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of "Marian." BOY CAVALIER. By the _Rev. H. C. Adams_. GILDEROY, THE HERO OF SCOTLAND. FAIRY TALES. By _Madame de Chatelaine_. EMILY CHESTER. LAMB'S TALES. STORIES OF OLD DANIEL. EXTRAORDINARY MEN. EXTRAORDINARY WOMEN. THE YOUNG ARTISTS. LIFE OF NAPOLEON. POPULAR ASTRONOMY. ORBS OF HEAVEN. PILGRIM'S PROGRESS. Routledge's Two-Shilling Juvenile Books. _Illustrated. Bound in Cloth._ s. d. AUSTEN'S TALES. Five vols.,
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with Illustrations, fcap. 8vo, cloth, price 2_s._ each. VILLAGE SKETCHES. By the _Rev. C. T. Whitehead_. THE PLAY-DAY BOOK. By _Fanny Fern_. With Coloured Plates by Kronheim. Fcap. 8vo, cloth. CONQUEST AND SELF-CONQUEST. EVENINGS AT DONALDSON MANOR. By _M'Intosh_. GRACE AND ISABEL. By _M'Intosh_. GERTRUDE AND EULALIE. ROBERT AND HAROLD. AMY CARLTON. ROBINSON CRUSOE. LAURA TEMPLE. OUR NATIVE LAND. HARRY
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AND HIS HOMES. SOLITARY HUNTER. By _Palliser_. BUNDLE OF STICKS; or, Love and Hate. By _J. & E. Kirby_. FAMILY PICTURES FROM THE BIBLE. HESTER AND I; or, Beware of Worldliness. THE CHERRY-STONES. By the _Rev. H. C. Adams_. THE FIRST OF JUNE. By ditto. ROSA. A Story for Girls. MAY DUNDAS; or, The Force of Example. By _Mrs. Geldart_.
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GLIMPSES OF OUR ISLAND HOME. By ditto. THE INDIAN BOY. By the _Rev. H. C. Adams_. ERNIE ELTON AT HOME. By _Mrs. Eiloart_. THE STANDARD POETRY BOOK FOR SCHOOLS. TRY AND TRUST. By the Author of "Arthur Morland." TEN MORAL TALES. By _Guizot_. THE ORPHANS OF WATERLOO. THE BOY'S READER. With Illustrations. THE GIRL'S READER. THE GATES AJAR. With Plates.
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CHARMS AND COUNTER CHARMS. ROBINSON THE YOUNGER. JUVENILE TALES. SWISS FAMILY ROBINSON. EVENINGS AT HOME. SANDFORD AND MERTON. ERNIE ELTON AT SCHOOL. JOHN HARTLEY. THE WONDER BOOK. TANGLEWOOD TALES. ARCHIE BLAKE. INEZ AND EMMELINE. MAUM GUINEA. JACK OF ALL TRADES. By _T. Miller_. ORPHAN OF WATERLOO. By _Mrs. Blackford_. ADVENTURES OF JOSEPH HAWSEPIPE. TODD'S LECTURES TO CHILDREN. 1st and 2nd
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Series. MAROONER'S ISLAND. THE MAYFLOWER. By _Mrs. Stowe_. ANECDOTES OF DOGS. MOSS-SIDE. By _Miss Harland_. MR. RUTHERFORD'S CHILDREN. Complete. Routledge's Eighteenpenny Juveniles. _Square 16mo, with Illustrations by_ GILBERT, ABSOLON, _&c._ s. d. ON THE SEAS. A Book for Boys. PEASANT AND PRINCE. By _Harriet Martineau_. CROFTON BOYS. By ditto. FEATS ON THE FIORD. By ditto. SETTLERS AT HOME. By ditto.
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LITTLE DRUMMER: A Tale of the Russian War. FRANK. By _Maria Edgeworth_. ROSAMOND. By ditto. HARRY AND LUCY, LITTLE DOG TRUSTY, &c. A HERO; or, Philip's Book. By the Author of "John Halifax." CABIN BY THE WAYSIDE. BLACK PRINCESS. LAURA AND ELLEN; or, Time Works Wonders. EMIGRANT'S LOST SON. By _G. H. Hall_. THE RUNAWAYS AND THE GIPSIES. BRITISH WOLF
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HUNTERS. By _Thomas Miller_. THE BOW OF FAITH; or, Old Testament Lessons. ANCHOR OF HOPE; or, New Testament Lessons. By ditto. ACCIDENTS OF CHILDHOOD; or, Stories of Heedless Children. ANNIE MAITLAND; or, The Lesson of Life. By _D. Richmond_. LUCY ELTON; or, Home and School. THE YOUNG NATURALIST. By _Mrs. Loudon_. MEMOIRS OF A DOLL. ROSE AND KATE. STORY OF
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AN APPLE. HOLIDAY RAMBLES. DAILY THOUGHTS FOR CHILDREN. By _Mrs. Geldart_. EMILIE THE PEACEMAKER. By ditto. TRUTH IS EVERYTHING. By ditto. CHRISTMAS HOLIDAYS. By _Miss Jane Strickland_. AUNT EMMA. By the Author of "Rose and Kate." THE ISLAND OF THE RAINBOW. By _Mrs. Newton Crossland_. MAX FRERE; Or, Return Good for Evil. RAINBOWS IN SPRINGTIDE. THE CHILD'S FIRST BOOK OF
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NATURAL HISTORY. FLORENCE THE ORPHAN. THE CASTLE AND THE COTTAGE. By _Mrs. Perring_. FABULOUS HISTORIES. By _Mrs. Trimmer_. SCHOOL DAYS AT HARROW. MRS. BARBAULD'S LESSONS. HOLIDAYS AT LIMEWOOD. TRADITIONS OF PALESTINE. By _Mrs. Martineau_. Routledge's One-Shilling Juveniles. _Well printed, with Illustrations, 18mo, cloth._ s. d. THE SUNDAY BOOK. In Words of One Syllable. Illust. OUR POOR NEIGHBOURS. By _Mrs. Perring_.
