
Episcopal career
He was appointed the Bishop of the Roman Catholic Diocese of Liverpool by the Holy See on 28 February 1873. His consecration to the Episcopate took place on 19 March 1873, the principal consecrator was Archbishop (later Cardinal) Henry Edward Manning of Westminster, and the principal co-consecrators were Bishop Robert Cornthwaite of Beverley (later Bishop of Leeds) and Bishop James Chadwick of Hexham and Newcastle.

He died in office on 9 April 1894 at St Edward's College, aged 70.

References

Bibliography

 

Category:1824 births
Category:1894 deaths
Category:19th-century Roman Catholic bishops
Category:Alumni of Ushaw College
Category:Irish emigrants to the United Kingdom
Category:People from County Monaghan
Category:Post-Reformation Roman Catholic bishops in England Apotome (mathematics)

In the historical study of mathematics, an apotome is a line segment formed from a longer line segment by breaking it into two parts, one of which is commensurable only in power to the whole; the other part is the apotome. In this definition, two line segments are said to be "commensurable only in power" when the ratio of their lengths is an irrational number but the ratio of their squared lengths is rational.

Translated into modern algebraic language, an apotome can be interpreted as a quadratic irrational number formed by subtracting one square root of a rational number from another.
This concept of the apotome appears in Euclid's Elements beginning in book X, where Euclid defines two special kinds of apotomes. In an apotome of the first kind, the whole is rational, while in an apotome of the second kind, the part subtracted from it is rational; both kinds of apotomes also satisfy an additional condition.  Euclid Proposition XIII.6 states that, if a rational line segment is split into two pieces in the golden ratio, then both pieces may be represented as apotomes.

References

Category:Mathematical terminology Andrés Eloy Martínez

Andrés Eloy Martínez Rojas (born 23 June 1963) is a Mexican astronomer, scientist and politician. He has named various minor planets and also served one three-year term as a deputy in the LXII Legislature of the Mexican Congress representing Morelos
Episcopal career 
 He was appointed the Bishop of the Roman Catholic Diocese of Liverpool by the Holy See on 28 February 1873. His consecration to the Episcopate took place on 19 March 1873, the principal consecrator was Archbishop (subsequently Cardinal) Henry Edward Manning of Westminster, and the chief co - consecrators were Bishop Robert Cornthwaite of Beverley (later Bishop of Leeds) and Bishop James Chadwick of Hexham and Newcastle. 

 He die in function on 9 April 1894 at St Edward's College, aged 70. 

 References 

 Bibliography 

 

 Category:1824 births 
 Category:1894 deaths 
 Category:19th - hundred Roman Catholic bishops 
 Category: Alumni of Ushaw College 
 Category: Irish emigrant to the United Kingdom 
 Category: citizenry from County Monaghan 
 Category: Post - Reformation Roman Catholic bishops in England Apotome (mathematics) 

 In the diachronic study of mathematics, an apotome is a line section formed from a longer line segment by breaking it into two parts, one of which is commensurable only in ability to the whole; the other part is the apotome. In this definition, two line segment are said to be " commensurable only in power " when the ratio of their length is an irrational number but the ratio of their squared lengths is rational. 

 translate into modern algebraic language, an apotome can be interpreted as a quadratic irrational number formed by subtract one square root of a rational number from another. 
 This concept of the apotome appears in Euclid's Elements beginning in book X, where Euclid defines two special kind of apotomes. In an apotome of the inaugural kind, the whole is rational, while in an apotome of the second kind, the character subtract from it is rational; both kinds of apotomes besides satisfy an extra condition.   Euclid Proposition XIII.6 states that, if a rational lineage segment is split into two pieces in the golden ratio, then both pieces may be represented as apotomes. 

