10 JEE-Mathematics
%ff&Tb e^vb /.,/ 1 . c%x&iodiod.. x æö æö =-+-ç÷ ç÷ èø èø
c%x& fs abcfnba fc .,/ 1 . iod..x æö -+-> ç÷ èø or fc .,/ 1 . iod.. x æö +<-ç÷ èø or fc . 1 . .%.,/& x - æö +>ç÷ èø or fc 1 . ./ x +> or fc 1 . . x > or fc x.,1 9 . or fc - 9 x 9 . \ A%c& : %-) .&
Illustration 7 : Cfna teb aom^fn c%x& : . X|x|2Z.. webrb X+Z abnotbs drb^tbst fntbdbr cun`tfon+
Solution : [ ] |x|2.. ->
so [ ] x2.. -> or [ ] x2.. -<-
[ ] x.3 > [ ] x3 <x.4 ³ or x3 <- %Kot Mossf_ib&
Þ x £ .4 or x ³ .4
sox Î %¥) .4Z È X.4) ¥&
Illustration 8 : Cfna teb r^ndb oc coiiowfnd cun`tfons 7
%f&c%x& : . 50sfnx -
Solution : %f&c%x& : . 50sfnx -
. £ sfnx £ . \ O^ndb oc c : .. ) ..2 éù êú ëû
%ff& c%x& : ( ) / / / iod/iod%.3sfnx.& -+
%ff&c%x& : ( ) / / / iod/iod%.3sfnx.& -+ . £ .3 sfn/ x ( . £ .4 \ - £ iod/ %.3 sfn/x (.& £ iod/ .4 \ / iod/ .4 £ / iod/ %.3 sfn/ x ( .& £ / Kow `onsfabr - 9 / iod/ %.3 sfn/x ( .& £ / \¥ 9 / / // iodX/iod%.3sfnx.&Ziod// -+£= \ teb r^ndb fs %¥) /Z
Illustration 9 : Cfna teb r^ndb oc c%x& : xXxZ .xXxZ+) webrb X+Z abnotbs drb^tbst fntbdbr cun`tfon+
Solution : y : xXxZ{x} .xXxZ.{x}= +-+ \ {} ....yy .x y{x}{x}y.y=+Þ=Þ=- £ {x} 9 . Þ y -. .y £< -
O^ndb : X-) .,/&
Ao yoursbic * 0 7
%f& Cfna aom^fn oc coiiowfnd cun`tfons 7
%^& ( ) / %x.& .. %x&sfn.xx/ iod + =-+++
%_& 0/ %/x.& %x& x0x/x + = -+
%ff& Cfna r^ndb oc coiiowfnd cun`tfons 7
%^& ( ) / /.,/ %x&iodiod%x1x1& =++
%_& . %x& /`os0x = -
3+BNR>I LO FABKQF@>I CRK@QFLK 7
Qwo cun`tfon c # d ^rb s^fa to _b bqu^i fc 7
%^& Qeb aom^fn oc c : teb aom^fn oc d
%_& Qeb `o*aom^fn oc c : `o*aom^fn oc d ^na
%`& c%x& : d %x&) cor bvbry x _biondfnd to tebfr `ommon aom^fn %f+b+ seouia e^vb teb s^mb dr^pe&
Illustration 10 : Qeb cun`tfons c%x& : iod %x .& iod %x /& ^na d%x& : iod x. x/æö ç÷èø ^rb fabntf`^i webn x ifbs fn teb fntbrv^i
%>& X.) /Z %?& X/) ¥& %@& %/) ¥& %A& %¥) ¥&
Solution : Pfn`b c%x& : iod %x .& iod %x /&+ Aom^fn oc c%x& fs x ; / or x Î %/) ¥& +++++%f& d%x& : iod x. x/æö ç÷èø fs abcfnba fc x. x/ ; - Þ x Î %¥) .& È %/) ¥&+++++%ff& Crom %f& ^na %ff&) x Î %/) ¥&+ >ns+ %@&
12 JEE-Mathematics
Ao yoursbic * 1 7
%f& >rb teb coiiowfnd cun`tfons fabntf`^i<
/ x x # f%x& : / x x %_& c%x& : x # f%x& : / x %`& c%x& : iod.-x/ # f%x& : /iod.-|x|
4+ELJLDBKBLRP CRK@QFLKP 7
> cun`tfon fs s^fa to _b eomodbnbous wfte rbspb`t to ^ny sbt oc v^rf^_ibs webn b^`e oc fts tbrms fs oc teb s^mb abdrbb wfte rbspb`t to teosb v^rf^_ibs+
Cor bx^mpibs 2x/ ( 0y/ xy fs eomodbnous fn x # y+ Pym_oif`^iiy fc) c%tx) ty& : tn c%x) y& tebn c%x) y& fs eomodbnbous cun`tfon oc abdrbb n+
Illustration 11 : Tef`e oc teb coiiowfnd cun`tfon fs not eomodbnbous < %>& x0 ( 5x/y ( 4 y0 %?& y/ ( x/ ( 2xy%@& // xy xy + %A& /xy. /yx. -+ -+
Solution : Ft fs `ib^r te^t %A& aobs not e^vb teb s^mb abdrbb fn b^`e tbrm+ >ns+ %A& 5+?LRKABA CRK@QFLK 7
> cun`tfon fs s^fa to _b _ounaba fc tebrb bxfsts ^ cfnftb J su`e te^t ½%x&½ £ J) " x Î A + 6+FJMIF@FQ # BUMIF@FQ CRK@QFLK 7