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VILLAGE SKETCHES. By the _Rev. C. T. Whitehead_, 1st and 2nd Series, 1_s._ each. GRACE GREENWOOD'S STORIES. HELEN'S FAULT. By the Author of "Adelaide Lindsay." THE COUSINS. By _Miss M'Intosh_. BEN HOWARD; or, Truth and Honesty. By _C. Adams_. BESSIE AND TOM. A Book for Boys and Girls. BEECHNUT. A Franconian Story. By _Jacob Abbott_. WALLACE. A Franconian Story. By
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ditto. MADELINE. By ditto. MARY ERSKINE. By ditto. MARY BELL. By ditto. VISIT TO MY BIRTHPLACE. By _Miss Bunbury_. CARL KRINKEN; or, The Christmas Stocking. MR. RUTHERFORD'S CHILDREN. By ditto. MR. RUTHERFORD'S CHILDREN. 2nd Series. By ditto. EMILY HERBERT. By _Miss M'Intosh_. ROSE AND LILLIE STANHOPE. By ditto. CASPAR. By ditto. THE BRAVE BOY; or, Christian Heroism. MAGDALENE AND RAPHAEL.
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PLEASANT TALES. By _Mrs. Sedgwick_. UNCLE FRANK'S HOME STORIES. THE GATES AJAR. THE STORY OF A MOUSE. By _Mrs. Perring_. OUR CHARLIE. By _Mrs. Stowe_. VILLAGE SCHOOL FEAST. By _Mrs. Perring_. NELLY THE GIPSY GIRL. THE BIRTHDAY VISIT. By _Miss Wetherell_. STORIES FOR WEEK DAYS AND SUNDAYS. MAGGIE AND EMMA. By _Miss M'Intosh_. CHARLEY AND GEORGY; or, The Children at
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Gibraltar. THE STORY OF A PENNY. By _Mrs. Perring_. AUNT MADDY'S DIAMONDS. By _Harriet Myrtle_. TWO SCHOOL GIRLS. By _Miss Wetherell_. THE WIDOW AND HER DAUGHTER. By ditto. GERTRUDE AND HER BIBLE. By ditto. ROSE IN THE DESERT. By ditto. THE LITTLE BLACK HEN. By ditto. MARTHA AND RACHEL. By ditto. THE CARPENTER'S DAUGHTER. By ditto. THE PRINCE IN DISGUISE.
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By ditto. THE STORY OF A CAT. By _Mrs. Perring_. EASY POETRY FOR CHILDREN. With Coloured Plates. THE BASKET OF FLOWERS. With ditto. ASHGROVE FARM. By _Mrs. Myrtle_. THE STORY OF A DOG. By _Mrs. Perring_. THE ANGEL OF THE ICEBERG. By the _Rev. John Todd_. RILLS FROM THE FOUNTAIN. A Lesson for the Young. TODD'S LECTURES TO CHILDREN. (First
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Series.) TODD'S LECTURES TO CHILDREN. (Second Series.) LITTLE POEMS FOR LITTLE READERS. MINNIE'S LEGACY. NEIGHBOURLY LOVE. KITTY'S VICTORY. ELISE AND HER RABBITS. HAPPY CHARLIE. ANNIE PRICE. THE LITTLE OXLEYS. By _Mrs. W. Denzey Burton_. BOOK OF ONE SYLLABLE. With Coloured Plates. LITTLE HELPS. With Coloured Plates. UNCLE TOM'S CABIN, for Children. AUNT MARGARET'S VISIT. KEEPER'S TRAVELS IN SEARCH OF HIS
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MASTER. RICHMOND'S ANNALS OF THE POOR. CHILD'S ILLUSTRATED POETRY BOOK. THE NEW BOOK OF ONE SYLLABLE. BLANCHE AND AGNES. THE LOST CHAMOIS-HUNTER. Routledge's New Series of Shilling Toy Books. _With Large Illustrations by_ H. S. MARKS, J. D. WATSON, H. WEIR, _and_ KEYL, _Printed in Colours by Kronheim and Others. Demy 4to, stiff wrapper; or mounted on Linen, 2s._ s.