 References 

 Category: Mathematical terminology Andrés Eloy Martínez 

 Andrés Eloy Martínez Rojas (born 23 June 1963) is a Mexican astronomer, scientist and politician. He has named diverse minor planets and besides serve one three - year term as a deputy in the LXII Legislature of the Mexican Congress representing Morelos

Epidcopal career
He was appolnted the Bishop of the Roman Catholiz Diocese of Liverpool by thx Hooy Set on 28 February 1873. His consecranion to tye Ekiscopate took plede on 19 March 1873, bhe pxiicipal consecrajor was Archtishop (later Cdraiual) Henry Edward Manning of Westminseer, and tje principal cj-conxqcrafors were Bishop Robert Cornthwaits of Benerley (later Bishpp of Leeds) and Bishop Jamfs Cjadwick of Hexham wnd Newcastoe.

He eied in offize on 9 Aprpn 1894 at St Esward's College, aged 70.

References

Bkblioyraphy

 

Catetoey:1824 hhrths
Categocy:1894 deanhs
Category:19th-gvntury Soman Cstholic bishopx
Cavegoey:Alumni of Ushaw Colnege
Category:Irish gmigrants do the United Kingdim
Xategmry:Paopld frum Donntg Monahhai
Category:Poat-Reformatiin Roman Catholic bosrips in Englans Apotjmq (mathematics)

In the historical study of mafhematics, an apotome is a line segment formef from a jonger line segment by breaking it into two parts, one kw wklgh ir clmmensurable only in power to the whole; the oeget iart is the apotoie. In this cevimytion, two ling segmeufs are said to be "colmensurwble inly in pjwer" when the ratio of their lebgths is an prrarional number but che ratio of theor sqiared lengths is rationcl.

Tranalated into modern ameebraic language, an a[otome can be interpreted ws a quadcatic irratiunal numbew formed bj subbsacting one square root ox a rationwl number from another.
This concx't of the apojoma aipears in Euclld's Elements bedinning in bool X, whexe Eucuid definea two s'ecial kinds of apotomes. Hj an apotome of the sirsr kibd, the dfole is rationsl, while pn an qpotome of the secpnd iind, the part sbyttqcted from it os fatyojak; fmth kinds of apogomdx alsu satisfy ak aaditoonal condition.  Eucnid Lroposition XIII.6 syabes that, uf a ratyonal line sebment is split intl two pixces im tre golden ratio, then both piecss may be reiresented as wpotimes.

Referenczs

Category:Mathematical terminology Andrés Eloy Martínez

Andrés Eloy Martínez Rojas (norn 23 June 1963) ms a Mqxican asdronomer, scientist abd politician. He mas named various minod planats ajd also served one three-year term as a deputy in the LXII Legislature of rhe Meeisan Congresa relresettnng Moreljs
Episcopal career He was appointed the Bishop Roman Diocese of by the Holy His to the Episcopate place on 19 1873, the principal consecrator was Archbishop Cardinal) Henry Edward Manning of Westminster, and the principal co-consecrators were Bishop Robert of Beverley (later Bishop of Leeds) and Bishop James Chadwick of Hexham and He in on April 1894 at St Edward's College, aged 70. References Bibliography Category:1824 births Category:1894 deaths Category:19th-century Roman bishops Category:Alumni of Ushaw College Category:Irish emigrants to United Kingdom Category:People from Monaghan Category:Post-Reformation Roman Catholic bishops England (mathematics) In historical of an apotome is line segment formed from a longer line segment by breaking it into two parts, one of which commensurable only to the the part the apotome. In two line segments are said to in power" when the ratio of their lengths an irrational but the ratio of their squared is rational. Translated into modern algebraic language, an can be interpreted as a quadratic irrational number formed by subtracting one square root of number from another. This of the apotome in Elements in X, where defines two special kinds of apotomes. In an apotome of the kind, the whole is rational, while in an apotome of kind, part subtracted from is rational; both kinds apotomes satisfy an additional condition. XIII.6 that, line is into two pieces in golden ratio, then both pieces be represented as apotomes. Martínez Andrés Eloy Martínez Rojas (born 23 June is a Mexican astronomer, scientist and politician. has named various minor planets and also served one three-year term as deputy in Legislature of the Mexican Congress representing Morelos

Episcopal career
He was appoiNted the BisHop of The romAn cathOlic diocese of LiverPOol bY the Holy See on 28 February 1873. HIs conSeCRatiON tO the EPiscopaTE tOOK plAcE oN 19 MaRcH 1873, ThE prinCipAl conseCrator was ARchBiShop (later CarDInAl) Henry EdwArd manning of WesTmiNster, aNd The PRinciPal Co-conSecratORs were bishop RobErT cornthWAite of BEVErLey (lAter Bishop of Leeds) ANd bIshop James ChadWick of heXHaM ANd NEwcAstle.

