-tree.Myrtil-tree. Laurell.Hasle [hazel tree].Aesculus.Apple-tree. Box-tree.Dog tree.Palm-tree.Pine-tree. Ram-thorn.Elm-tree. 
Twelve members of man distributed to the signs.The head. The Neck.The Armes.The Brest [breast].The Heart.The Belly. The kidnies [kidneys].Genitals.Hamnes.Knees.Leggs.Feet. In the lesser world.


Chapter xv. Of the Numbers which are above twelve, and of their powers and vertues.

The other numbers also which are above twelve, are endowed with many, and various effects, the vertues whereof you must understand by their originall, and parts, as they are made of a various gathering together of simple numbers, or maner of multiplication. Sometimes as their significations arise from the lessening, or exceeding going before, especially more perfect, so they contain of themselves the signs of certain divine mysteries. So you see the third number above ten, shews the mysteries of Christs appearing to the Gentiles, for the thirteenth day after his birth a Star was a guide to the wise men. The fourteenth day doth typifie Christ, who the fourteenth day of the first moneth [month] was sacrificed for us; upon which day the children of Israel were commanded by the Lord to celebrate the Passeover [Passover]. This number Mathew [Matthew] doth so carefully observe, that he passed over some generations, that he might every where observe this number in the generations of Christ. The fifteenth number is a token of spirituall ascensions, therefore the song of degrees is applyed to that in fifteen Psalms. Also fifteen yeers [years] were added to the life of King Hezekiah: and the fifteenth day of the seventh moneth [month] was observed, and kept holy. The number sixteen, the Pythagorians call the number of felicity. It also comprehends all the Prophets of the Old Testament, and the Apostles, and Evangelists of the new. The number eighteen, and twenty, Divines interpret to be unhappy, for in the former, Israel served Eglon King of Moab; and in the other Jacob served, and Joseph was sold. And lastly, amongst creatures that have many feet, there is none that hath above twenty feet. The twenty two signifies the fullness of wisdom, and so many are the Characters of the Hebrew letters, and so many Books doth the old Testament contain. To the number twenty eight, the favour of the Moon is designed, for the motion thereof is distant from the course of other Stars, & as it were alone is compleated the twenty eighth day, when it returns to the same point of the Zodiake [zodiac] from whence it came. Hence twenty eight Mansions of the Moon, having singular vertue, and influence, are numbered in the heavens. The number thirty is memorable for many mysteries, Our Lord Jesus Christ was baptized the thirtieth yeer [year] of his Age, and began to do miracles, and to teach the Kingdom of God. Also John Baptist was thirty yeers old when be began to preach in the wilderness, and to prepare the wayes of the Lord. Also Ezekiel at the same age began to prophecy; and Joseph was brought out of Prison on the thirtieth yeer of his Age, and received the government of Egypt from Pharaoh. The number thirty two, the Hebrew Doctors ascribe to wisdom, and so many paths of wisdom are described by Abraham. But the Pythagorians call this the number of Justice, because it is alwaies divisible into two parts, even unto a unity. The number fourty [forty], the Ancients did honour with great observation, concerning which they did celebrate the feast Tessarosten: It is said that it doth conduce to the account of birth, for in so many daies the seed is fitted, and transformed in the womb, untill it be by its due, and harmoniacall proportions brought unto a perfect organicall body, being disposed to receive a rationall soul. And so many dayes they say women be, after they have brought forth, before all things are setled [settled] within them, and they purifled, and so many dayes infants refrain from smiling, are infirme, and live with a great deal of hazard. This also is in Religion a number of expiation, and penitency, and signifying great mysteries. For in the time of the deluge the Lord rained fourty daye, and nights upon the earth: The children of Israel lived fourty yeers in the wilderness; fourty dayes the destruction of Nineveh was put off. The same number was accounted as holy in the fasts of the Saints: For