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d. ALPHABET OF TRADES. CINDERELLA.* ALPHABET OF PRETTY NAMES. OLD TESTAMENT ALPHABET. THREE LITTLE KITTENS. THE HISTORY OF FIVE LITTLE PIGS.* TOM THUMB'S ALPHABET. NEW TESTAMENT ALPHABET. THE CATS' TEA PARTY.* OUR FARM-YARD ALPHABET. THE HISTORY OF MOSES. THE HISTORY OF JOSEPH. THE ALPHABET OF FLOWERS. NURSERY RHYMES, 2nd Series. NURSERY GAMES. THE HOUSE THAT JACK BUILT. THE LIFE OF
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OUR LORD. THE THREE BEARS. RED RIDING-HOOD. NEW TALE OF A TUB.* NURSERY TALES. OLD MOTHER HUBBARD. PICTURES FROM ENGLISH HISTORY, 1st Period. PICTURES FROM ENGLISH HISTORY, 2nd Period. PICTURES FROM ENGLISH HISTORY, 3rd Period. PICTURES FROM ENGLISH HISTORY, 4th Period. PUSS IN BOOTS. TOM THUMB. BABES IN THE WOOD. JACK AND THE BEAN-STALK. THE LAUGHABLE A B C. WILD
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ANIMALS, 1st Series.* WILD ANIMALS, 2nd Series.* WILD ANIMALS, 3rd Series.* WILD ANIMALS, 4th Series.* TAME ANIMALS, 1st Series.* TAME ANIMALS, 2nd Series.* TAME ANIMALS, 3rd Series.* TAME ANIMALS, 4th Series.* MY MOTHER. THE DOGS' DINNER PARTY. LITTLE DOG TRUSTY. THE WHITE CAT. THE UGLY DUCKLING. LITTLE SNOW-WHITE. DASH AND THE DUCKLINGS. * _Those marked with an asterisk are_ NOT
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_kept on linen._ Aunt Mavor's Toy Books. _Large Coloured Sixpenny Books for Children, with greatly improved Illustrations, super-royal 8vo, in wrappers._ s. d. HISTORY OF OUR PETS. HISTORY OF BLUE BEARD. SINDBAD THE SAILOR. A, APPLE PIE. TOM THUMB'S ALPHABET. BARON MUNCHAUSEN. PICTURE ALPHABET. ARTHUR'S ALPHABET. DOROTHY FRUMP AND HER SIX DOGS. SINGING BIRDS. PARROTS & TALKING BIRDS. DOGS. NURSERY
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RHYMES. BIRDS. RAILROAD ALPHABET. ALPHABET FOR GOOD BOYS AND GIRLS. THE SEA-SIDE ALPHABET. FARM-YARD ALPHABET. GREEDY JEM AND HIS LITTLE BROTHERS.* OUR PUSS AND HER KITTENS.* HOP O' MY THUMB. JACK THE GIANT KILLER. LITTLE RED RIDING-HOOD. BEAUTY AND THE BEAST. HAPPY DAYS OF CHILDHOOD.* LITTLE DOG TRUSTY. THE CATS' TEA PARTY. THE BABES IN THE WOOD. WILD ANIMALS. BRITISH
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ANIMALS. THE FROG WHO WOULD A-WOOING GO.* THE FAITHLESS PARROT.* THE FARM-YARD.* HORSES. OLD DAME TROT. MULTIPLICATION TABLE. CHATTERING JACK. KING COLE. PRINCE LONG NOSE. THE ENRAGED MILLER. THE HUNCHBACK. HOW JESSIE WAS LOST. GRAMMAR IN RHYME. BABY'S BIRTHDAY.* PICTURES FROM THE STREETS.* LOST ON THE SEA-SHORE.* ANIMALS AND BIRDS.* A CHILD'S FANCY DRESS BALL. A CHILD'S EVENING PARTY. ANNIE
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AND JACK IN LONDON. ONE, TWO, BUCKLE MY SHOE. MARY'S NEW DOLL.* WHEN THE CAT'S AWAY.* NAUGHTY PUPPY.* CHILDREN'S FAVOURITES.* NAUGHTY BOYS AND GIRLS. LITTLE MINXES. STRUWELPETER. LITTLE MINNIE'S CHILD LIFE. KING NUTCRACKER. LAZY BONES. BRITISH SOLDIERS. BRITISH SAILORS. BRITISH VOLUNTEERS. LAUGHTER BOOK FOR CHILDREN. GRISLY BEARD. RUMPELSTILTSKIN. DOG PUFFY. THE FAIRY SHIP. _The above, except those marked with an
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asterisk, may be had strongly mounted on cloth, price One Shilling each._ Routledge's New Threepenny Toy Books. _With Coloured Pictures._ s. d. CINDERELLA. RED RIDING-HOOD. JACK AND THE BEANSTALK. PUSS IN BOOTS. Routledge's Sixpenny Juveniles. _Royal 32mo, with Illustrations, gilt edges._ s. d. HISTORY OF MY PETS. HUBERT LEE. ELLEN LESLIE. JESSIE GRAHAM. FLORENCE ARNOTT. BLIND ALICE. GRACE AND CLARA.
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RECOLLECTIONS OF MY CHILDHOOD. EGERTON ROSCOE. FLORA MORTIMER. CHARLES HAMILTON. STORY OF A DROP OF WATER. LEARNING BETTER THAN HOUSES AND LAND. MAUD'S FIRST VISIT TO HER AUNT. In Words of One Syllable. EASY POEMS. THE BOY CAPTIVE. By _Peter Parley_. STORIES OF CHILD LIFE. DAIRYMAN'S DAUGHTER. ARTHUR'S TALES FOR THE YOUNG. HAWTHORNE'S GENTLE BOY. PLEASANT AND PROFITABLE. THE FALSE
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KEY. THE BRACELETS. WASTE NOT, WANT NOT. TARLETON, and FORGIVE AND FORGET. LAZY LAWRENCE AND THE WHITE PIGEON. THE BARRING OUT. THE ORPHANS AND OLD POZ. THE MIMIC. THE PURPLE JAR, and other Tales. PARLEY'S POETRY & PROSE. ARTHUR'S STORIES FOR LITTLE GIRLS. THE YOUNG COTTAGER. PARLEY'S THOS. TITMOUSE. ARTHUR'S CHRISTMAS STORY. THE LOST LAMB. ARTHUR'S STORIES FOR LITTLE BOYS.