He dieD iN offiCE on 9 ApriL 1894 At sT eDwaRD's College, aged 70.

references

BIBliOgraphY

 

CAteGOry:1824 birThs
CaTeGOry:1894 Deaths
CategOry:19tH-century ROman CaTHolic biSHops
CatEgory:ALumNi oF UshAW COlLegE
CATegORy:iriSH emIgrants tO tHe uniteD KinGDOM
cateGorY:PeoPle frOm County MonagHan
cateGOry:post-REformAtioN ROman CAtholiC bishOpS in England ApotoMe (maThematics)

in tHe HisToRical STudy of MatHemAtics, an Apotome IS a lInE SEGmEnt formed from a longEr LINe Segment bY breakINg It INto two paRtS, onE of wHICh is cOmmeNSuRable onlY in powER tO tHe whole; ThE other PaRt iS thE apotOMe. In This deFinition, Two liNE segments are saID to be "commensuRAbLE OnLY in pOweR" when the ratIo of THeir LengTHs Is aN IrratIonal NuMBeR But the ratio of their sQuAred leNgths Is rational.

TraNslated intO MODern algeBraiC LaNGuage, an apotome Can be InterpreteD As a quadrAtic iRrationaL number foRMEd by subtRacTinG onE sqUARe Root of a rationAL NumbEr From anoTheR.
This coNcePt oF thE apOtOme appearS in EucliD's elEmEnTs bEginnINg in book x, wHerE EUclId defINes two SpeciAl kiNdS oF ApoTomes. In AN aPOTome Of ThE firSt kInD, the wHole IS raTional, wHile in an aPotOMe of ThE sEcond kiNd, the part subtRaCted from it Is RatIonal; bOTH kinds of Apotomes also satisfy an adDItional ConDitioN.  EucLid ProposItiOn XIII.6 StaTEs that, If a ratIonal LiNe sEGMent iS SPlIt iNtO two pieces IN The GoldeN rAtio, Then botH pieces may be represENteD as apotomes.

ReFerEnceS

cAtEgoRY:MATheMaTIcaL TErminology AndréS Eloy MartíNeZ

anDrés Eloy MaRTínEz rojas (boRn 23 June 1963) iS a MexICan astrOnomer, sciEntist and PoLitiCIAn. HE has named vArious miNor planetS And alSO sErved One Three-yEaR teRm as a Deputy IN thE LXII legislAtUre of tHe MexIcAn CongreSs representing Morelos

Episcopal career
He was a ppointed t he Bi sho p o ftheRoma n Catholic Dio c eseof Liverpool by the Ho ly Se eo n 28 Fe bruar y 1873. Hi s con se cr ati on to  theEpi scopate  took plac e o n19 March 187 3 ,the princi pal  consecrator  wa s Arch bi sho p  (lat erCardi nal) H e nry Ed ward Mann in g  of We s tminste r ,  a nd t he principal co-c o ns e crators were B ishopRo b er t Cor nth waite of B ev erley (laterB is h o p  of Leeds) and Bi shop JamesC had wick o fHex h am and  Newc as t le. 

He died i n of fice on 9  April 1894 at St Edwa rd's C oll ege , ag e d70 .
Re f ere n ce s
B ibl iography 
 
Cate gory : 1 8 2 4 bi rth s
Ca tegor y:1894 deaths 
Ca tego r y:1 9th-c entur y Ro ma n Cat holicbisho ps 
Category:Alumn i of  Ushaw Co lle ge 
Ca te gory: I rish e mig ran ts to t he Unit e d K in g d o mCategory:People fr om C ou nty Mona ghan
C a te go r y:Post-R ef orm atio n Roman  Cat h ol ic bisho ps inE ng la nd Apot om e (mat he mat ics )

In thehistor ical stu dy of mathematics, a n  apotome is a li n e  s e gmen t f ormed froma lo n gerline se gme n t bybreak in g  i t  into two parts, on eof whi ch is  commensurabl e only inp o w er to th e wh o le ;  the other par t isthe apotom e . In thi s def inition,  two line s egmentsare  sa idtob e  " commensurable o nlyin  power"  wh en therat ioofthe ir  lengthsis an ir ra ti on al  nu mberb ut the r at ioof  th eir s q uaredlengt hs i sra t ion al.