> cun`tfon abcfnba _y ^n bqu^tfon not soivba cor teb abpbnabnt v^rf^_ib fs `^iiba ^n fmpif`ft cun`tfon+ b+d+ teb bqu^tfons x0 ( y0 : . # xy : yx) abcfnbs y ^s ^n fmpif`ft cun`tfon+ Fc y e^s _bbn bxprbssba fn tbrms oc x ^ionb tebn ft fs `^iiba ^n Bxpif`ft cun`tfon+
Illustration 12 : Tef`e oc teb coiiowfnd cun`tfon fs fmpif`ft cun`tfon <
%>& /x . xb2 y .`osx++ = -
%?& y : x/ %@& xy sfn%x ( y&:- %A& / xiodx y sfnx =
Solution : Ft fs `ib^r te^t fn %@& y fs not `ib^riy bxprbssba fn x+ >ns+ %@& Ao yoursbic * 2 7
%f& Cfna teb _ounanbss oc teb cun`tfon c%x& : / 1 x x. +
%ff& Tef`e oc teb coiiowfnd cun`tfon fs fmpif`ft cun`tfon< %>& xy `os%x ( y& : -
%?& y : x0
%@& y : iod%x/ ( x ( .& %A& y : |x|
%fff& @onvbrt teb fmpif`ft corm fnto teb bxpif`ft cun`tfon 7
%^&xy : . %_&x/y : .+
.-+>MMIF@>QFLKP LC CRK@QFLK>I ORIB 7
Illustration 13 : Abtbrmfnb ^ii cun`tfons c s^tfscyfnd teb cun`tfon^i rbi^tfon+
./%./x& %x& .xx%.x& - æö += ç÷ èø webrb xΡ{-).}
Solution : Dfvbn ./%./x&// %x& .xx%.x&x.x - æö +==ç÷ èø +++%f&
Obpi^`fnd x _y . .x wb o_t^fn ../ /%.x&.. .x .. .x.x
æö +=-ç÷ ç÷èø ç÷ ç÷ è-øÞ ../ ./x.xxx æöæö ç÷ç÷+-=-+èøèø +++%ff&
>d^fn rbpi^`fnd x _y . . x æöç÷ èø fn %f& wb o_t^fn
Þ ..// . . .. x . .... x xx æö ç÷ æö ç÷ ç÷-+=-æöæö ç÷ èøç÷ç÷ç÷ èøèøèø
Þ ./x .%x&/x xx. æö ç÷-+=- èø ++++%fff&
su_tr^`tfnd %ff& crom %f& tebn ./ %x&./xx.x æö --=ç÷ - èø
Kow ^aafnd %fff& ^na %fv& wb dbt /x/ /%x& x..x =Þ x. %x& x. + = -
..+?>PF@ QO>KPCLOJ>QFLKP LK DO>MEP 7
%f&Ar^wfnd teb dr^pe oc y : c%x& ( _) _ Î ¡) crom teb hnown dr^pe oc y : c%x&
y=f(x)+b,b > 0
y=f(x)
y=f(x)–b,b < 0
Ft fs o_vfous te^t aom^fn oc c%x& ^na c%x& ( _ ^rb teb s^mb+ Ibt us t^hb ^ny pofnt x- fn teb aom^fn oc c%x&+ - xx yc%x& = = +
Qeb `orrbsponafnd pofnt on c%x& ( _ wouia _b c%x-& ( _+
Cor _ ; - Þ c%x-& ( _ ; c%x-& ft mb^ns te^t teb `orrbsponafnd pofnt on c%x& ( _ wouia _b iyfnd ^t ^ afst^n`b $_$ unfts ^_ovb teb pofnt on c%x&+
Cor _ 9 - Þ c%x-& ( _ 9 c%x-& ft mb^ns te^t teb `orrbsponafnd pofnt on c%x& ( _ wouia _b iyfnd ^t ^ afst^n`b $_$ unfts _biow teb pofnt on c%x&+
>``orafndiy teb dr^pe oc c%x& ( _ `^n _b o_t^fnba _y tr^nsi^tfnd teb dr^pe oc c%x& bftebr fn teb posftfvb y*^xfs afrb`tfon %fc _ ; -& or fn teb nbd^tfvb y*^xfs afrb`tfon %fc _ 9 -&) teroude ^ afst^n`b |_| unfts+
%ff&Ar^wfnd teb dr^pe oc y : c%x& crom teb hnown dr^pe oc y : c%x&
Qo ar^w y : c%x&) t^hb teb fm^db oc teb `urvb y : c%x& fn teb x*^xfs ^s pi^nb mfrror+ y=–f(x)
%fff&Ar^wfnd teb dr^pe oc y : c%x& crom teb hnown dr^pe oc y : c%x&
Qo ar^w y : c%x&) t^hb teb fm^db oc teb `urvb y : c%x& fn teb y*^xfs ^s pi^nb mfrror+ y=f(–x)
%fv&Ar^wfnd teb dr^pe oc y : |c%x&| crom teb hnown dr^pe oc y : c%x& |c%x&| : c%x& fc c%x& ³ - ^na |c%x&| : c%x& fc c%x& 9 -+ Ft mb^ns te^t teb dr^pe oc c%x& ^na |c%x&| wouia `ofn`fab fc c%x& ³ - ^na cor teb portfons webrb c%x& 9 - dr^pe oc |c%x&| wouia _b fm^db oc y : c%x& fn x*^xfs+