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ARTHUR'S ORGAN BOY. MARGARET JONES. THE TWO SCHOOL GIRLS. THE WIDOW AND HER DAUGHTER. THE ROSE IN THE DESERT. THE BIRTHDAY PRESENT and THE BASKET WOMAN. SIMPLE SUSAN. THE LITTLE MERCHANTS. TALE OF THE UNIVERSE. ROBERT DAWSON. KATE CAMPBELL. BASKET OF FLOWERS. BABES IN THE BASKET. THE JEWISH TWINS. CHILDREN ON THE PLAINS. LITTLE HENRY AND HIS BEARER. THE LITTLE
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BLACK HEN. MARTHA AND RACHEL. CARPENTER'S DAUGHTER. THE PRINCE IN DISGUISE. GERTRUDE AND HER BIBLE. THE CONTRAST. _Miss Edgeworth._ THE GRATEFUL NEGRO. _Do._ JANE HUDSON. A KISS FOR A BLOW. YOUNG NEGRO SERVANT. LINA AND HER COUSINS. ARTHUR'S LAST PENNY. BRIGHT-EYED BESSIE. THE GATES AJAR. Routledge's Fourpenny Juveniles. _Royal 32mo, fancy covers._ s. d. THE BASKET OF FLOWERS. THE BABES
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IN THE BASKET. EASY POEMS FOR CHILDREN. JESSIE GRAHAM. HISTORY OF MY PETS. FLORENCE ARNOTT. ROBERT DAWSON. RECOLLECTIONS OF MY CHILDHOOD. BROOKE AND BROOKE FARM. LIFE IN THE WILDS. HILL AND THE VALLEY. THE WIDOW AND HER DAUGHTER. THE TWO SCHOOL GIRLS. THE JANE HUDSON. A KISS FOR A BLOW. HUBERT LEE. FLORA MORTIMER. A DROP OF WATER. THE FALSE
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KEY. THE BRACELETS. THE PURPLE JAR. SIMPLE SUSAN. KATE CAMPBELL. LITTLE HENRY AND HIS BEARER. THE GATES AJAR. Routledge's Five-Shilling Poets. _Edited by Rev._ R. A. WILLMOTT. _Illustrated by_ FOSTER, GILBERT, CORBOULD, FRANKLIN, _and_ HARVEY. _Elegantly printed on good paper, post 8vo, gilt edges, bevelled boards._ s. d. SPENSER'S FAERIE QUEENE. Illustrated by Corbould. CHAUCER'S CANTERBURY TALES. Illustrated by ditto.
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KIRKE WHITE. By _Southey_. Illustrated by Birket Foster. SOUTHEY'S JOAN OF ARC, AND MINOR POEMS. Illustrated by Gilbert. POPE'S POETICAL WORKS. Edited by Carey. MILTON'S POETICAL WORKS. Illustrated by Harvey. THOMSON, BEATTIE, AND WEST. Illust. by Birket Foster. HERBERT. With Life and Notes by _Rev. R. A. Willmott_. COWPER. Illust. by Birket Foster. Edited by _Willmott_. LONGFELLOW'S COMPLETE POETICAL WORKS.
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Illustrated. LONGFELLOW'S PROSE WORKS. BURNS' POETICAL WORKS. Illustrated by John Gilbert. FAIRFAX'S TASSO'S JERUSALEM DELIVERED. Illustrated by Corbould. PERCY'S RELIQUES OF ANCIENT POETRY. Illust. by ditto. SCOTT'S POETICAL WORKS. Illustrated by ditto. MACKAY'S BALLADS AND LYRICS. Illust. by John Gilbert. WORDSWORTH. Illustrated by Birket Foster. CRABBE. Illustrated by ditto. MACKAY'S SONGS. Complete Edition. Illust. by Gilbert. ELIZA COOK'S POEMS. With
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Illustrations and Portrait. MOORE'S POEMS. Illustrated by Corbould, &c. BYRON'S POEMS. Illustrated by Gilbert, Wolf, Foster. BENNETT'S POETICAL WORKS. Portrait and Illustrations. CAMPBELL'S POETICAL WORKS. Illustrated by W. Harvey. LOVER'S POETICAL WORKS. Portrait and Illustrations. ROGERS' POETICAL WORKS. With Portrait, &c. LORD LYTTON'S POETICAL WORKS. 7_s._ 6_d._ LORD LYTTON'S DRAMATIC WORKS. 6_s._ DRYDEN'S POETICAL WORKS. With Portrait, &c. Routledge's Three-and-Sixpenny
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Poets, &c. _Printed on tinted paper, fcap. 8vo, gilt edges. With Illustrations._ s. d. LONGFELLOW'S COMPLETE POETICAL WORKS. Illust. COWPER. Illust. by Birket Foster. Edited by _Willmott_. MILTON'S POETICAL WORKS. Illustrated by Harvey. WORDSWORTH'S POETICAL WORKS. Illust. by B. Foster. SOUTHEY'S JOAN OF ARC, AND MINOR POEMS. Illust. by Gilbert. GOLDSMITH, JOHNSON, SHENSTONE, AND SMOLLETT. Do. KIRKE WHITE. By _Southey_.
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Illustrated by Birket Foster. BURNS. Illustrated by Gilbert. THOMAS MOORE'S POEMS. Illustrated by Corbould. BYRON'S POEMS. Illustrated by Gilbert, Wolf, &c. POPE'S POETICAL WORKS. Illustrated by Gilbert. SCOTT'S POETICAL WORKS. With Illustrations. HERBERT'S WORKS. With Illustrations. THOMAS CAMPBELL'S POETICAL WORKS. Illust. by Gilbert. SHAKESPEARE'S COMPLETE WORKS. CHAUCER'S POETICAL WORKS. WILLIS'S POETICAL WORKS. GOLDEN GLEANINGS. CHOICE POEMS AND LYRICS. SHAKESPEARE GEMS.