Moses, Elias, and Christ fasted fourty dayes. Christ was carried fourty weeks in the womb of a Virgin, Christ tarryed fourty dayes after his birth at Bethelem [Bethlehem] before he was presented in the Temple: He preached fourty months publickly: He lay fourty [forty] hours dead in the Sepulchre, the fourtieth day after his resurrection he ascended into heaven, all which Divines say, were not done without some occult property, and mysterie of this number. The number fifty signifies remission of sins, of servitudes, and also liberty. According in the Law, on the fiftieth year they did remit debts, and every one did return to his own possessions. Hence by the yeer of Jubilee, and by the Psalm of repentance it shews a sign of indulgency, and repentance. The law also, and the holy Ghost are declared in the same: For the fiftieth day after Israels going forth out of Egypt, the Law was given to Moses in mount Sinai: The fiftieth day after the resurrection, the holy Ghost came down upon the Apostles in mount Sion; Whence also it is called the number of grace, and attributed to the Holy Ghost. The number sixty, was holy to the Egyptians, for it is proper to the Crocodile, that as she in sixty dayes brings forth sixty eggs, and so many dayes sits on them, so she is said also to live so many yeers, and to have so many teeth: and so many dayes every yeer to rest solitary without any meat. The number seventy hath also its mysteries, for so many yeers the fire of the sacrifice in the Babylonian Captivity lay under the water, and was alive: so many yeers Jeremiah foretold the destruction of the Temple, and so many yeers the Babylonian Captivity endured, and in so many yeers the desolation of Jerusalem was finished. Also there were seventy Palms in the place where the children of Israel pitched their Tents. The Fathers went down to Egypt with seventy souls. Also seventy Kings with their fingers, and toes cut off did gather meat under the table of Adonibezeck seventy sons came forth of the loins of Joas, seventy men, all sons of Jero, seventy weights of silver were given to Abimelech, and so many men Abimelech slew upon one stone: Abdon had seventy sons, and Nephews, who rod upon seventy Foals of Asses; Solomon had seventy thousand men which carried burdens. Seventy sons of King Ahab were beheaded in Samaria; seventy yeers, according to the Psalmist, are the Age of man. Lamech shall be avenged seventy seven fold; Thou shalt forgive thy brother if he offend against thee, seventy seven times. Also the number <seventy seven times. Also the number> seventy two was famous for so many languages, for so many Elders of the Synagogue, for so many interpreters of the old Testament, for so many Disciples of Christ: It hath also a great Communion with the number twelve; hence in the heavens, every sign being divided into six parts, there result seventy two fives, over which so many angels bear rule; and so many are the names of God; and every five is set over one Idiom with such efficacy, that the Astrologers, and Physiognomists can know from thence from what Idiom everyone ariseth. Answerable to these are so many manifest joynts in mans body, whereof in every finger and toe there are three, which together with the twelve Principal reckoned before in the number twelve make up seventy two. The number a hundred in which the sheep that was found, was placed, which also passeth from the left hand to the right, is found holy: and because it consists of tens it shews a complete perfection. But the Complement of all numbers is a thousand which is the four square measure of number ten, signifying a complete, and absolute perfection. There are also two numbers especially celebrated by Plato in his Repub. [Republic] and not disallowed by Aristotle in his Politicks, by which great mutations in Cities are foretold: These are the square of ten [*twelve], and the four square measure thereof, viz. the fourty four above a hundred, and seven hundred twenty eight above a thousand, which number is fatall: to which when any City, or Common Wealth hath attained, it shall afterward with a compleat four square measure decline: but in squares it undergoeth a change, but for the better, if it be governed with prudent discipline, and then it shall not with fate, but imprudency fall. And let thus much suffice for numbers in particular.