%v&Ar^wfnd teb dr^pe oc y : c%|x|& crom teb hnown dr^pe oc y : c%x&
Ft fs `ib^r te^t) c%|x|& : c%x&)xc%x&)x-
c%x& wouia _b fabntf`^i fn teb cfrst ^na teb courte qu^ar^nts %^s x ³ -& ^na ^s su`e teb dr^pe oc c%|x|& wouia _b symmbtrf` ^_out teb y*^xfs %^s %|x|& fs bvbn&+
%vf&Ar^wfnd teb dr^pe oc |y| : c%x& crom teb hnown dr^pe oc y : c%x& @ib^riy |y| ³ -+ Fc c%x& 9 -) dr^pe oc |y| : c%x& wouia not bxfst+ >na fc c%x& ³ -) |y| : c%x& wouia dfvb y : ±c%x&+ Ebn`b dr^pe oc |y| : c%x& wouia bxfst oniy fn teb rbdfons webrb c%x& fs non* nbd^tfvb ^na wfii _b rbcib`tba ^_out teb x*^xfs oniy fn teosb rbdfons+ y x |y|=f(x)
y x y=f(x)
%vff&Ar^wfnd teb dr^pe oc y : c%x ( ^&) ^ Î ¡ crom teb hnown dr^pe oc y : c%x&
y=f(x+a),a>0 y=f(x) y=f(x–a) a<0
%f& Fc ^ ; -) sefct teb dr^pe oc c%x& teroude $^$ unfts tow^ras ibct oc c%x&+ %ff& Fc ^ 9 -) sefct teb dr^pe oc c%x& teroude $^$ unfts tow^ras rfdet oc c%x&+ %vfff&Ar^wfnd teb dr^pe oc y : ^c%x& crom teb hnown dr^pe oc y : c%x& y=af(x), a >1 y=f(x) y=af(x), 0<a<1 x
Ft fs `ib^r te^t teb `orrbsponafnd pofnts %pofnts wfte s^mb x `o*orafn^tbs& wouia e^vb tebfr orafn^tbs fn teb r^tfo oc . 7 ^+
26 JEE-Mathematics
Tef`e fs ^ strf`tiy fn`rb^sfnd cun`tfon+ Qeus c%x& fs fngb`tfvb) dfvbn te^t c%x& fs onto+ Ebn`b teb dfvbn cun`tfon c%x& fs fnvbrtf_ib+
Fntbr`e^ndfnd x # y
Þ %y&/ ( 0%y& ( . bx : \ ( ) ( ) xx 061+.b021b y // -±---±+
Ebn`b ( ) x . 021b c%x& /-++ =
Ao yoursbic * 6 7
%f& Ibt c 7 X.) .Z ® X.) .Z abcfnba _y c%x& : x|x|) cfna c.%x&+
%ff& %x& : . ( ln%x ( /&) cfna c.%x&+ .2+LAA # BSBK CRK@QFLKP 7
@onsfabr ^ cun`tfon %x& su`e te^t _ote x ^na x ^rb fn fts aom^fn tebn
Fc
%x&%x&tebn fs s^fa to _b ^n bvbn cun`tfon %x&%x&tebn fs s^fa to _b ^n oaa cun`tfon
Kotb 7
%f& %x& - %-x& : - Þ %x& fs bvbn # %x& ( %-x& : - Þ %x& fs oaa+
%ff&> cun`tfon m^y nbftebr _b oaa nor bvbn+
%fff&Qeb oniy cun`tfon wef`e fs abcfnba on teb bntfrb num_br ifnb # fs bvbn ^na oaa ^t teb s^mb tfmb fs %x& : -+
%fv&Bvbry `onst^nt cun`tfon fs bvbn cun`tfon+
%v&Fnvbrsb oc ^n bvbn cun`tfon fs not abcfnba+
%vf&Bvbry bvbn cun`tfon fs symmbtrf` ^_out teb y*^xfs # bvbry oaa cun`tfon fs symmbtrf` ^_out teb orfdfn+
Ppb`f^i Kotb 7 Fc ^ cun`tfon %x& fs abcfnba ^s %^ ( x& : %^ x& tebn tefs cun`tfon fs symmbtrf` ^_out ifnb x : ^
%vff&Bvbry cun`tfon wef`e e^s $x$ fn ft$s aom^fn webnbvbr $x$ fs fn ft$s aom^fn) `^n _b bxprbssba ^s teb sum oc ^n bvbn # ^n oaa cun`tfon + f+b+
node06\B0B0-BA\Kota\JEE(Advanced)\Module Coding (V-Tag)\Enthuse\Maths\Function & Inverse Trigo. Function (II & III)\Eng\01_Function.p65
%vfff&Fc %x& fs oaa ^na abcfnba ^t x : -) tebn %-& : -+
%x&d%x& %x& ( d%x& %x& d%x& %x& + d%x& %x&,d%x&%do & %x&%od&%x& oaa oaa oaa oaa bvbn bvbn oaa oaa bvbnbvbn bvbn bvbn bvbn bvbn bvbn bvbn oaa bvbnnbftebr oaa nor bvbnnbftebr oaa nor bvbn oaa oaa bvbn bvbn bvbn oaanbftebr oaa nor bvbnnbftebr oaa nor bvbn oaa oaa bvbn bvbn