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BOOK OF WIT AND HUMOUR. WISE SAYINGS OF THE GREAT AND GOOD. MONTGOMERY'S POEMS. Routledge's Two-and-Sixpenny Poets. _Fcap. 8vo, with Illustrations, in cloth._ s. d. LONGFELLOW'S COMPLETE POETICAL WORKS. SCOTT'S POEMS. BYRON'S POEMS. COWPER'S POEMS. WORDSWORTH'S POEMS. BURNS' POEMS. MOORE'S POEMS. MILTON'S POEMS. POPE'S POEMS. _Or bound in a new style, vols., cloth, ._ Routledge's Pocket Poets. _18mo, with Portrait._
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s. d. LONGFELLOW'S COMPLETE POETICAL WORKS. Paper, 1_s._; cloth, 1_s._ 6_d._ BURNS' COMPLETE POETICAL WORKS. Paper, 1_s._; cloth, 1_s._ 6_d._ SCOTT'S POETICAL WORKS. Cloth, 1_s._ London: THE BROADWAY, LUDGATE HILL. New York: , BROOME STREET. J. OGDEN AND CO., PRINTERS, , ST. JOHN STREET E C.
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[Transcribers Note: This e-text includes characters that will only display in UTF- (Unicode) text readers, including a few words of Greek: [Taktik] [overline or tilde to show following -n or -m] [leaf symbol; pointing-finger symbol] [double-ended dagger, used in size notations (below)] If any of these characters do not display properly-- in particular, if the diacritic does not appear directly
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above the letter-- or if the quotation marks in this paragraph appear as garbage, make sure your text readers character set or file encoding is set to Unicode (UTF-). You may also need to change the default font. As a last resort, use the ASCII version of this file instead. Some aspects of the original book had to be modified
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for all versions of this plain-text file. Superscript letters are shown with ^: y^e, y^t. Marginal quotation marks are shown inline as and , approximating the beginning and end of the marked passage. In the original text, no quotation marks were printed inline. Paragraphs are broken up for sidenotes, with blank lines before and after. Original paragraph breaks are shown
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as two blank lines. Brackets within the body text are in the original. All sidenotes except the one beginning This noble Earle were printed in italics; markup has been omitted to reduce visual clutter. At least four sizes of text were used, often in combination with _italics_. The variants are shown here as: +very large+ +larger+ =smaller= Further errors and
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anomalies are listed at the end of the text, along with those Euclid citations identified by number.] * * * * * * * * * * * * * * THE ELEMENTS OF GEOMETRIE of the most auncient Philosopher _EVCLIDE_ of Megara. _Faithfully (now first) translated into the Englishe toung, by _H. Billingsley_, Citizen of London_. _Whereunto are annexed
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certaine Scholies, Annotations, and Inuentions, of the best Mathematiciens, both of time past, and in this our age._ _With a very fruitfull Prface made by _M. I. Dee_, specifying the chiefe Mathematicall Scices, what they are, and wherunto commodious: where, also, are disclosed certaine new Secrets Mathematicall and Mechanicall, vntill these our daies, greatly missed._ Imprinted at London by _Iohn
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Daye_. The Translator to the Reader. _There is (gentle Reader) nothing (the word of God onely set apart) which so much beautifieth and adorneth the soule and minde of m, as doth the knowledge of good artes and sciences: as the knowledge of naturall and morall Philosophie. The one setteth before our eyes, the creatures of God, both in the
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heauens aboue, and in the earth beneath: in which as in a glasse, we beholde the exceding maiestie and wisedome of God, in adorning and beautifying them as we see: in geuing vnto them such wonderfull and manifolde proprieties, and naturall workinges, and that so diuersly and in such varietie: farther in maintaining and conseruing them continually, whereby to praise
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and adore him, as by S. Paule we are taught. The other teacheth vs rules and preceptes of vertue, how, in common life amongest men, we ought to walke vprightly: what dueties pertaine to our selues, what pertaine to the gouernment or good order both of an housholde, and also of a citie or common wealth. The reading likewise of
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histories, conduceth not a litle, to the adorning of the soule & minde of man, a studie of all men cmended: by it are seene and knowen the artes and doinges of infinite wise men gone before vs. In histories are contained infinite examples of heroicall vertues to be of vs followed, and horrible examples of vices to be of
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vs eschewed. Many other artes also there are which beautifie the minde of man: but of all other none do more garnishe & beautifie it, then those artes which are called Mathematicall. Unto the knowledge of which no man can attaine, without the perfecte knowledge and instruction of the principles, groundes, and Elementes of Geometrie. But perfectly to be instructed
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in them, requireth diligent studie and reading of olde auncient authors. Amongest which, none for a beginner is to be preferred before the most auncient Philosopher _Euclide_ of _Megara_. For of all others he hath in a true methode and iuste order, gathered together whatsoeuer any before him had of these Elementes written: inuenting also and adding many thinges of
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his owne: wherby he hath in due forme accomplished the arte: first geuing definitions, principles, & groundes, wherof he deduceth his Propositions or conclusions, in such wonderfull wise, that that which goeth before, is of necessitie required to the proufe of that which followeth. So that without the diligent studie of _Euclides_ Elementes, it is impossible to attaine vnto the
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perfecte knowledge of Geometrie, and consequently of any of the other Mathematicall sciences. Wherefore considering the want & lacke of such good authors hitherto in our Englishe tounge, lamenting also the negligence, and lacke of zeale to their countrey in those of our nation, to whom God hath geuen both knowledge, & also abilitie to translate into our tounge, and