Chapter xvi. Of the notes of numbers, placed in certain gesturings.

I have often read in the books of Magicians, and their works, and experiments certain, wonderful, & as they seemed to me ridiculous gesturings, and I did think they were certain occult agreements of the divels, by reason of which I did reject them: but after I did more seriously examine the matter, then I did presently understand that they were not the compacts of divels [devils]; but that there lay in them the reason of numbers, by which the ancients did by the various bending forward, and backward, their hands, and fingers represent numbers, by whose gesturings the Magiciand did silently signifie words unknown by sound, various with numbers, yet of great vertue, by their fingers joyned together, and sometimes changed, and did with sacred silence worship the Gods that rule over the world. The rites whereof Martianus also makes mention of in his Arithmetick, saying, The fingers of the Virgin were moved all manner of wayes, who after she went in, did by expressing seven hundred and seventeen numbers with her bended fingers call upon Jupiter. But, that these things may be the better understood, I shall bring something out of the sayings of Beda who saith, When thou sayest one, bend in the litle [little] finger on thy left hand, and set it in the middle of the Palme; when thou sayest two, place the next finger to the litle finger in the same place; when three, the middle finger after the same manner; when four, thou shalt lift up thy little finger; when five, the next to it after the same manner; when six, the middle, that finger alone which is called the ring finger, being fixt on the middle of the Palme: when thou sayest seve, thou shaly put only thy little finger above the root of thy Palm, tthe rest in the mean time being lifted up; and by it when thou sayest eight, thy ring finger; when thou sayest nine, thou shalt set thy middle finger contrary to them; when thou sayest ten, thou shall set the naile of thy fore-finger, or the middle joynt [joint] of thy thumb. When thou sayest twenty, thou shalt put the top of thy middle finger close betwixt the joynts of thy thumb, and forefinger. When thou sayest thirty, thou shalt joyn the naile of thy thumb, and fore-finger lightly together. When thou sayest fourty [forty], thou shalt bring the inside of thy thumb to the outside of thy fore-finger, both being lifted up. When thou sayest fiftym thou shalt bend thy thumb with the outward joynt like to the Greek Gamma to the Palme. When thou sayest sixty, compass about thy thumb being bended as before, with thy fore-finger bowed over it. When thou sayest seventy, thou shalt supply thy fore-finger being bowed about as before, with thy thumb stretched at length, the naile thereof being lifted up before the middle joynt of thy fore-finger. When thou sayest eighty, thou shalt supply thy fore-finger bowed about as before, with thy thumb stretched forth at length, the naile thereof being set upon the middle joynt of the fore-finger. When thou sayest ninty, thou shall set the naile of thy fore-finger bent into the root of thy thumb stretched out. Thus much for the left hand. Now thou shalt make 100. on thy right hand, as thou sisdt ten of thy left; and 200. on thy right, as thou didst twenty on thy left; 2000. on thy right, as thou didst two on thy left, and so to 9000. Moreover when thou sayest 10000. thou shalt put thy left hand upward on thy brest, thy fingers only being lifted towards Heaven. When thou sayest 20000. thou shalt put the same spread forth upon thy breast. When thou sayest 30000. thou shalt put thy thumb on the same hand downwards, on the cartilage of the middle of thy brest. When thou sayest 40000. thou shalt lay the same upright, and stretched forth on thy navell. When thou sayest 50000. thou shalt lay thy thumb of the same hand downard [downward] on thy navell. When thou sayest 60000. thou shalt hold thy left thigh with the same, being downards [downwards]. When thou sayest 70000. the same shalt put upon thy thumb upright. When thou sayest 80000. thou shalt put the same downward on thy thigh. When thou sayest 90000. thou shalt hold thy loyns [loins] with the same, thy thumb being turned downwards. But when thou sayest 100000. or 200000. and so unto to 900000. thou shalt in the same order as we have spoken, fill them up on the right part of thy body. But when thou sayest 1000000. thou shall joyn thy hands together, and clasp thy fingers one within the other. Let these suffice which have been observed out of Beda; Thou shalt finde more of these in Brother Luke of Saint Sepulchers, in his great Arithmetick.

Chap. xvii. Of the various notes of numbers observed amongst the Romans.

The notes of numbers are made diverse wayes in divers nations, The Romans did figure them by these following notes, which Valerius Probus ascribes concerning the ancient letters, and which are still in use, viz.

One.
I.
Five.
V.
Ten.
X.
Fifty.
L.
A hundred.
C.
Two hundred.
figure 2-1CC.
Five hundred.
D.
A thousand.
figure 2-2
Five thousand.
figure 2-3
Ten thousand.
figure 2-4
Fifty thousand.
figure 2-5
A hundred thousand.
figure 2-6
Two hundred thousand.
figure 2-7
Five hundred thousand.
figure 2-8
A thousand thousand.
figure 2-9

There are also other notes of numbers now a dayes used amongst Arithmeticians, and Calculators, which according to the order of numbers are made after this manner. 1. 2. 3. 4. 5. 6. 7. 8. 9. to which is added a note of privation signed with the mark 0 which although it signifie no number, yet makes others to signifie, either tens, or hundreds, or thousands, as is well known to Arithmeticians. Also there are some that mark the number ten with a line downward, and another made cross it; and five by that line which toucheth the other, but doth not go cross it, and a unity by that which is put by it self, as you may see in this example, + signifies ten, +- signifies ten and five, signifies sixteen, ten and seven; and the round o being put by it self signifies a hundred; but being joyned to others, signifies so many hundreds as the numbers are to which it is put, as thus, oo or thus IIo signifies two hundred, thus ooo or thus IIIo three hundred five hundred, ten hundred or a thousand. And these notes are commonly seen added in Magicall Characters.

Chap. xviii. Of the notes or figures of the Græcians.