Illustration31 : Tef`e oc teb coiiowfnd cun`tfons fs %^rb& bvbn) oaa or nbftebr 7
%f&c%x& : x/sfnx %ff&c%x& : sfnx `osx %fff&c%x& : xx bb /+
Solution :
%f&c%x& : %x&/ sfn%x& : x/ sfnx : c%x&+Ebn`b c%x& fs oaa+
%ff&c%x& : sfn%x& `os%x& : sfnx `osx+
Ebn`b c%x& fs nbftebr bvbn nor oaa+
%fff&c%x& : x%x&xx bbbb // ++ = : c%x&+ Ebn`b c%x& fs bvbn
Illustration32: Fabntfcy teb dfvbn cun`tfons ^s oaa) bvbn or nbftebr 7
%f&c%x& : x xx . b./ ++%ff& f(x + y) = f(x) + f(y) for all x, y Î ¡
Solution : %f&c%x& : x xx . b./ ++ -
@ib^riy aom^fn oc c%x& fs ¡ ~ {-}+ Tb e^vb)
c%x& :
: xx xxxx x.. b./b./ +-+=++ : c%x& Ebn`b c%x& fs ^n bvbn cun`tfon+
%ff&c%x ( y& : c%x& ( c%y&cor ^ii x) y Î ¡
Obpi^`fnd x) y _y zbro) wb dbt c%-& : /c%-& Þ c%-& : Obpi^`fnd y _y x) wb dbtc%x& ( c%x& : c%-& : - Þ c%x& : c%x& Ebn`b c%x& fs ^n oaa cun`tfon+
Ao yoursbic * .- 7
%f& Tef`e oc teb coiiowfnd cun`tfons fs %^rb& bvbn) oaa or nbftebr 7
%^&c%x& : x0 sfn 0x %_&c%x& : // xx bb /x +
%`&c%x& : xx xx bb bb + %a&c%x& : x/ ( /x
.3+MBOFLAF@ CRK@QFLK 7
> cun`tfon %x& fs `^iiba pbrfoaf` fc tebrb bxfsts ^ posftfvb num_br Q su`e te^t %x(Q& : %x& : %x Q&) cor ^ii v^iubs oc x wftefn teb aom^fn oc+ Pm^iibst posftfvb Q %fc bxfsts& fs `^iiba cuna^mbnt^i pbrfoa oc cun`tfon %x&+
Kotb 7
%f&Laa powbrs oc sfnx) `osx) sb`x) `osb`x ^rb pbrfoaf` wfte pbrfoa /p
%ff&Konb zbro fntbdr^i powbrs oc t^nx) `otx ^rb pbrfoaf` wfte pbrfoa p+ %fff&Kon zbro bvbn powbrs or moauius oc sfnx) `osx) sb`x) `osb`x ^rb pbrfoaf` wfte pbrfoa p %fv& %Q& : %-& : %-Q& ) webrb Q fs teb pbrfoa+
%v&fc %x& e^s ^ pbrfoa Q tebn %^x ( _& e^s ^ pbrfoa Q,|^|%^ ¹ -&+
Mrooc 7
Ibt %x ( Q& : %x& ^na X^%x ( Q$& ( _Z : %^x ( _& %^x ( _ ( ^Q$& : %^x ( _& %y ( ^Q$& : %y& : %y ( Q& Þ Q : ^Q$ Þ Q$ : Q ^
%vf&Fc %x& # d %x& ^rb pbrfoaf` wfte pbrfoa Q. # Q/ rbspb`tfvbiy) tebn ^ pbrfoa %nbba not _b cuna^mbnt^i& oc %x& ±d%x& fs I+@+J+ oc %Q.) Q/&+
%^&I@J oc Q. # Q/ fs abcfnba webn Q.,Q/ fs r^tfon^i+
%_&I@J oc ^pI@J oc %^) p& ) _qE@C oc %_) q&
Fn `^sb fc tebrb bxfsts ^ posftfvb H su`e te^t H 9 I@J oc Q. ^na Q/ ^na ovbr^ii cun`tfon rbpb^ts ftsbic ^ctbr bvbry H) tebn cuna^mbnt^i pbrfoa oc teb cun`tfon wfii _b H+
%vff&Bvbry `onst^nt cun`tfon fs ^iw^ys pbrfoaf`) weosb cuna^mbnt^i pbrfoa fs unabcfnba+ %vfff&Mbrfoaf` cun`tfons ^rb non fnvbrtf_ib+
Illustration 33 : Cfna teb cuna^mbnt^i pbrfoas %fc pbrfoaf`& oc teb coiiowfnd cun`tfons) webrb X+Z abnotbs teb drb^tbst fntbdbr cun`tfon
%f&c%x& : bln%sfnx& ( t^n0x `osb`%0x 2&%ff& c%x& : x Xx _Z) _ Î ¡
%fff&c%x& : sfnx`osx sfnx`osx + +
%fv&c%x& : t^n / p XxZ
%v&c%x& : `os%sfnx& ( `os%`osx& %vf&c%x& : %.sfnx&%.sb`x& %.`osx&%.`osb`x& ++ ++
%vff&c%x& : xXxZ`osx`os/x++++++++`osnb -+p+p++p
Solution : %f&c%x& : bln%sfnx& ( t^n0x `osb`%0x 2& Mbrfoa oc blnsfnx : /p) t^n0 x : p
`osb` %0x 2& : 2 3 p \ Mbrfoa : /p
%ff&c%x& : x Xx _Z : _ ( {x _} \ Mbrfoa : .