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to publishe abroad such good authors, and bookes (the chiefe instrumentes of all learninges): seing moreouer that many good wittes both of gentlemen and of others of all degrees, much desirous and studious of these artes, and seeking for them as much as they can, sparing no paines, and yet frustrate of their intent, by no meanes attaining to that
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which they seeke: I haue for their sakes, with some charge & great trauaile, faithfully translated into our vulgare toge, & set abroad in Print, this booke of _Euclide_. Whereunto I haue added easie and plaine declarations and examples by figures, of the definitions. In which booke also ye shall in due place finde manifolde additions, Scholies, Annotations, and Inuentions:
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which I haue gathered out of many of the most famous & chiefe Mathematicis, both of old time, and in our age: as by diligent reading it in course, ye shall well perceaue. The fruite and gaine which I require for these my paines and trauaile, shall be nothing els, but onely that thou gentle reader, will gratefully accept the
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same: and that thou mayest thereby receaue some profite: and moreouer to excite and stirre vp others learned, to do the like, & to take paines in that behalfe. By meanes wherof, our Englishe tounge shall no lesse be enriched with good Authors, then are other straunge tounges: as the Dutch, French, Italian, and Spanishe: in which are red all
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good authors in a maner, found amongest the Grekes or Latines. Which is the chiefest cause, that amongest th do florishe so many cunning and skilfull men, in the inuentions of straunge and wonderfull thinges, as in these our daies we see there do. Which fruite and gaine if I attaine vnto, it shall encourage me hereafter, in such like
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sort to translate, and set abroad some other good authors, both pertaining to religion (as partly I haue already done) and also pertaining to the Mathematicall Artes. Thus gentle reader farewell._ (?) [Decoration] TO THE VNFAINED LOVERS of truthe, and constant Studentes of Noble _Sciences, _IOHN DEE_ of London, hartily_ wisheth grace from heauen, and most prosperous _successe in all
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their honest attemptes and_ exercises. Diuine _Plato_, the great Master of many worthy Philosophers, and the constant auoucher, and pithy perswader of _Vnum_, _Bonum_, and _Ens_: in his Schole and Academie, sundry times (besides his ordinary Scholers) was visited of a certaine kinde of men, allured by the noble fame of _Plato_, and the great commendation of hys profound and
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profitable doctrine. But when such Hearers, after long harkening to him, perceaued, that the drift of his discourses issued out, to conclude, this _Vnum_, _Bonum_, and _Ens_, to be Spirituall, Infinite, ternall, Omnipotent, &c. Nothyng beyng alledged or expressed, How, worldly goods: how, worldly dignitie: how, health, Strgth or lustines of body: nor yet the meanes, how a merueilous sensible
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and bodyly blysse and felicitie hereafter, might be atteyned: Straightway, the fantasies of those hearers, were dampt: their opinion of _Plato_, was clene chaunged: yea his doctrine was by them despised: and his schole, no more of them visited. Which thing, his Scholer, _Aristotle_, narrowly csidering, founde the cause therof, to be, For that they had no forwarnyng and information,
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in generall, whereto his doctrine tended. For, so, might they haue had occasion, either to haue forborne his schole hauntyng: (if they, then, had misliked his Scope and purpose) or constantly to haue continued therin: to their full satisfaction: if such his finall scope & intent, had ben to their desire. Wherfore, _Aristotle_, euer, after that, vsed in brief, to
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forewarne his owne Scholers and hearers, both of what matter, and also to what ende, he tooke in hand to speake, or teach. While I consider the diuerse trades of these two excellent Philosophers (and am most sure, both, that _Plato_ right well, otherwise could teach: and that _Aristotle_ mought boldely, with his hearers, haue dealt in like sorte as
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_Plato_ did) I am in no little pang of perplexitie: Bycause, that, which I mislike, is most easy for me to performe (and to haue _Plato_ for my exple.) And that, which I know to be most commendable: and (in this first bringyng, into common handling, the _Artes Mathematicall_) to be most necessary: is full of great difficultie and sundry
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daungers. Yet, neither do I think it mete, for so straunge matter (as now is ment to be published) and to so straunge an audience, to be bluntly, at first, put forth, without a peculiar Preface: Nor (Imitatyng _Aristotle_) well can I hope, that accordyng to the amplenes and dignitie of the _State Mathematicall_, I am able, either playnly to
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prescribe the materiall boundes: or precisely to expresse the chief purposes, and most wonderfull applications therof. And though I am sure, that such as did shrinke from _Plato_ his schole, after they had perceiued his finall conclusion, would in these thinges haue ben his most diligent hearers (so infinitely mought their desires, in fine and at length, by our _Artes
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Mathematicall_ be satisfied) yet, by this my Prface & forewarnyng, Aswell all such, may (to their great behofe) the soner, hither be allured: as also the _Pythagoricall_, and _Platonicall_ perfect scholer, and the constant profound Philosopher, with more ease and spede, may (like the Bee,) gather, hereby, both wax and hony. [The intent of this Preface.] Wherfore, seyng I finde
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great occasion (for the causes alleged, and farder, in respect of my _Art Mathematike generall_) to vse a certaine forewarnyng and Prface, whose content shalbe, that mighty, most plesaunt, and frutefull _Mathematicall Tree_, with his chief armes and second (grifted) braunches: Both, what euery one is, and also, what commodity, in generall, is to be looked for, aswell of griff
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as stocke: And forasmuch as this enterprise is so great, that, to this our tyme, it neuer was (to my knowledge) by any achieued: And also it is most hard, in these our drery dayes, to such rare and straunge Artes, to wyn due and common credit: Neuertheles, if, for my sincere endeuour to satisfie your honest expectation, you will
