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Alexander I Aleksander Pavlovich
Alexander I. (aleksander Pavlovich) (1777-1825), Emperor Of Russia, Son Of The Grand-duke Paul Petrovich, Afterwards Paul I., And Maria Fedorovna, Daughter Of Frederick Eugene Of Wurttemberg, Was Born On Dec. 28, The Strange Contradictions Of His Character Make Alexander One Of The Most Interesting As He Is One Of The ...

Alexander I
Alexander I. Was Bishop Of Rome From About Io6 To 115. He Has Been Identified, Without Any Foundation, With Alexander, A Martyr Of The Via Nomentana, Whose Day Is May 3. ...

Alexander Ii
Alexander Ii. (anselmo Baggio), Pope From Io6i To Io73, Was A Native Of Milan. As Bishop Of Lucca He Seconded The Efforts Of Hildebrand (afterwards Gregory Vii.) For The Sup Pression Of Simony And The Enforcement Of The Celibacy Of The Clergy. By Hildebrand's Influence He Was Elected Pope, 'but ...

Alexander Iii
Alexander Iii. (orlando Bandinelli), Pope From '159 To Ii8i, Was A Siennese, And Teacher Of Canon Law In Bologna And Author Of The Stroma, Or The Summa Magistri Rolandi, One Of The Earliest Commentaries On The Decretum Gratiani And Of Sentences, Based On The Lntroductio Ad Theologiam Of Abelard. In ...

Alexander Iii_2
Alexander Iii. (1845-1894), Emperor Of Russia, Sec Ond Son Of Alexander Ii., Was Born On March Io, 1845. In Natural Disposition He Bore Little Resemblance To His Soft-hearted, Liberal Minded Father, And Still Less To His Refined, Philosophic, Sentimen Tal, Chivalrous, Yet Cunning Grand-uncle, Alexander I. He Rather Gloried In ...

Alexander Iii_3
Alexander Iii. (124t-1285), King Of Scotland, Son Of Alexander Ii. By His Second Wife Mary De Coucy, Succeeded To The Throne In 1249, At The Age Of Eight. The Years Of His Minority Were Marked By An Embittered Struggle For The Control Of Affairs Between Two Rival Parties, The One ...

Alexander Ii_2
Alexander Ii. (1818-1881), Emperor Of Russia, Eldest Son Of Nicholas I., Was Born On April 29, 1818. Up To The Moment Of His Accession In 1855 No One Ever Imagined That He Would Be Known To Posterity As A Great Reformer. In So Far As He Had Any Decided Political ...

Alexander Ii_3
Alexander Ii., King Of Epirus (succeeded 272 B.c.). In 264 He Invaded Macedonia But Was Driven Out Of That Country And His Own Kingdom By Demetrius, Son Of Antigonus Gonatas. He Was Later Restored To Epirus. He Subsequently Recovered His Kingdom (polybius Ii. 45, Ix. 34; Plutarch, Pyrrhus, 9; Justin ...

Alexander Ii_4
Alexander Ii. (i 198-1249), Ldng Of Scotland, Son Of William The Lion, Whom He Succeeded In 1214. He Joined The English Barons In Their Struggle Against King John, Marched Into England And Besieged Norham Castle In 1215. In 1217 He Again Invaded„ England But Eventually Made Peace With Henry Iii., ...

Alexander Iv
Alexander Iv. (rinald0), Pope From 1254 To 1261, Was A Member Of The Family Of The Counts Of Segni. On The Death Of Innocent Iv. He Was Elected Pope At Naples On Dec. 12, 1254. He Is Described As A Stout Man, Kindly, Cheerful, But Of No Great Brilliancy. He ...

Alexander I_2
Alexander I., King Of Epirus About 342 B.c., Brother Of Olympias The Mother Of Alexander The Great, And Son-in-law Of Philip Of Macedon, Whose Daughter Cleopatra He Married (336). In 332 He Crossed Over To Italy To Assist The Tarentines Against The Lucanians, Bruttians And Samnites. He Gained Considerable Successes, ...

Alexander I_3
Alexander I. (c. 1078-1124), King Of Scotland, Was The Fourth Son Of Malcolm Canmore By His Wife Margaret. On The Death Of His Brother Edgar In 1107 He Became King Of Scotland North Of The Forth And Clyde, Southern Scotland Being Reserved For His Brother David. He Founded Many Abbeys ...