The Græcians [Greeks] use the Alphabeticall letters for their notes ofnumbers, and that three wayes; first by every Element according to the series of the Alphabet signifying the number of its place. For in the order of which any number doth possesse the place of the Alphabet, it represents the number thereof, as here you may see.
1.
a
2.
b
3.
g
4.
d
5.
e
6.
z
7.
h
8.
q
9.
i
10.
k
11.
l
12.
m
13.
n
14.
x
15.
o
16.
p
17.
r
18.
s
19.
t
20.
u
21.
f
22.
c
23.
y
24.
w

And this is the first order of numbeers amongst the Greeks. Secondly, the Greeks divide the whole Alphabet into three Classes, whereof the first beginning from Alpha, is of unites. The second beginning from Iota is of tens. The third begining from Rho is of hundreds; and this order by the latter of the Greeks is instituted after the imitation of the Hebrews. Now because threir Alphabet wants by that rule, three letters, it is necessary to add to them three figures and to interlace them with the letters, by which, viz. they explain the sixt, the ninetieth, and the nine hundreth, as is manifest in the following Classes.
1.
A
2.
B
3.
G
4.
D
5.
E
6.
z
7.
Z
8.
H
9.
Q
10.
I
20.
K
30.
L
40.
M
50.
N
60.
X
70.
O
80.
P
90.
100.
R
200.
S
300.
T
400.
U
500.
F
600.
C
700.
Y
800.
W
900.

Now if to any of these letters there be subscribed the stroke of an acute tone, then it signifies so many thousands, as in these examples.

1000.
/ A
10000.
/ I
100000.
/ P

After the third manner, the Greeks use only six letters in signifying their numbers, viz. I, for an Unite, P for the number five, because it is the head of the word pente (i.e.) five. D for the number ten, from deka. H for a hundred from ekaton. X for a thousand from the word cilia, M for ten thousand from muria. From which six letters joyned in number after their manner unto four, or to other numbers, they make other numbers, besides P which is not multiplyed, nor joyned to it self, but alwayes aignifies the fives of others, as appears in the following examples.

1
I
2
II
3
III
4
IIII
5
P
6
PI
7
PII
8
PIII
9
PIIII
10
D
11
DI
12
DII
13
DIII
14
DIIII
15
DP
16
DPI
20
DD
21
DDI
50
60
D
100
H
200
HH
500
1000
C
5000
10000
M
50000


Chap. xix. Of the notes of the Hebrews, and Caldeans [Chaldaeans], and certain other notes of Magicians.

The Hebrew letters also have marks of numbers, but far more excellently then in any other languages, since the greatest mysteries lie in Hebrew letters, as is handled concerning these in that part of Cbaly which they call Notariacon. Now the principall Hebrew letters are in number twenty two, whereof five have divers other figures in the end of a word, which therefore they call the five ending letters, which being added to them aforesaid make twenty seven, which being then divided into three degrees, signifie the unites, which are in the first degree; tens which are in the second, and hundreds which are in the third degree. Now every one of them if they be marked with a great Character signifies so many thousands, as here

3000.
â
2000.
á
1000.
à

Now the Classes of the Hebrew numbers are these,

9.
è
8.
ç
7.
æ
6.
å
5.
ä
4.
ã
3.
â
2.
á
1.
à
90.
ö
80.
ô
70.
ò
60.
ñ
50.
ð
40.
î
30.
ì
20.
ë
10.
é
900.
õ
800.
ó
700.
ï
600.
í
500.
ê
400.
ú
300.
ù
200.
ø
100.
÷

Now there are some which do not use those finall letters, but instead of them write thus.

1000.
à
900.
úú÷
800.
úú
700.
úù
600.
úø
500.
ú÷

And by those simple figures by the joyning them together they desfribe all other compound numbers, as eleven, twelve, a hundred and ten, a hundred and eleven, by adding to the number ten, those which are of unites; and in like manner to the rest after their manner; yet they describe the fifteenth number not by ten, and five, but by nine, and six, viz. thus åè and that out of honor to the divine name äé which imports fifteen, lest it should happen that the sacred name should be abused to prophane things. Also the Egyptians, Æthiopians [Ethiopians], Caldeans [Chaldaeans], and Arabians, have their marks of numbers, which also often times happen amongst Magicall Characters. He therefore that would know them, must seek them, of them that are skilful of these letters. For the Caldeans [Chaldaeans] mark the numbers with the letters of their Alphabet after the manner of the Hebrews. We have set down their Alphabet in the end of the first book. Moreover I found in two most ancient books of Astrologers, and Magicians, certain most elegant marks of numbers, which I thought good to set down in this place; Now they were in both Volums [volumes] such.