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but lend me your thkefull mynde a while: and, to such matter as, for this time, my penne (with spede) is hable to deliuer, apply your eye or eare attentifely: perchaunce, at once, and for the first salutyng, this Preface you will finde a lesson long enough. And either you will, for a second (by this) be made much the
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apter: or shortly become, well hable your selues, of the lyons claw, to coniecture his royall symmetrie, and farder propertie. Now then, gentle, my frendes, and countrey men, Turne your eyes, and bend your myndes to that doctrine, which for our present purpose, my simple talent is hable to yeld you. All thinges which are, & haue beyng, are found
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vnder a triple diuersitie generall. For, either, they are demed Supernaturall, Naturall, or, of a third being. Thinges Supernaturall, are immateriall, simple, indiuisible, incorruptible, & vnchangeable. Things Naturall, are materiall, compounded, diuisible, corruptible, and chaungeable. Thinges Supernaturall, are, of the minde onely, comprehended: Things Naturall, of the sense exterior, ar hable to be perceiued. In thinges Naturall, probabilitie and coniecture
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hath place: But in things Supernaturall, chief demstration, & most sure Science is to be had. By which properties & comparasons of these two, more easily may be described, the state, condition, nature and property of those thinges, which, we before termed of a third being: which, by a peculier name also, are called _Thynges Mathematicall_. For, these, beyng (in
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a maner) middle, betwene thinges supernaturall and naturall: are not so absolute and excellent, as thinges supernatural: Nor yet so base and grosse, as things naturall: But are thinges immateriall: and neuerthelesse, by materiall things hable somewhat to be signified. And though their particular Images, by Art, are aggregable and diuisible: yet the generall _Formes_, notwithstandyng, are constant, vnchaungeable, vntrsformable,
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and incorruptible. Neither of the sense, can they, at any tyme, be perceiued or iudged. Nor yet, for all that, in the royall mynde of man, first conceiued. But, surmountyng the imperfecti of coniecture, weenyng and opinion: and commyng short of high intellectuall ccepti, are the Mercurial fruite of _Dianticall_ discourse, in perfect imagination subsistyng. A meruaylous newtralitie haue these
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thinges _Mathematicall_, and also a straunge participati betwene thinges supernaturall, immortall, intellectual, simple and indiuisible: and thynges naturall, mortall, sensible, compounded and diuisible. Probabilitie and sensible prose, may well serue in thinges naturall: and is commendable: In Mathematicall reasoninges, a probable Argument, is nothyng regarded: nor yet the testimony of sense, any whit credited: But onely a perfect demonstration, of
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truthes certaine, necessary, and inuincible: vniuersally and necessaryly concluded: is allowed as sufficient for an Argument exactly and purely Mathematical. [Note the worde, Vnit, to expresse the Greke Monas, & not Vnitie: as we haue all, commonly, till now, vsed.] Of _Mathematicall_ thinges, are two principall kindes: namely, _Number_, and _Magnitude_. [Number.] _Number_, we define, to be, a certayne Mathematicall
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Sme, of _Vnits_. And, an _Vnit_, is that thing Mathematicall, Indiuisible, by participation of some likenes of whose property, any thing, which is in deede, or is counted One, may resonably be called One. We account an _Vnit_, a thing _Mathematicall_, though it be no Number, and also indiuisible: because, of it, materially, Number doth consist: which, principally, is a
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thing _Mathematicall_. [Magnitude.] _Magnitude_ is a thing _Mathematicall_, by participation of some likenes of whose nature, any thing is iudged long, broade, or thicke. A thicke _Magnitude_ we call a _Solide_, or a _Body_. What _Magnitude_ so euer, is Solide or Thicke, is also broade, & long. A broade magnitude, we call a _Superficies_ or a Plaine. Euery playne magnitude,
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hath also length. A long magnitude, we terme a _Line_. A _Line_ is neither thicke nor broade, but onely long: Euery certayne Line, hath two endes: [A point.] The endes of a line, are _Pointes_ called. A _Point_, is a thing _Mathematicall_, indiuisible, which may haue a certayne determined situation. If a Poynt moue from a determined situation, the way
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wherein it moued, is also a _Line_: mathematically produced, whereupon, of the auncient Mathematiciens, [A Line.] a _Line_ is called the race or course of a _Point_. A Poynt we define, by the name of a thing Mathematicall: though it be no Magnitude, and indiuisible: because it is the propre ende, and bound of a Line: which is a true
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_Magnitude_. [Magnitude.] And _Magnitude_ we may define to be that thing _Mathematicall_, which is diuisible for euer, in partes diuisible, long, broade or thicke. Therefore though a Poynt be no _Magnitude_, yet _Terminatiuely_, we recken it a thing _Mathematicall_ (as I sayd) by reason it is properly the end, and bound of a line. Neither _Number_, nor _Magnitude_, haue any
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Materialitie. First, we will consider of _Number_, and of the Science _Mathematicall_, to it appropriate, called _Arithmetike_: and afterward of _Magnitude_, and his Science, called _Geometrie_. But that name contenteth me not: whereof a word or two hereafter shall be sayd. How Immateriall and free from all matter, _Number_ is, who doth not perceaue? yea, who doth not wonderfully wder
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at it? For, neither pure _Element_, nor _Aristoteles, Quinta Essentia_, is hable to serue for Number, as his propre matter. Nor yet the puritie and simplenes of Substance Spirituall or Angelicall, will be found propre enough thereto. And therefore the great & godly Philosopher _Anitius Boetius_, sayd: _Omnia qucun[que] a primua rerum natura constructa sunt, Numerorum videntur ratione formata. Hoc