Alexander I_4
Alexander I., King Of The Serbs, Croats And Slovenes , Was Born At Cetinje On Dec. 4, 1888, The Second Son Of Prince Peter Karagjorgjevic, Later King Of Serbia, And Of Zorka, Third Daughter Of Prince Nicholas Of Montenegro. His Mother Died In 189o, And During His Early Years He ...

Alexander Nevski
Alexander Nevski (122o-1263), Russian Hero And Saint, Grand Duke Of Vladimir, Spent The Early Years Of His Life In Constant Warfare With The Germans, Swedes And Lithuanians, Who Sought To Rescue Novgorod And Pskov From Russia. He Is Called Nevski From His Victory Over The Swedish General, Birger Jarl, On ...

Alexander Of Aphrodisias
Alexander Of Aphrodisias, Pupil Of Aristocles Of Messene, Greek Commentator On The Writings Of Aristotle, And Styled, By Way Of Pre-eminence, 4777w-* ("the Expositor"), Was A Native Of Aphrodisias In Caria. He Came To Athens Towards The End Of The 2nd Century A.d., Became Head Of The Lyceum And Lectured ...

Alexander Of Hales Alexander
Alexander Of Hales (alexander Halensis), Known As Doctor Irrefragabilis, Was One Of The First English Scholars And Theologians To Make His Influence Felt In Paris. Born C. 1175 In Gloucestershire, He Went To Study At Paris, Where He Became A Master Of Arts Sometime Before 1210. About 1231 He Entered ...

Alexander Of Tralles A
Alexander Of Tralles (a Le Xander Trallianus), Greek Physician, Born At Tralles In Lydia, Lived Probably About The Middle Of The 6th Century B.c. The Greek Text Of His Boma Larpu<6. Was Printed At Paris In 1548 And His De Lumbricis At Venice In 157o. See E. Milward, Trallianus Reviviscens ...

Alexander Severus Marcus Aurelius
Alexander Severus (marcus Aurelius Severus Alexander) (208-235), Roman Emperor From A.d. 222 To 235, Was Born At Arca Caesarea, In Palestine, On Oct. 1, 208. He Was The Son Of An Imperial Procurator. In 221 His Grandmother, Julia Maesa, Persuaded Her Nephew, The Emperor Heliogabalus, To Adopt Him As Successor ...

Alexander The Great The
Alexander The Great - The Romance Of Alexander The Figure Of Alexander Naturally Impressed Itself Upon The Imagination Of The World Which His Career Had Shaken. The Ro Mance Of Alexander Is Found Written In The Languages Of Nearly All Peoples From The Indian Ocean To The Atlantic, But All ...

Alexander The Paphlagonian
Alexander The Paphlagonian, A Celebrated Impostor And Worker Of False Oracles, Was Born At Abonouteichos (see Ineboli) In Paphlagonia In The Early Part Of The End Century A.d. The Vivid Narrative Of His Career Given By Lucian Might Be Taken As Fictitious But For The Corroboration Of Certain Coins Of ...

Alexander V
Alexander V. (peter Philarges), Pope From 1409 To 141o, Was Born In Crete Of Unknown Parents And Entered The Order Of St. Francis. He Was A Member In Turn Of The Universities Of Oxford And Paris, And Finally Settled In Lombardy, Where, Thanks To The Favour Of Gian Galeazzo Visconti, ...

Alexander Vi
Alexander Vi. (rodrigo Borgia), (1431-1503), Pope From 1492 Until His Death, Is The Most Memorable Of The Corrupt And Secular Popes Of The Renaissance. He Was Born, Jan. 1, 1431, At Xativa, Near Valencia Ih Spain. He Assumed The Name Of His Mother's Family, Borgia Or Borja, On The Elevation ...

Alexander Vii
Alexander Vii. (fabio Chigi), Pope From 1655 To 1667, Was Born At Siena On Feb. 13, 1599. He Was Successively Inquisitor At Malta, Vice-legate At Ferrar And Nuncio In Cologne (1639-51). Innocent X. Subsequently Made Him Cardinal-secretary Of State. When Innocent Died, Chigi, The Candidate Favoured By Spain, Was Elected ...

Alexander Viii
Alexander Viii. (pietro Otto Boni), Pope From 1689 To 1691, Was Born In R 6 I O Of A Noble Vene Tian Family, Was Created Cardinal, And Then Successively Bishop Of Brescia And Datary. The Ambas Sador Of Louis Xiv. Succeeded In Procuring His Election, Oct. 6, 1689, As Successor ...