Now by these mark turned to the left hand are made tens, after this manner.

And by those markes which are turned downwards on the right hand, are made hundreds; on the left thousands, viz. thus.

And by the composition, and mixture of these markes other mixt and compounded numbers also are most elegantly made, as you may perceive by these few.

According to the example of which we must proceed in other compound numbers; And so much suffice for the marks of numbers.

Chap. xx. What numbers are attributed to letters; and of divining by the same.

The Pythagorians [Pythagorians] say (Aristotle, and Ptolemy are of the same opinion) that the very Elements of letters have some certain divine numbers, by which collected from proper names of things, we may draw conjectures concerning occult things to come. Whence they call this kind of divination Arithmancy, because, viz. it is done by numbers, as Terentianus hath made mention of it in these verses.

Names are, they say, made of but letters few
Unfortunate, of many, do foreshew
Success; so
Hector did Patroclus slay,
So
Hector to Achilles was a prey.

Also Pliny saith, That there was added to what Pythagoras invented, an uneven number of vowels of imposed names, which did betoken lameness, or want of eyes, and such like misfortunes, if they be assigned to the right side parts; but an even number to them of the left. And Alexandrinus the Philosopher taught, How that by the number of letters we may find out the ruling Stars of any one that is born, and whether the husband or wife shall dye [die] first, and know the prosperous, or unhappy events of the rest of our works. His traditions which were not disallowed by Ptolemy the Astrologer we shall here add, and put under. But those numbers, which are deputed to each letter, we have above shewed in the Greek, and Hebrew letters, the Alphabet being divided into three Classes, whereof the first is of unites, the second of tens, the third of hundreds. And seeing in the Roman Alphabet there are wanting four to make up the number of twenty seven Characters, their places are supplyed with I, and V sinple consonants, as in the names of John, and Valentine, and hi, and hu aspirate consonants as in Hierom, and Huilhelme, although the Germans for hu the asperate use a double vv; the true Italians, and French in their vulgar speech put G joymed with U instead thereof, writing thus, Vuilhelmus, and Guilhelmus.

1.
A.
2.
B.
3.
C.
4.
D.
5.
E.
6.
F.
7.
G.
8.
H.
9.
I.
10.
K.
20.
L.
30.
M.
40.
N.
50.
O.
60.
P.
70.
Q.
80.
R.
90.
S.
100.
T.
200.
V.
300.
X.
400.
Y.
500.
Z.
600.
I.
700.
V.
800.
HI.
900.
HV.

But if thou desirest to know the ruling Star of any one that is born, compute his name, and of both his parents, through each letter according to the number above written, and divide the sum of the whole being gathered together by nine, substracting it as often as thou canst; and if there remaine a unity, or four, both signifie the Sun; if two or seven, both signifie the Moon; but three, Jupiter; five, Mercury; six, Venus; eight, Saturne; nine, Mars; and the reasons thereof are shewed else where. In like manner if thou desirest to know the horoscope of any one that is born, compute his name, and of his Mother, and Father, and divide the whole collected together by twelve, if there remain a unity, it signifies the Lyon; if Junos dewce, Aquarius; if the Vestall three, Capricorn; if four, Sagittarius; if five, Cancer; if Venus six, Taurus; if Palladian seven, Aries; if Vulcans eight, Libra; if Mars his nine, Scorpio; if ten, Virgo; if eleven, Pisces; if Phoebus twelve, they represent Geminos; and the reasons of them are given elswhere. And let no mam wonder that by the numbers of names many things may be Prognosticated, seeing (thr Pythagorian Philosophers, and Hebrew Cabalists testifying the same) in those numbers lye [lie] certain occult mysteries understood by few: for the most High created all things by number, measure, and weight, from whence the truth of letters, and names had its originall, which were not instituted casually, but by a certain rule (although unknown to us.) Hence John in the Revelation saith, Let him which hath understanding compute the number of the name of the beast, which is the number of a man. Yet these are not to be understood of those names, which a disagreeing difference of Nations, and divers rites of Nations according to the causes of places, or education have put upon men; but those which were inspired into every one at his birth, by the very Heaven with the conjunction of Stars, and those which the Hebrew Mecubals, and wise men of Egypt long since taught to draw from the generation of every one.

Chap. xxi. What numbers are consecrated to the Gods, and which are ascribed, and to what Elements.