%fff&c%x& : sfnx`osx sfnx`osx + +
Pfn`b pbrfoa oc |sfnx ( `osx| : p ^na pbrfoa oc |sfnx| ( |`osx| fs / p + Ebn`b c%x& fs pbrfoaf` wfte p ^s fts pbrfoa
%fv&c%x& : t^n / p XxZ
t^n / p Xx ( QZ: t^n / p XxZ Þ / p Xx ( QZ : np ( / p XxZ \ Q : / \ Mbrfoa : /
%v&Ibt c%x& fs pbrfoaf` tebn c%x ( Q& : c%x& Þ `os%sfn%x ( Q&&( `os%`os%x ( Q&& : `os%sfnx& ( `os%`osx& Fc x : - tebn `os%sfnQ& ( `os%`osQ& : `os%-& ( `os%.& : `os `os / p æö ç÷ èø ( `os sfn / p æö ç÷ èø
Ln `omp^rfnd Q : / p
%vf&c%x& :
%.sfnx&%.sb`x& %.`osx&%.`osb`x& ++ ++ :
%.sfnx&%.`osx&sfnx `osx%.sfnx&%.`osx& ++ ++
Þ c%x& : t^nx
Ebn`b c%x& e^s pbrfoa p+
%vff&c%x& : xXxZ`osx`os/x++++++++`osnb -+p+p++p
Mbrfoa oc x XxZ : .
Mbrfoa oc |`ospx| : .
Mbrfoa oc |`os/px| : . /
Mbrfoa oc |`osnpx| : . n
Po pbrfoa oc c%x& wfii _b I+@+J+ oc ^ii pbrfoa : .
Illustration 34 : Cfna teb cuna^mbnt^i pbrfoas %fc pbrfoaf`& oc teb coiiowfnd cun`tfons) webrb X+Z abnotbs teb drb^tbst fntbdbr cun`tfon
%f&c%x& : bxXxZ ( sfnx %ff&c%x& : sfn`osxx /0 pp + %fff& c%x& : sfn`osxx 0/0 pp +
Solution : %f&Mbrfoa oc bxXxZ : . pbrfoa oc sfnx : /p
Q I+@+J+ oc r^tfon^i ^na ^n frr^tfon^i num_br aobs not bxfst+ \ not pbrfoaf`+
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be brought from a vessel which had recently reached the coast. A great event was the arrival of three vessels with two hundred Spaniards, eighty horses, and a full complement of arms, ammunition, and other effects, partly bought and partly enlisted by the agents whom Cortés had despatched to the Islands during the previous autumn. Among the new-comers were Julian de Alderete of Tordesillas, appointed royal treasurer for New Spain, and the Franciscan Pedro Melgarejo de Urrea of Seville, bearing a supply of papal indulgences for the men who had been engaged in the crusade. That the soldiers were conscious of frequent transgressions may be judged from the suggestive and not wholly reverential observation of Bernal Diaz, that “after patching their defects the friar returned to Spain within a few months, a rich man.”[1075]
Cortés was cheered by offers of submission and alliance, owing partly to the good offices of Tezcucans and other allies. Some came from places quite distant, such as Nautla and Tuzapan, on the coast north of Villa Rica, laden as usual with presents.[1076] Another pleasing evidence of still more devoted loyalty came not long after from the south, from the country of the valiant Chinantecs, of the long pikes. During the great uprising, when Spaniards in small or straggling parties had everywhere been slaughtered, this people faithfully protected the two soldiers who happened to be with them, and were in return aided by their prowess and advice to achieve victories over adjoining tribes. One of these men, Captain Hernando de Barrientos, sent two natives in April with a letter to his countrymen imparting the assurance that Chinantla and its six subtowns were loyal.[1077]
The recent successes and the arrival of the two hundred men induced Cortés once more to propose peace to Quauhtemotzin. To this end, during passion week, he bade some of the captured nobles proceed to Mexico with a letter as a symbol of their commission, and
impress upon their master the superiority in arms and skill of the Spanish forces, their constant and large reinforcements, and their unvarying success in the field. They must point out the generous and humane treatment of the provinces which had submitted, and assure the Aztec leaders that equal forgiveness would be accorded them. Refusal to return to their allegiance would lead to the destruction of themselves and their city. Only two of the captives ventured to accept the commission, for according to Aztec articles of war any noble who returned to his country after having been captured by an enemy was doomed to decapitation unless he had performed some extraordinary deed.[1078]
No answer came from Mexico, and it was afterward learned that the messengers had suffered death. The Aztec ruler had not even given a thought to peace. He was watching his opponents, prepared to take advantage of any neglect or relaxation in their effort. No sooner had Sandoval been induced by peaceful appearances to retire from Chalco than Aztec forces again prepared to invade the province. The Chalcans had due warning, and close upon the heels of Sandoval came two messengers lamenting louder than ever, and exhibiting a painting wherein were named the many towns whose forces were coming upon them, fully fifty thousand strong. These constant menaces and movements were exasperating, and Cortés resolved personally to inflict a lesson which might be lasting. At the same time he proposed to complete his reconnoissance of the lake region and encourage his troops with spoils from hostile localities whereon the Aztecs yet relied for support.[1079]
Cortés selected thirty horse, three hundred infantry, a number of Tlascaltecs, and over twenty thousand Tezcucans, under Prince Ixtlilxochitl, to which twice that number of other allies were added on the way. A large proportion of archers and aquebusiers were taken, together with Alvarado, Olid, Alderete, Melgarejo, and others, while Sandoval was left in charge of Tezcuco, with instructions to watch
and promote the completion of the brigantines against which several incendiary attempts had been made.