Alexander
Alexander (1893-192o), King Of The Hellenes, Second Son Of King Constantine And Queen Sophia, Was Born Aug. T, 1893, And Ascended The Throne Of Greece On The Dethronement Of His Father, June 14,1917. The Government Itself Was For The Time In The Hands Of Venizelos, Who Had The Confidence Of ...

Alexanders
Alexanders (botanical Name, Smyrnium Olusatrum Family Umbelliferae), A Stout Herbaceous Plant With A Furrowed, Much-branched Stem I-3ft. High, And Large Compound Leaves With Broad Sheathing Stalks, And Broad, Cut Or Lobed Segments. The Small Yellow Flowers Are Borne In Compound Umbels. The Plant Is A Native Of The Mediterranean Region, ...

Alexandersbad
Alexandersbad, A Watering-place, Bavaria, Germany, Romantically Situated In The Fichtelgebirge, Near Wunsiedel, T. Above The Sea. Its Waters Are Ferruginous And Largely Used In Nervous And Rheumatic Disorders. In The Neighbourhood Is The Luisenburg (or Luxburg), A Hill Commanding A Fine View Of The Whole Fichtelgebirge. ...

Alexander_2
Alexander (146i-1506), King Of Poland, Succeeded His Brother John Albert In 'so'. He Carried On The Hopeless Struggle Of The Crown Against The Growing Power Of The Polish Senate And Nobles, Who Deprived Him Of Financial Control And Curtailed His Prerogative. For Want Of Funds, Alexander Was Unable To Assist ...

Alexander_3
Alexander, Despot Of Pherae In Thessaly From 369 To B.c. His Tyranny Caused The Aleuadae Of Larissa To Invoke The Aid Of Alexander Ii. Of Macedon, But After His Withdrawal Alex Ander Treated His Subjects As Cruelly As Before. The Thessalians Now Applied To Thebes; Pelopidas, Who Was Sent To ...

Alexander_4
Alexander, Son Of Numenius, Greek Rhetorician, Flourished In The First Half Of The Second Century A.d., Author Of A Treatise On Rhetoric (llepi Twv Trls (51.avotas Tiffs X €ws Qx?µarwv), Of Which Only An Abridgment Is Extant; It Was Fol Lowed As An Authority By Later Writers. Later Epitomes Were ...

Alexandra
Alexandra (1844-1925), Queen Consort Of Edward Vii., King Of Great Britain And Ireland, Eldest Daughter Of Prince Christian Of Gluecksburg, Afterwards King Christian Ix. Of Denmark, And Louise, Daughter Of The Landgrave William Of Hesse, Was Born At Copenhagen Dec. 1, 1844, Her Full Name Being Alexandra Caroline Maria Charlotte ...

Alexandretta
Alexandretta, A City Of Syria, On The Gulf Of The Same Name. Pop. 15,000, Two-thirds Muslim. Iskanderun (its Turkish Name) Preserves The Name But Probably Not The Exact Site Of The City Founded To Commemorate Alexander's Victory Over The Persians At Issus (333 B.c.) . The Name "little Alexandria" Ap ...

Alexandria Troas
Alexandria Troas, An Ancient Greek City Of The Troad, Situated On The West Coast At Nearly Its Middle Point, A Little South Of Tenedos. It Was Built By Antigonus, Perhaps About 310 B.c., And Was Called By Him Antigonia Troas. Early In The Next Century The Name Was Changed By ...

Alexandria
Alexandria, A City And Chief Seaport Of Egypt, And For Over A Thousand Years From Its Foundation The Capital Of The Coun Try, Situated On The Mediterranean In 31 ° I 2' N., 29° I 5' E., And 129m. By Rail N.w. Of Cairo. The Ancient Canopic Mouth Of The ...

Alexandrian School
Alexandrian School, A Term Applied To Certain Tendencies In Literature, Science And Art, Which Took Their Rise In Alexandria. That City, Founded By Alexander The Great, Was In Every Way Admirably Adapted For Becoming The New Centre Of The World's Activity And Thought. Its Situation Brought It Into Com Mercial ...

Alexandria_2
Alexandria, Town In Bonhill Parish, Dumbartonshire, Scotland, On The Right Bank Of The Leven, About 3m. N. Of Dum Barton, Served By The L.n.e.r. And L.m.s.r. It Owes Its Origin Almost Entirely To Cotton Printing And Bleaching Works Based On An Abundant Supply Of Excellent Water And Contains A Large ...