Moreover the Pythagorians have dedicated to the Element, and dieties [deities] of Heaven sacred numbers; for to the Aire they have assigned the number eight, and to fire five, to the earth six, to the water twelve. Besides, unity is ascribed to the Sun, which is the only King of the Stars, in which God put his Tabernacle; and that this also is of Jupiter, doth the Causative power of his ideal and intellectuall species testifie, who is the head, and the father of the Gods, as unity is the beginning, and parent of numbers: The number two is ascribed to the Moon, which is the second great light, and figures out the soul of the world, and is called Juno, because betwixt that and unity there is the first conjunction, and neer fellowship; it is also ascribed to Saturn, and Mars, two unfortunate Planets with the Astrologers; so the number three is ascribed to Jupiter, the Sun, and Venus, viz. three fortunate planets, and is deputed to Vesta, Hecata, and Diana; hence they say,

Threefold is Hecate, three mouths Diana
The Virgin hath -----

The number three therefore is dedicated to this Virgin whom they say to be powerfull in Heaven, and in Hell. The number four is of the Sun, which by that number constitutes the corners of the heavens, and distinguisheth seasons: it is also ascribed to Cyllenius, because he alone is called the four square God. The number five consisting of the first even, and the first odd, as of female, and male, both sexes, is assigned to Mercury; it is also attributed to the Celestiall world, which beyond the four Elements is it self under another form, the fist. The number six, which consists of two threes, as a Commixtion of both sexes, is by the Pythagorians ascribed to generation, and marriage, and belongs to Venus, and Juno. The number seven is of rest, and belongs to Saturn; the same also doth dispence the motion, and light of the Moon, and therefore is called by the name of Tritonia the Virgin, because it begets nothing. It is assigned to Minerva, because it proceeds of nothing; also to Pallas the Virago, because it consists of nuumbers, as of males, and females. This also Plutarck ascribes to Apollo. The number eight, by reason it containes the mysterie of justice, is ascribed to Jupiter; it is also dedicated to Vulcan, for of the first motion, and the number two, which is Juno drawn twice into it self, it consists; It is also attributed to Cybele the mother of the Gods, to whom every four square is attributed. Plutarck assigns it to Bacchus, or Dionysius, who is said to be born the eighth moneth [month]: others, because Infants of the wight moneth do not live, have attributed it to Saturn, and the three Ladies of destiny. The number nine belongs to the Moon, the utmost receptacle of all Celestiall influences, and vertues, as also it is dedicated to the nine Muses, as also to Mars, from whom is the end of all things. The number ten is Circular, and belongs to the Sun, after the same manner as unity; also it is attributed to Janus, because it is the end of the first order, and from whence begins the second unity; it is also ascribed to the world. In like manner the number twelve, because the Sun going round twelve signes, distributes the yeer [year] into twelve moneths, is attributed to the world, the Heaven, and the Sun. The number eleven, because it is semicircular, is attributed to the Moon, and also deputed to Neptune.

Chap. xxii. Of the tables of the Planets, their vertues, forms, and what Divine names, Intelligencies, and Spirits are set over them.