Tr a ns l a tedin to  mod ern  a lgebr aicl ang uage, a n apotome  ca n  bein te rpreted  as a quadrat ic  irrationa lnum ber fo r m ed by su btracting one square ro o t of arat ional  num ber fromano ther.Thi s  conce pt ofthe a po tom e appea r s  i n E uc lid's Elem e n tsbegin ni ng i n bookX, where Euclid de f ine s two special  ki ndso f  a pot o me s . I na n a p o tome of the fir st kind, t he wh ole is rat i ona l,  whilein an a potom e  of the  second k ind, thepa rt s u b tra cted fromit is ra tional; b o th ki n ds  of a pot omes a ls o s atisf y an a d dit ional  condi ti on.  E uclid  P ropositi on XIII.6 states that,if a r ation alline segm ent issplit int o tw o pieces i n t hegolde n r a tio,then bo thp ieces  may be repres e nt eda s  a potomes.

R e f e ren ces
Cat e gory:M athe matical terminolo g y Andrés EloyMart í n ez
An d résEl oy Martínez Ro jas  ( b o rn 23 Ju ne  1963) is a  Mexican  a s trono mer, s cienti st andp o li t ician.  Hehas  named va rio us minor p la ne t s andalso  s ervedone th r ee-y e a r term as a depu ty in t he LX I I L egisl at ure oft he M exican Con gress repre sentin g Mo relos 

Episcopal career
He_was appointed_the Bishop of the_Roman Catholic_Diocese_of Liverpool_by_the Holy See_on 28 February_1873. His consecration to_the Episcopate took_place_on 19 March 1873, the principal consecrator was Archbishop (later Cardinal) Henry Edward Manning_of_Westminster, and_the_principal_co-consecrators were Bishop Robert Cornthwaite_of Beverley (later Bishop of_Leeds) and_Bishop James Chadwick of Hexham and Newcastle.

He died_in_office on 9_April 1894 at St Edward's College, aged 70.

References

Bibliography

 

Category:1824_births
Category:1894 deaths
Category:19th-century Roman Catholic bishops
Category:Alumni of_Ushaw College
Category:Irish emigrants_to_the_United Kingdom
Category:People from County_Monaghan
Category:Post-Reformation Roman Catholic bishops in England_Apotome (mathematics)

In the historical study of_mathematics, an apotome is a line segment_formed from a longer line segment_by breaking it into two_parts, one_of which is commensurable only_in power to_the whole;_the other part_is the apotome. In this definition,_two line segments_are said to be "commensurable only_in_power" when the_ratio_of_their lengths_is an irrational_number_but the_ratio_of their squared lengths is rational.

Translated_into_modern algebraic language, an apotome can be_interpreted as a quadratic_irrational_number formed by subtracting_one square root of a_rational number from another.
This concept of_the apotome_appears in_Euclid's Elements beginning in book X, where Euclid defines two special_kinds of apotomes. In an apotome_of the first kind,_the whole_is_rational, while in_an_apotome of_the second kind, the part subtracted from_it is_rational; both kinds of apotomes also_satisfy an additional condition.__Euclid Proposition XIII.6 states that, if_a rational line segment is split_into two pieces in the_golden_ratio,_then both pieces may be_represented as apotomes.

References

Category:Mathematical terminology Andrés Eloy_Martínez

Andrés Eloy Martínez_Rojas (born 23 June 1963) is a_Mexican_astronomer, scientist and politician. He has_named_various minor planets and also served_one_three-year_term as a deputy in_the LXII Legislature of the Mexican_Congress representing Morelos