Alexandria_3
Alexandria, A City Of Louisiana, U.s.a., On The South Bank Of The Red River, In The Centre Of The State; The Capital Of Rapides Parish. It Is On Federal Highways 71 And 165, And Is Served By The Louisiana Railway And Navigation Company, The Texas And Pacific, The Rock Island, ...

Alexandria_4
Alexandria, A City And A Port Of Entry In Northern Virginia, U.s.a., On The W. Bank Of The Potomac River, 7m. Below Washington, D.c.; Contiguous To, But Independent Of, Arlington County. It Is Served By The Richmond, Fredericksburg And Potomac, The Southern, And The Old Dominion Railways, And By The ...

Alexandrine Verse
Alexandrine Verse, A Name Given To The Leading Measure In French Poetry. It Is The Heroic French Verse, Used In Epic Narrative, In Tragedy, And In The Higher Comedy. There Is Some Doubt As To The Origin Of The Name; But Most Probably It Is Derived From A Collection Of ...

Alexandrists
Alexandrists, The Name Given To Those Philosophers Of The Renaissance, Who, In The Great Controversy On The Subject Of Personal Immortality, Adopted The Explanation Of The De Anima Given By Alexander Of Aphrodisias. According To The Orthodox Thomism Of The Roman Catholic Church, Aristotle Rightly Re Garded Reason As A ...

Alexandrite
Alexandrite, A Variety Of Chrysoberyl (q.v.) Discovered In The Urals In 1833, On The Day Set Apart For Celebrating The Ma Jority Of The Russian Cesarevich, Afterwards The Tsar, Alexander Ii., In Whose Honour The Stone Was Named. It Is Remarkable For Being Strongly Dichroic, That Is, Exhibiting Different Colours ...

Alexandrovsk
Alexandrovsk, A Town In Sakhalin Island In The Far Eastern Area Of The R.s.f.s.r. Lat. 51° Io' N. Long. 142° 5' E. Pop. (1926) 7,807. It Is A Port On The West Coast In The Coal And Naphtha Area And Is The Administrative Centre For The Russian Part Of The ...

Alexis
Alexis, Greek Comic Poet Of The Middle Comedy, Was Born At Thurii And Taken Early To Athens, Where He Became A Citizen. He Wrote During The Latter Half Of The 4th Century And Perhaps The Early Part Of The 5th. Plutarch Says That He Lived To The Age Of 106, ...

Alexisbad
Alexisbad, A Spa Of Anhalt, Germany, Under The Harz Mountains, 1,000f T. Above Sea-level, Noted For Its Medicinal Waters, Of Which The Alexisbrunnen, A Ferruginous Spring, Is Used For Drink Ing, While The Selkebrunnen Supplies The Baths, Which Are Of Use In Feminine Disorders. The Place Was Founded In 18 ...

Alexius I
Alexius I. (1048-1118), Emperor Of The East, Was The Third Son Of John Comnenus, Nephew Of Isaac Comnenus, Emperor His Father Declined The Throne On The Abdication Of Isaac, Who Was Accordingly Succeeded By Four Emperors Of Other Families Between That Date And 1081. Under One Of These Emper Ors, ...

Alexius Ii Comnenus
Alexius Ii. (comnenus) (1167-1183), Emperor Of The East, Was The Son Of Manuel Comnenus And Maria, Daughter Of Raymund, Prince Of Antioch, And Was Born At Constantinople On Sept. I O, I I 6 7. On Manuel's Death, Maria, Who Had Been Immured In A Convent Under The Name Of ...

Alexius Iii
Alexius Iii. (angelus), Emperor Of The East, Was The Sec Ond Son Of Andronicus Angelus, Nephew Of Alexius I. In While His Brother Isaac Ii. Was Away Hunting In Thrace, He Was Proclaimed Emperor By The Troops; He Captured Isaac At Stagira, In Macedonia, Put Out His Eyes, And Kept ...

Alexius Iv
Alexius Iv. (d. 1204), Byzantine Emperor, When Isaac Ii. Was Dethroned And Blinded By His Brother Alexius Iii., His Son Alexius Escaped, In 1201, To Germany, Where He Persuaded His Brother-in-law, Philip Of Suabia, And Boniface Of Montferrat, The Leader Of The Crusaders, To Divert The Fourth Crusade To Constantinople. ...