It is affirmed by Magicians, that there are certain tables of numbers distributed to the seven planets, which they call the sacred tables of the planets, endowed with many, and very great vertues of the Heavens, in as much as they represent that divine order of Celestiall numbers, impressed upon Celestials by the Idea's of the divine mind, by means of the soul of the world, and the sweet harmony of those Celestiall rayes, signifying according to the proportion of effigies, supercelestiall Intelligencies, which can no other way be expressed, then by the marks of numbers, and Characters. For materiall numbers, and figures can do nothing in the mysteries of hid things, but representatively by formall numbers, and figures, as they are governed, and informed by intelligencies, and divine numerations, which unite the extreams of the matter, and spirit to the will of the elevated soul, receiving through great affection, by the Celestiall power of the operator, a power from God, applyed through the soul of the universe, and observations of Celestiall constellations, to a matter fit for a form, the mediums being disposed by the skill, and industry of Magicians; But let us hasten to explain the tables severally. The first of them is assigned to Saturn, and consists of a square of three, containing the particular numbers of nine, and in every line three every way, and through each Diameter making fifteen. Now the whole sum of numbers is fourty five/ Over this are of Divine names set such names as fill up the numbers with an Intelligency to what is good, with a spirit to what is bad, and out of the same numbers is drawn the seal, or Character of Saturn, and of the spirits thereof, such as we shall beneath ascribe to its table. They say that this table being with a fortunate Saturn engraved on a plate of lead, doth help to bring forth, or birth, and to make a man safe, and powerfull, and to cause success of petitions with princes, and powers: but if it be done with an unfortunate Saturn, that it hinders buildings, plantings, and the like, and casts a man from honours, and dignities, and causes discords, and quarrellings, and disperses an Army. The second is called the table of Jupiter, which consists of a Quaternian drawn into it self [i.e. 4 times 4], containing sixteen particular numbers, and in every line, and Diameter four, making thirty four. Now the Sum of all is 136. And there are over it divine names with an Intelligence to good, with a spirit to bad, and out of it is drawn the Character of Jupiter, and the spirits thereof. They say that if it be impressed upon a Silver plate with Jupiter being powerfull, and ruling, it conduceth to gain, and riches, favor, and love, peace, and concord, and to appease enemies, to confirm honors, dignities, and counsels, and dissolve enchantments if it be engraven on a corall. The third table belongs to Mars, which is made of a square of four containing twenty five numbers, and of these in every side and Diameter five, which make sixty five, and the sum of all is 325. And there are over it Divine names with an Intelligence to good, with a spirit to bad, and out of it is drawn the Character of Mars, and of his spirits. These with Mars being fortunate, being engraven on an Iron plate, or sword, makes a man potent in war, and judgments, and petitions, and terrible to his enemies, and victorious against them; and if engraven upon the Stone Correola, it stops blood, and the mestrues [menses]; but if it be engraven with Mars being unfortunate, on a plate of red Brass, it hinders buildings, casts down the powerfull from dignities, honors, and riches, and causeth discord, strife, and hatred of men, and beasts, chaseth away Bees, Pigeons, and Fish, and hinders Mils, and renders them unfortunate that go forth to hunting, or fighting, and causeth barreness in men and women, and other Animals, and strikes a terror in all enemies, and compels them to submit. The fourth table is of the Sun, and is made of a square of six, and contains thirty six numbers, whereof six in every side, and Diameter, produce 111, and the sum of all is 666. There are over it divine names with an Intelligency to what is good, with spirit to what is evil, and out of it is drawn Characters of the Sun, and the spirits thereof. This being engraven on a Golden plate with the Sun being fortunate, renders him that wears it to be renowned, amiable, acceptable, potent in allhis works, and equals a man to Kings, and Princes, elevating him to high fortunes, inabling to do whatsoever he pleaseth: but with an unfortunate Sun, it makes a tyrant, and a man to be proud, ambitious, unsatisfiable, and to have an ill ending. The fifth table is of Venus, consisting of a square of seven drawn into it self, viz. of fourty nine numbers, whereof seven on each side and Diameter make 175. and the sum of all is 1225. And there are over it divine names with an Intelligency to good, and spirit to evil; And there is drawn out of it the Character of Venus, and the spirits thereof. This being engraven on a Silver plate, Venus being fortunate, procureth concord, endeth strife, procureth the love of women, conduceth to conception, is good against barreness, causeth ability for generation, dissolves enchantments, and causeth peace between man, and woman, and maketh all kind of Animals and Cattle fruitful; and being put into a Dove-house, causeth an increase of Pigeons. It conduceth to the cure of all melancholy distempers, and causeth joyfulness; and being carryed about travellers make them fortunate. But if it be formed upon Brass with an unfortunate Venus, it causeth contrary things to all that hath bin above said. The sixt table is of Mercury resulting from the square of eight drawn into it self, containing sixty four numbers, whereof eight on every side and by both Diameters make 260. and the sum of all 2080. and over it are set divine names with an Intelligency to what is good, with a spirit to what is evil, and from it is drawn a Character of Mercury, and the spirits thereof; and if it be with Mercury being fortunate engraven upon Silver, or Tin, or yellow Brass, or be writ upon Virgin Parchment, it renders the bearer thereof gratefull, and fortunate to do what he pleaseth: it bringeth gain, and prevents poverty, conduceth to memory, understanding, and divination, and to the understanding of occult things by dreams: and if it be an unfortunate Mercury, doth all things contrary to these. The seventh table is of the Moon, of a square of nine multiplied into it self, having eighty one numbers, in every side and Diameter nine, producing 369. and the sum of all 3321. And there are over it divine names with an Intelligency to what is good, and a spirit to what is bad. And of it are drawn the Characters of the Moon, and of the spirits thereof. This fortunate Moon being engraven on Silver, renders the bearer thereof grateful, aimiable [amiable], pleasant, cheerfull, honored, removing all malice, and ill will. It causeth security in a ourney, increase of riches, and health of body, drives away enemies and other evil things from what place thou pleaseth; and if it be an unfortunate Moon engraven in a plate of Lead, where ever it shall be buried, it makes that place unfortunate, and the inhabitants thereabouts, as also Ships, Rivers, Fountains, Mills, and it makes every man unfortunate, against which it shall be directly done, making him fly from his Country, and that place of his abode where it shall be buried, and it hinders Physitians [physicians], and Orators, and all men whatsoever in their office, against whom it shall be made. Now how the seals, and Characters of the Stars, and spirits are drawn from these tables, the wise searcher, and he which shall understand the verifying of these tables, shall easily find out.