The expedition left Friday, the 5th of April, and passed through Chalco, Tlalmanalco, and Chimalhuacan,[1080] and crossing in a south-westerly direction into the Totolapan province, they entered the hills which form the southern border of the Mexican valley. By this time the forces had assumed proportions hardly inferior to those of the Iztocan campaign, when over one hundred thousand moved against the foe. Highly picturesque was the spectacle of this army, its naked hordes of warriors relieved by plumage and glittering iztli points which rose above the broad line of gaudy shields; its white adventurers in mail of cotton and metal, surmounted by bright helmets, and armed knights on proudly stepping steeds: picturesque in particular as it wound in almost endless line along the rounded slopes of the cliffs, or climbed in clearly defined file across the hilltops, only to descend again into gulches gloomy as their own sinister purpose.
Alarmed by the invasion, the inhabitants had abandoned their valley homes, and had sought refuge on the summits, whence they hurled missiles at the passing lines. Little attention was paid these irregular bands, composed as they were to a great extent of women and children. On entering the Tlayacapan Valley, however, and observing on the craggy sides of an almost perpendicular isolated rock, perched there like an eagle’s nest, a place of refuge peopled with more pretentious opposers, in a fit of insensate folly Cortés ordered the place to be assailed. He seemed to think the honor of the army demanded it, and was ready to stake the lives of valuable men on its destruction.
Orders were given to attack from three several sides, the steepest being assigned to Alférez Corral, a brave and spirited leader. Verdugo and Villafuerte were given another side, and Ircio
and Monjaraz the third. Each party consisted of about threescore men, and included archers and arquebusiers. At a given signal all rushed forward to the ascent. Soon they were on hands and knees, crawling over projections and pulling themselves up by means of shrubs. All the while stones and darts rattled on helmet and breastplate; and huge rocks came rolling down upon them. In vain they sought shelter in crevices and under crags; they must face the storm. Bernal Diaz followed Corral, and after receiving many a hard knock they gained what was called two turns of the rock. There they paused and looked around, wondering at their success thus far. Supporting himself against a small tree, his face bathed in blood, his banner rent, Corral said, “Señor Diaz, it is useless to advance farther; not a man will survive.” Then they shouted a warning to Pedro Barba, at the head of his archers, not to climb farther “The order is to advance!” was the reply. The next moment Barba was wounded by a stone, and a soldier at his side was killed. Cortés then sounded the recall, but not until eight brave men had laid down their lives, victims of their commander’s puerility, and of the rest most of them returned wounded.[1081]
The recall was likewise prompted by the approach of a considerable force in the valley. This the cavalry charged and quickly routed, following in close pursuit, though the broken ground soon enabled the fugitives to gain shelter. During this ride some of the horsemen came, a league beyond, to another hill fortress, strong in its natural features, and held by a large force. Near by were some springs. The need of water was pressing, which afforded a plausible excuse for abandoning the scaling of Tlayacapan, and the whole force was moved to the springs. Early next morning Cortés examined the approaches to the new stronghold. It extended over three hills, the central one exceedingly steep and held by the largest force; the others easier of ascent, though higher, and occupied by smaller numbers. In reconnoitring, Cortés advanced toward the
centre. This movement led the occupants of the other hills to infer an attack on the central height, and they began to abandon their positions with a view to reënforce the threatened point. Observing this, Cortés ordered Barba to occupy the most commanding elevation with some fifty arquebusiers and archers, while he himself continued to scale the centre as a feint, for there was little hope of capturing a point so steep and strongly held. The stones and darts rained here as previously, and man after man was struck down, some bleeding freely from the wounds sustained.[1082]
Meanwhile Barba’s sharp-shooters had made so effective a use of their weapons that within half an hour the volleys from the fortress ceased, and the women began to wave their robes in token of truce, shouting their submission. Cortés graciously met the advances, and extended full pardon. He also prevailed on the chiefs to induce the Tlayacapans to submit. On the extensive surface of the rock were collected all the inhabitants of the neighborhood, with their effects, which Cortés ordered not to be touched.[1083]
The army remained encamped for two days to refresh themselves after their arduous march, and after sending the wounded to Tezcuco, Cortés proceeded to Huastepec. The report of the clemency extended to preceding settlements had a reassuring effect on this town, whose cacique came forth to welcome them, and tender his palace for their entertainment. This was situated in a garden, celebrated throughout New Spain for its beauty and extent, and the immense variety of its plants, collected partly for scientific purposes. A river with tributary canals flowed through its grounds, which extended over a circuit of nearly two leagues, murmuring its melody in unison with winged songsters hidden in arbors or playing between bush and hedge, mingling their bright color with the green expanse. Adjacent were steep rocks, on whose smooth surface were sculptured the portraits of noted warriors, statesmen, and orators, with hieroglyphic inscriptions of their fame. It was a paradise formed
equally for student and idler, and to the weary soldiers no spot could perhaps have proven so grateful. Cortés certainly grows ecstatic in describing it, declaring it “the largest, most beautiful, and freshest garden ever seen.”[1084] Tempting as was the retreat, Cortés tore himself from it the following day, and proceeded in a south-westerly direction to Yauhtepec. Although many warriors were gathered there, they fled on the approach of the Spaniards, and were chased, with some slaughter, for about two leagues, into the town of Xiuhtepec. [1085] The women and effects there found were appropriated as spoils, and rendered agreeable the two days’ stay. The ruler failing to appear, the place was fired, and terrified by this warning the lord of Yauhtepec hastened to proffer submission.