Alexius Mikhailovich
Alexius Mikhailovich (1629-1676), Tsar Of Mus Covy, The Son Of Tsar Michael Romanov And Eudoxia Stry Eshnevaya, Was Born On March 9, 1629. A Youth At His Father's Death (1645), He Was Committed To The Care Of Boris Ivanovich Morozov, Who Recognized The Needs Of His Country And Was Acces ...

Alexius V
Alexius V., Eastern Roman Emperor, Was Proclaimed Em Peror Feb. 5, 1204, During The Siege Of Constantinople By The Latins (fourth Crusade). His Name Was Alexius Ducas Mur Zuphlus, And He Was A Connection Of The Imperial House Of The Angeli. His Elevation Was The Result Of A Revolution In ...

Alfa Or Halfa
Alfa Or Halfa, The North African Name Of A Species Of Esparto Grass. (see Esparto.) ...

Alfalfa Weevil
Alfalfa Weevil, A Snout-beetle, Or Weevil (hypera Postica) Of Old World Origin. Which Feeds Upon Alfalfa, Or Lucerne (medicago Sativa). Although Widely Distributed In Eu Rope, Where Its Host Plant Is Extensively Grown, It Attracted Little Attention Until It Was Accidentally Introduced Into The United States In The Early Years ...

Alfalfa
Alfalfa, The Name In The United States, Canada And Cer Tain Other Countries For The Leguminous Plant Medicago Sativa, Known Elsewhere As Lucerne (see Lucerne). ...

Alfeld
Alfeld, Chief Town Of A Subdivision Of The District Of Hildesheim, In The Prussian Province Of Hanover, On The River Leine, About 15m. S.s.w. Of Hildesheim. Pop. (1933) 7,221. It Has A Handsome Church With Twin Spires. Its Industries Embrace Paper-making, Iron-founding And The Production Of Agricultural Machinery. ...

Alfred Ernest Albert
Alfred Ernest Albert (1844-19oo), Duke Of Saxe Coburg And Gotha, And Duke Of Edinburgh, Second Son And Fourth Child Of Queen Victoria, Was Born At Windsor Castle On Aug. 6, 1844. He Passed A Most Creditable Examination For Midshipman In Aug. 1858, And Being Appointed To The "euryalus," At Once ...

Alfred Or Aelfred
Alfred Or Aelfred, Known As The Great (848? Goo), King Of England, Was Born At Wantage, And Was The Fifth Son Of King Aethelwulf And His First Wife Osburh. He Seems To Have Been A Child Of Singular Attractiveness And Promise, And Stories Of His Boyhood Were Remembered. At The ...

Alfred Ringer
Ringer, Alfred (1837-1904), English Divine And Man Of Letters, Was Born In London On Feb. 9, 1837, The Son Of An Architect. He Was Educated At King's College, London, And At Trinity College, Cambridge, And Was Ordained In 186o To A Curacy At Alrewas, Near Rugeley. His Connection With The ...

Alfred
Alfred, A Village In Allegany County, N.y., U.s.a., On The Erie Railroad About 75 M. S.e. Of Buffalo. It Is Situated Among Rugged Hills, At The Intersection Of Two Valleys. The Population Was 639 In 193o. On The West Slope Of Pine Hill, 1,800 Ft. Above Sea-level, Is Alfred University ...

Alfreton
Alfreton, Urban District, Derbyshire, England, 14m. N. By E. Of Derby, On The L.m.s. Railway. Population (193 ) 21,232. It Lies Above A Small Tributary Of The Derwent. The Church Of St. Martin Is Early English And Later. The Neighbourhood Abounds In Ironworks, Collieries, Quarries And Potteries, And Is Thickly ...

Alfurs
Alfurs, A General Name Given To Tribes Of Low Culture And Mixed Origin Inhabiting Parts Of The Eastern Islands Of The In Donesian Archipelago, Halmahera, Ceram, Timorlaut And Timor And The Adjacent Islets. They Are Probably Of Proto-malay And Indonesian Extraction With A Strong Admixture Of Papuan Ele Ments; And ...

Algae Occurrence Anddistribution
Algae - Occurrence And Distribution Benthos.—most Algae Grow Permanently Submerged, And Are Either Attached (benthos) Or Free-floating (plankton). In Fresh Waters The Algae Of The Benthos Grow On Stones, Twigs, And Larger Aquatics, While The Benthic Seaweeds Are Nearly All Lithophytes (i.e., Fixed To Rocks) . Few Algae (chara, Caulerpa) ...