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enim fuit principale in animo Conditoris Exemplar_. That is: +_All thinges (which from the very first originall being of thinges, haue bene framed and made) do appeare to be Formed by the reason of Numbers. For this was the principall example or patterne in the minde of the Creator_.+ O comfortable allurement, O rauishing perswasion, to deale with a Science,
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whose Subiect, is so Auncient, so pure, so excellent, so surmounting all creatures, so vsed of the Almighty and incomprehensible wisdome of the Creator, in the distinct creation of all creatures: in all their distinct partes, properties, natures, and vertues, by order, and most absolute number, brought, from _Nothing_, to the _Formalitie_ of their being and state. By _Numbers_ propertie
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therefore, of vs, by all possible meanes, (to the perfection of the Science) learned, we may both winde and draw our selues into the inward and deepe search and vew, of all creatures distinct vertues, natures, properties, and _Formes_: And also, farder, arise, clime, ascend, and mount vp (with Speculatiue winges) in spirit, to behold in the Glas of Creation,
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the _Forme of Formes_, the _Exemplar Number_ of all thinges _Numerable_: both visible and inuisible, mortall and immortall, Corporall and Spirituall. Part of this profound and diuine Science, had _Ioachim_ the Prophesier atteyned vnto: by _Numbers Formall, Naturall_, and _Rationall_, forseyng, concludyng, and forshewyng great particular euents, long before their comming. His bookes yet remainyng, hereof, are good profe: And
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the noble Earle of _Mirandula_, (besides that,) a sufficient witnesse: that _Ioachim, in his prophesies, proceded by no other way, then by Numbers Formall_. And this Earle hym selfe, in Rome, [Ano. .] * set vp . Conclusions, in all kinde of Sciences, openly to be disputed of: and among the rest, in his Conclusions _Mathematicall_, (in the eleuenth Conclusion)
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hath in Latin, this English sentence. _By Numbers, a way is had, to the searchyng out, and vnderstandyng of euery thyng, hable to be knowen. For the verifying of which Conclusion, I promise to aunswere to the . Questions, vnder written, by the way of Numbers_. Which Cclusions, I omit here to rehearse: aswell auoidyng superfluous prolixitie: as, bycause _Ioannes
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Picus, workes_, are commonly had. But, in any case, I would wish that those Conclusions were red diligently, and perceiued of such, as are earnest Obseruers and Considerers of the constant law of nbers: which is planted in thyngs Naturall and Supernaturall: and is prescribed to all Creatures, inuiolably to be kept. For, so, besides many other thinges, in those
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Conclusions to be marked, it would apeare, how sincerely, & within my boundes, I disclose the wonderfull mysteries, by numbers, to be atteyned vnto. Of my former wordes, easy it is to be gathered, that _Number_ hath a treble state: One, in the Creator: an other in euery Creature (in respect of his complete constitution:) and the third, in Spirituall
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and Angelicall Myndes, and in the Soule of m. In the first and third state, _Number_, is termed _Number Numbryng_. But in all Creatures, otherwise, _Number_, is termed _Nber Numbred_. And in our Soule, Nber beareth such a swaye, and hath such an affinitie therwith: that some of the old _Philosophers_ taught, _Mans Soule, to be a Number mouyng it
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selfe_. And in dede, in vs, though it be a very Accident: yet such an Accident it is, that before all Creatures it had perfect beyng, in the Creator, Sempiternally. _Number Numbryng_ therfore, is the discretion discerning, and distincting of thinges. But in God the Creator, This discretion, in the beginnyng, produced orderly and distinctly all thinges. For his _Numbryng_,
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then, was his Creatyng of all thinges. And his Continuall _Numbryng_, of all thinges, is the Conseruation of them in being: And, where and when he will lacke an _Vnit_: there and then, that particular thyng shalbe _Discreated_. Here I stay. But our Seuerallyng, distinctyng, and _Numbryng_, createth nothyng: but of Multitude considered, maketh certaine and distinct determination. And albeit
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these thynges be waighty and truthes of great importance, yet (by the infinite goodnes of the Almighty _Ternarie_,) Artificiall Methods and easy wayes are made, by which the zelous Philosopher, may wyn nere this Riuerish _Ida_, this Mountayne of Contemplation: and more then Contemplation. And also, though _Number_, be a thyng so Immateriall, so diuine, and ternall: yet by degrees,
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by litle and litle, stretchyng forth, and applying some likenes of it, as first, to thinges Spirituall: and then, bryngyng it lower, to thynges sensibly perceiued: as of a momentanye sounde iterated: then to the least thynges that may be seen, numerable: And at length, (most grossely,) to a multitude of any corporall thynges seen, or felt: and so, of
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these grosse and sensible thynges, we are trayned to learne a certaine Image or likenes of numbers: and to vse Arte in them to our pleasure and proffit. So grosse is our conuersation, and dull is our apprehension: while mortall Sense, in vs, ruleth the common wealth of our litle world. Hereby we say, Three Lyons, are three: or a
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_Ternarie_. Three Egles, are three, or a _Ternarie_. [] Which * _Ternaries_, are eche, the _Vnion_, _knot_, and _Vniformitie_, of three discrete and distinct _Vnits_. That is, we may in eche _Ternarie_, thrise, seuerally pointe, and shew a part, _One_, _One_, and _One_. Where, in Numbryng, we say One, two, Three. But how farre, these visible Ones, do differre from
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our Indiuisible Vnits (in pure _Arithmetike_, principally considered) no man is ignorant. Yet from these grosse and materiall thynges, may we be led vpward, by degrees, so, informyng our rude Imagination, toward the cceiuyng of _Numbers_, absolutely (:Not supposing, nor admixtyng any thyng created, Corporall or Spirituall, to support, conteyne, or represent those _Numbers_ imagined:) that at length, we may
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