Divine names answering to the numbers of Saturn.

3.Ab.áà
9.Hod.ãä
15Iah.äé
15.Hod.ãåä
45Jehovah extended. àä åàå àä ãåé
45Agiel The Intelligence of Saturn ìàéâà
45Zazel The spirit of Saturn ìæàæ


Divine names answering to the numbers of Jupiter.

4Abab àáà
16 äåä
16 éäà
34El Ab áàìà
136Johphiel The Intelligence of Jupiter ìàéôäé
136Hismael The spirit of Jupiter ìàîñä


Names answering to the numbers of Mars.

5He the letter of the Holy Name ä
25 éäé
65Adonay éðãà
325Graphiel The Intelligence of Mars. ìàéôàøâ
325Barzabel The spirit of Mars. ìàáàöøá


Names answering to the numbers of the Sun.

6Vau the letter of the Holy Name. å
6He extended, the letter of the Holy Name. àä
56Eloh äìà
111Nachiel The Intelligence of the Sun. ìàéëð
666Sorath The spirit of the Sun úøåñ


Names answering to the numbers of Venus.

7  àäà
49Hagiel The Intelligence of Venus. ìàéâä
157Kedemel The spirit of Venus. ìàîã÷
1252Bne Seraphim The Intelligencies of Venus. íéôøù éðá


Names answering to the numbers of Mercury.

8Asboga, eight extended. äâáæà
64Din. ïéã
64Doni éðã
260Tiriel. ìàéøéè
2080Taphthartharath úøúøúôú


Names answering to the numbers of the Moon.

9Hod ãä
81Elim íéìà
369Hasmodai the spirit of the Moon. éàãåîùä
3321Schedbarschemoth Scharthathan,the spirit of the spirits of the Moon.
   ïúúøù úòîäùøáãù
3321 Malcha betharsism hed beruah schehalim The Intelligency of the Intelligence of the Moon.
   íé÷äù ãåøá ãò íéñéùøáá àëìî


The Table of Saturn in his compass.


figure 2-27

In Hebrew notes.


figure 2-28


The Seales or Characters.

Of Saturn.


figure 2-29

Of the Intelligence of Saturn.


figure 2-30

Of the Spirit of Saturn.


figure 2-31


The Table of Jupiter in his compass.


figure 2-32

In Hebrew notes.


figure 2-33


The Seales or Characters.

Of Jupiter.


figure 2-34

Of the Intelligence of Jupiter.


figure 2-35

Of the Spirit of Jupiter.


figure 2-36


The Table of Mars in his compass.


figure 2-37

In Hebrew notes.


figure 2-38


The Seales or Characters.

Of Mars.


figure 2-39

Of the Intelligence of Mars.


figure 2-40

Of the Spirit of Mars.


figure 2-41


The Table of the Sun in his compass.


figure 2-42

In Hebrew notes.


figure 2-43


The Seales or Characters.

Of the Sun.


figure 2-44

Of the intelligence of the Sun.


figure 2-45

Of the Spirit of the Sun.


figure 2-46


The Table of Venus in her Compass.


figure 2-47

The Table of Venus in Hebrew notes.


figure 2-48

The Seals, or Characters.

Of Venus.
figure 2-49

Of the Intelligence of Venus.


figure 2-50

Of the Spirit of Venus.


figure 2-51

Of the Intelligences of Venus.


figure 2-52


The Table of Mercury in his compass.

figure 2-53

The Table of Mercury in Hebrew notes.

figure 2-54

The Seals or Characters of Mercury.

figure 2-55

Of the Intelligency Of Mercury.

figure 2-56

Of the Spirit of Mercury.

figure 2-57


The Table of the Moon in her Compass.

figure 2-58

The Table of the Moon in Hebrew notes.

figure 2-59

The Seals or Characters

Of the Moon.

figure 2-60

Of the Spirit of the Moon.

figure 2-61

Of the Spirits of the spirits of the Moon.

figure 2-62

Of the Intelligence of the Intelligences of the Moon.

figure 2-63




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