Algae Phylogeny
Algae - Phylogeny There Can Be Little Doubt That Algae Originated In The Water And That They Preceded In Their Evolution The More Elaborate Land Plants. The Different Classes, As Well As Some Prevalently Flagellate Groups Dealt With Elsewhere (see Protophyta), Are Distinguished By Special Pigments In The Chromatophores And ...

Algae Structure Andreproduction
Algae - Structure And Reproduction The Algae Exhibit A Diversity Of Form Not Found In Any Other Group Of Plants, Ranging From One-celled Organisms Through Mani Fold Colonial Types To Simple Or Branched Rows Of Cells (filaments) And Onwards To Elaborate Massive Growths Attaining Dimensions And Complexities Of Structure That ...

Algae
Algae. The Algae Comprise Seaweeds, Pond-scums, And A Great Variety Of Microscopic Plants Inhabiting Fresh And Salt Waters In Countless Numbers. Many Are Found In Or On The Soil Or On Rocks And Tree-trunks, And No Region Of The Earth Is Devoid Of Them (see Occurrence And Distribution, P. 6oi ...

Algarve Or
Algarve Or The Algarves, Ancient Kingdom And Prov Ince In The Extreme South Of Portugal, Corresponding With The Modern Administrative District Of Faro, And Bounded On The North By Alentejo, East By The Spanish Province Of Huelva, And South And West By The Atlantic Ocean. Population (192o) 268,294; Area Square ...

Algau Or Allgau
Algau Or Allgau, A Small District In South-west Ba Varia, Belonging To The Province Of Suabia And Neuburg. The Name Formerly Applied To A Much Larger Territory, Extending To The Danube On The North, The Inn On The South And The Lech On The West. The Algau Alps Contain Several ...

Algebra Artificial Numbers
Algebra - Artificial Numbers The Numbers Used In Counting Objects Have Long Been Known As Natural Numbers. Numbers That Are Not Naturally Used In Counting Objects Are Commonly Called Artificial Numbers, A Term That Is Open To Certain Objections. From Various Points Of View The Number A Is As Natural ...

Algebra Fundamental Principlesassumed
Algebra - Fundamental Principles Assumed There Are Certain Axioms Which Are Often Set Forth In Textbooks, As The Statement "if Ab=p, Then A=p/b," But Others, Equally Important From The Standpoint Of Logic Are Properly Assumed Tacitly. Such For Example, Are The Statements That A+b=b+a, The Commutative Law Of Addition; That ...

Algebra Linear Transformations
Algebra - Linear Transformations Progress Made In The Study Of Equations, Symmetric Functions, And Series, Had Already Begun To Rank As A Special Branch Of Mathe Matics. ...

Algebra
Algebra, According To Present English Usage That Branch Of Mathematics Which Considers Primarily The Representation Of Numbers By Means Of Letters. Speaking More Precisely, That Part Of Mathematics Which Considers The Relations And Properties Of Numbers By The Aid Of General Symbols, Usually Letters (a,b,c, . . . X,y,z) And ...

Algebraic Forms Apolarity
Algebraic Forms - Apolarity For Geometry, Co-ordinates Or Variables All Of One Kind Are Not Sufficient. The Theory Of Duality Demands, In A Plane, Point Co-ordinates And Line Co-ordinates; And, In Three-space, Points And Planes Are Dual, While Lines, Dual To Lines, Require A Third Kind Of Co-ordinates. A Polarity ...

Algebraic Forms Binaryforms
Algebraic Forms - Binary Forms The Rational Invariants Of A Single Binary Form Of Order Less Than Ten Have Been Thoroughly Studied And Tabulated. First To Be Noticed Was Naturally The Discriminant Or Determinant Of A Quadric Form, For It Was Known To Vanish When The Quadric Has Two Equal ...

Algebraic Forms Finitenessof
Algebraic Forms - Finiteness Of System Of Invariants: Hilbert's Extensions The Third Major Problem Is Concerned With The Finiteness Of Reduced Systems Of Invariant Comitants. Reduction By Tamisage May Show That, For Degrees And Orders Proposed, All Covariants Are Reducible, I.e., Rationally Expressible In Terms Of Those Of Lower Degrees. ...

Algebraic Forms Generallaws
Algebraic Forms - General Laws Of Structure The First Major Problem In The Theory Of Forms Is The Determina Tion Of General Laws For Structure Of Invariants. For Binary Forms Containing One Set Of Variables It Is Proved That Invariant Forms Consist Of A Finite Number Of Terms Composed Of ...