After a day’s hard march the army came in sight of Quauhnahuac,[1086] capital of the Tlahuicas. They were one of the Nahuatlaca tribes, which according to tradition had entered the Anáhuac country to supplant the Toltecs. Coming rather late, they found their brethren already in possession of the lake region, and so they crossed the range to seek a home on the headwaters of the Zacatula, where soon a number of settlements rose round Quauhnahuac. They afterward fell under the sway of the Chichimecs, and finally the Aztecs took advantage of internal discord to establish sovereignty,[1087] maintaining it by a garrison in the capital. This was a natural stronghold, situated on a tongue of land between two steep ravines over forty feet in depth, and through which ran a little stream during the rainy season. It was further protected by strong walls, particularly on the side where a strongly guarded gate opened to a fine stretch of country. Two other entrances faced the ravines, sometimes spanned by bridges, which were now removed.
Situated at the gateway to the tropical southern valleys, between which and the colder lake region interposed a range of mountains,
the spot stood as a new Eden in its manifold beauties. A sight even of the pine-fringed mountains that rolled off toward the north, with their green slopes shaded by oak and birch, and bathed in soft though bracing airs, was refreshing to the indolent inhabitants of the burning plain beyond. On the other hand the sturdy toilers of the northern plateaux might in this sunny south seek relaxation in the varied charms of a softer air balmy with the incense of a more lustrous vegetation.[1088]
It was an opulent community that of Quauhnahuac, surrounded as it was by endless resources and advantages, and the people were in no mood tamely to yield their wealth to invaders. And in this determination they were sustained by their lord, Yohuatzin,[1089] who was not only a vassal but a relative of Quauhtemotzin. Confident in the impregnable position of his city, in which supplies were ample, he replied with volleys to the demands of the Spanish forces as they appeared on the other side of the ravines. It seemed almost impossible to effect a crossing and climb the steep wall of the ravine to the city; nevertheless Cortés selected a position and began to open fire so as to occupy the attention of the garrison and cover the scaling parties.
While they were thus busied a brave Tlascaltec reconnoitred and came to a point half a league beyond, where the ravine was steepest and narrowed to an abyss. On the two sides grew two large trees, which inclined toward each other, with branches intertwined, forming a sort of natural bridge, though by no means secure. He called the attention of his party to this and led the way across, followed by several Spaniards. The natives, who were more accustomed to this kind of tactics, found comparatively little difficulty in swinging themselves across; but to the soldiers it was far from easy, and three of them, overcome by dizziness or weight of armor, slipped and fell. [1090]
The attention of the inhabitants being attracted elsewhere, a number of the invaders had gained a secure foothold within the city before they were observed. Even now a few resolute men might have driven them back, but such were wanting, and the sudden appearance of the dreaded white men, as if indeed they had dropped into the stronghold from some cloud made radiant by the sun whose reputed children they were, struck terror to the hearts of the poor natives. All impotent and nerveless, they permitted the daring strangers to lower the drawbridge, and turned to spread the panic. Meanwhile the reports of a formidable army advancing from the rear so wrought on the fears of the garrison that, when the handful who had crossed on the bushy bridge fell on them, they offered no resistance. This also allowed the scaling forces to pour in, so that within a short time the siege was turned into a rout, wherein the cavalry played a prominent part. The zeal of the allies was already indicated by smoky columns in different parts of the city, and the foot-soldiers hastened to share in the rich plunder and intercept the women.
Most of the fugitives had gathered on an adjacent height, and though no attempt was made that day to molest them, yet they began to fear that men who could so readily capture one of the strongest fortresses in the country, would find no difficulty in reaching them anywhere; therefore, after listening to the advice of messengers sent by Cortés, Yohuatzin concluded to surrender, and presented himself on the following day with a large retinue and rich presents. The Mexicans were as usual blamed for the opposition offered. He would have submitted before, but thought it best to expiate the fault of resistance by allowing the Spaniards to pursue, so that after spending their fury they might be more ready to forgive. [1091]
There was no time at present to extend the reconnoissance farther in this direction, and after a brief rest Cortés turned northward
to the lakes. The route over the mountains proved far more difficult than before, and after issuing from the pine forest the army entered a desert country terminating in a three-league pass through the Ajuzco Mountains. Here thirst became so intense that several natives succumbed.[1092] This suffering was relieved in a hamlet not far from the pass.
On the following day they passed through a fine and cultivated country toward Xochilmilco, that is to say, Field of Flowers, aptly named, for round almost every house, particularly on the outskirts, was a flower-garden enclosed by canals. Many of them were of the chinampa class, or floating gardens,[1093] the outgrowth of early Aztec weakness, now forming a picturesque border to the lake towns. Altogether the aspect was most pleasing, while the buildings of the central parts were artistic and striking. Besides the strength added by canals and moats, pile buildings were frequent, and intrenchments had been thrown up and drawbridges raised to defend the approach against any enemy of the Aztecs, for its loyalty to the queen city was fully as great as that of Iztapalapan. It was the most important place on the thickly settled fresh-water lake. Bishop Garcés relates that angels were heard to sing praises in the Mexican tongue when it was converted.[1094] The usual summons was issued by the Spaniards, and no heed being given, they attacked in three divisions by different approaches. The enemy fell back behind the raised bridges and intrenchments, whence they kept up a steady volley. The archers and arquebusiers replied briskly, and covered the van as it plunged into not very deep water and waded across to capture the fortifications. This effected, the foe was driven from one retreat to another. Seeing how affairs went, they sought to parley, but the pursuers paid no heed, regarding it as a trick to gain time for the removal of their families and property. Within half an hour the greater part of the city was won, and soldiers and allies were sacking as they advanced. The foe rallied now and then to cover their retreat, and in
one instance managed to despatch two soldiers who had allowed avarice to overcome prudence.