Algebraic Forms Historicalnote
Algebraic Forms - Historical Note Prior To The Year I800 The Study Of Algebraic Forms Was Con Fined To Questions Of Factors, Multiples, Powers, Differentiation And Elimination. Resultants, Discriminants And In Particular Determinants Were Chief Objects Of Interest. Early In The I9th Century, However, The Invention Or Formulation Of Projective ...

Algebraic Forms Orderlyproduction
Algebraic Forms - Orderly Production And Enumeration This Contravariant Ii Is Noteworthy As Being Strictly Dual To F Itself; I.e., If Variables (u) And (x) Are Exchanged, And Invariants And Contravariants Derived From The Altered Ii, As From F, Then The New Ii Altered By The Same Exchange Of Variables ...

Algebraic Forms Ternaryforms
Algebraic Forms - Ternary Forms If Three Ternary Linear Forms Vanish For The Same Values Of The Variables, Not All Zero, I.e., If A1x1 + A2x2+ A3x3 = O B1 Xl + B2x2+ B3x3 = O Cixi+c2x2+c3x3=o, Then Their Determinant, Denoted By Or Merely (abc), Is Zero. No Linear Transformation ...

Algebraic Forms
Algebraic Forms. An Algebraic Form Is A Polynomial, All Of Whose Terms Are Of The Same Degree In Two Or More Variables. Thus Axe+ By +c Is Not A Form, But Of Order Two In Three Variables X, Y, Z Is A Quadratic Ternary Form. A Form Is Also Called ...

Algeciras Conference
Algeciras Conference. On 8, 1904, A Treaty Was Concluded In London By Which France Accorded Ab Solute Liberty Of Action To Great Britain In Egypt In Return F Or A Similar Acknowledgment Of French Interests In Morocco. By A Subsequent Treaty (oct. 1904) France Concluded A Secret Arrange Ment With ...

Algeciras Or Algeziras
Algeciras Or Algeziras, A Seaport And Railway Ter Minus Of Southern Spain, In The Province Of Cadiz, 6m. W. Of Gibraltar, On The Opposite Side Of The Bay Of Algeciras. Pop. (193o) 21,431. The Name (arabic, "island") Is Derived From A Small Islet On One Side Of The Harbour. The ...

Algeria History
Algeria - History The History Of Algeria, Which Constitutes The Central Part Of Barbary Or Moghreb, Has Almost Always Been Bound Up With That Of Morocco And Tunisia, Which Are Respectively The Western And The Eastern Parts Of That Great Natural Region. The Actual Name Of Algeria, Or Rather Of ...

Algeria Under The French
Algeria Under The French The Settlement Of The French In Algiers Opened A New Period In The History Of North Africa. In The 16th Century Traders From Marseille Set Up Coral Fisheries On The Barbary Coast, At Bone, At Calle And At The Bastion De France. France Had Maintained More ...

Algeria
Algeria, A Country In North Africa Under French Domin Ion, Bounded West By Morocco, North By The Mediterranean, East By Tunisia, And South By Italian Libya And French West Africa. North Algeria Has An Area Of 2o7,915sq.km. Between 37° And 34° N. Lat. And 2° I O' And 8° 5o' ...

Alghero
Alghero, Seaport And Episcopal See, Province Of Sassari, West Sardinia, 21m. S\v. By Rail From Sassari. Pop. (1931) 13,781. The Cathedral Is 12th Century; The See Dates From 1503. Founded By The Doria Family Of Genoa About 1102, It Was Occu Pied By The House Of Aragon In 1354, Who ...

Algidus Mons
Algidus Mons, The East Part Of The Ridge Of The Larger Crater Of The Alban Volcano (see Albanus Mons), Traversed By A Narrow Opening (now Called The Cava D'aglio) Used For The Via Latina. There Was A Temple To Diana, The Site Of Which Is Unknown. ...

Algiers
Algiers, Capital Of Algeria, The Seat Of The Governor-general, And Of The Algerian Assemblies, Of A Court Of Appeal, Of The Xix Army Corps And Of An Archbishop. It Is Built On The West Side Of The Bay Of Algiers, 36° 47' N., 3° 4' E., On The Slopes Of ...

Algoa Bay
Algoa Bay, A Wide, Shallow Bay Between Capes Recife And Padrone, South Africa, Formed By Erosion Of Rocks Of The Bokke Veld And Uitenhage Series By The Sea, Which Has Left A Belt Of More Resistant Table Mountain Sandstones Projecting Eastwards, And Forming The South-west Border Of The Bay. In ...

Algol
Algol, A Well Known Variable Star, Also Designated Per Sei. Its Fluctuation Of Brightness Was Noticed By G. Montanari In 1669; But The Arabic Name, Which Signifies The Demon, Seems To Hint That The Behaviour May Have Been Known In Ancient Times. The Brightness Varies Regularly Between Magnitudes 2.1 And ...

Algonkin
Algonkin, A Tribe, Group And Family Of American Indians. The Tribe Lived On Gatineau River East Of Ottawa. The Name Came Gradually To Include Related Tribes Or Bands In Quebec And Ontario, Where They Now Number Between 3,00o And 4,000. They Were Friends Of The French, Foes Of The Iroquois ...

Algorism
Algorism, A Name Applied In The Middle Ages To Arithmetic Employing The Indo-arabic Numerals. (see Algebra For Moham Med Ibn Musa Al-khowarizmi, Who Wrote Liber Algorism, "the Book Of Al-khowarizmi.") It Appeared In Mediaeval French As Augrisme And Augrime, And Was Thence Carried To England As Augrym Or Augrim, As ...

Alguazil
Alguazil, A Spanish Title Often To Be Met In Stories And Plays, Derived From The Arabic "visir" And The Article "al." The Alguazil Among The Early Spaniards Was A Judge, And Sometimes The Governor Of A Town Or Fortress. In Later Times He Has Gradually Sunk Down To The Rank ...

Algum Or Almug Tree
Algum Or Almug Tree. The Hebrew Words Algummin Or Almuggim Are Translated Algum Or Almug Trees In The Author Ized Version Of The Bible (see Kings X. I 1, 1 2 ; 2 Chron. Ii. 8, And Ix. Io, 1 I) ; Almug Is An Erroneous Form (see Max Muller, ...

Alhama De Granada
Alhama De Granada, Southern Spain, Province Of Granada, 24m. S.w. Of Granada. Pop. (193o) 8,204. Alhama Is On A Sloping Shelf Of Limestone Over A Deep Gorge Of The River Marchan Or Alhama; The Rugged Peaks (6,800ft.) Of The Sierra De Alhama Rise Behind It. On Christmas Day 1884 An ...

Alhambra
Alhambra, A City Of Los Angeles County, California, U.s.a., At The Entrance To The San Gabriel Valley; Bounded By The Cities Of Los Angeles, South Pasadena, And San Gabriel, And By The East Side Industrial Area Which Adjoins Los Angeles. It Is Served By The Southern Pacific And The Pacific ...

Alhazen
Alhazen (al-hah'zen) [aim Ali Al-hasan Ibn Alha San], Arabian Mathematician Of The Th Centur, Was Born At Basra And Died At Cairo In O38. He Is To Be Distinguished From Another Alhazen Who Translated Ptolemy's Almagest In The Loth Century. Having Boasted That He Could Construct A Machine For Regulating ...

Ali
Ali, In Full, 'ali Ben Abu Talib (c. 600-661), The Fourth Of The Caliphs Or Successors Of Mohammed, Was Born At Mecca About The Year A.d. 600. His Father, Abu Talib, Was An Uncle Of The Prophet, And Ali Himself Was Adopted By Mohammed And Edu Cated Under His Care. ...

Aliaga
Aliaga, A Municipality (with Administrative Centre And 14 Barrios Or Districts) Of The Province Of Nueva Ecija, Luzon, Philip Pine Islands, Almost Due West From The Capital Cabanatuan And About Tom. N. By W. Of Manila. Pop. (1918) 12,703, Of Whom 6,428 Were Male, 6,271 Female. The White Population Numbered ...

Alias
Alias, A Term Used To Connect The Different Names Of A Person Who Has Passed Under More Than One, In Order To Conceal His Identity Or For Other Reasons, Or To Describe Compendiously An Adopted Name. ...

Alibi
Alibi, In Law, The Defence Resorted To In Criminal Prosecutions, Where The Person Charged Alleges That He Was So Far Distant At The Time From The Place Where The Crime Was Committed That He Could Not Have Been Guilty. An Alibi, If Substantiated, Is The Most Con Clusive Proof Of ...

Alicante
Alicante, Capital Of The Province Of That Name, Episcopal See With Modern Cathedral, Rising In A Crescent From The Bay Up The Low Surrounding Hills With White Flat-roofed Houses Ending In An Old Citadel On Bare Rock (400ft.). Pop. (1930) 73,071. A Dry And Equable Climate Makes It A Health-resort, ...