Not long after, a body of some ten thousand warriors, reënforced by fugitives from the city, was seen advancing from the rear as if to cut off retreat. They were already close at hand when first observed, and without losing a moment Cortés charged them at the head of a body of cavalry.[1095]
At first they boldly faced the animals, and fought so well as to severely wound four, besides several riders; but the mounted body kept breaking through their ranks and then turned to fall on the rear. This movement proved decisive, and the enemy dispersed in flight, the horsemen scattering in pursuit. Already weakened by the severe march across the mountains, the horse of Cortés became quite exhausted, and while its rider was striking right and left into a large body of fugitives, it fell. No other horseman being near, the enemy gathered courage and rushed upon the general, who had risen to his feet and stood with sword in hand to defend himself. It was a critical moment, and had not a brave Tlascaltec warrior come to his rescue thus opportunely, the career of the Estremaduran would have ended there; for he had already received a severe blow on the head and was about to be dragged away when thus rescued. The general’s body-guard then came up and cut in pieces his late stupid assailants —stupid because they might so easily have killed him, and did not. [1096] The pursuit was not long maintained, tired as the horses were, and remounting his steed Cortés led the way back to camp in the square.
Late as it was he superintended the filling of all the channels which broke the causeways, and the erection of defences, and ordered the soldiers to put in order their arms and prepare arrows. The forces were distributed at three points, and extra guards were posted for the night, together with bodies of troops at probable
landing-points. These precautions were prompted chiefly by the evident effort of the last body of the enemy to shut up the army within the city, a movement which boded other attempts, as Cortés rightly supposed.
When Quauhtemotzin heard that the Spaniards had marched against Xochimilco he called a council to consider the course to adopt, and the result was the despatch of reënforcements. Finding that the city had so easily fallen, he became furious. The gods were indignant at the outrages of the strangers. Arms must be employed more manfully, and, these failing, the loyal ones must let their nails grow, as the last means of protection. The first step should be the recovery of Xochimilco. That very night two thousand canoes were sent with some twelve thousand warriors, and a similar force by land, all approaching stealthily, without music.[1097]
The rumor of a probable night attack kept the Spanish camp on the alert, and advised of this, the enemy made no attack. At dawn their canoes were already swarming round the city, the inmates rending the air with loud and repeated shouts, and brandishing their weapons, those of the chiefs being captured Spanish swords. “With your own arms you shall be killed, and we will eat you!” they cried. “We fear you not, for Montezuma is dead!” At the same time the land forces were seen approaching, evidently to assist the fleet in besieging the Spaniards within the city, which would give the Mexicans greater advantage, as they had well learned during the siege of Mexico. Cortés understood the manœuvre, and leaving the greater part of the infantry and allies to guard the city, he sallied with most of the horse, in three parties, a few of the infantry and several hundred Tlascaltecs, breaking through the enemy’s ranks and gaining the foot of a hill in their rear, the Tepechpan.
While the enemy were rallying, Cortés led the horse round to their denser flank, and gave orders to the infantry to allure the
Mexicans by climbing the steepest part of the hill and pretending to escape. This succeeded, and the next moment they were attacked in several directions with such effect as to cause a panic and drive them in flight toward a quarter where one division of horse had taken a stand. Five hundred Mexicans covered the field and five leaders were among the captured, while the Spanish loss was only one soldier and a few allies, including three Tlascaltec chiefs, although a number were wounded. During the pursuit the foremost division of horse came upon a further Mexican reënforcement, estimated at ten thousand, which rallied the fugitives and caused the pursuers to halt. Soon, however, the remaining force came up, the charge was continued, and the Mexicans routed.[1098]
Too tired for long pursuit, the Spaniards returned by ten o’clock in the morning to Xochimilco, where their garrison had repulsed the lake force. The fight had been fierce, and the soldiers had exhausted all their ammunition, capturing in return two Spanish swords. These victories brought little satisfaction, however, for the captives gave information that the forces so far sent were but detachments of the armies destined for Xochimilco, which must be recovered, and the Spaniards driven forth, if it cost the lives of all the men in Mexico. The Spaniards might defeat force after force, but even victory must so weaken them that the Mexicans would finally triumph. This seemed to be confirmed by the movements of the fleet, which, though repulsed, was still hovering thereabout.
Cortés now gave orders to burn the city, as a warning to the wilful inhabitants and preparatory to its evacuation. The soldiers, who had been interrupted in their plundering the day before, obeyed with alacrity. Xochimilco was a wealthy city, and not a Spaniard or ally but obtained an abundance of robes, feathers, and other effects, and even some gold, which helped to cheer those whom ordinary merchandise and slaves did not satisfy. The enemy had been watchful, however, and in their canoes they flitted round the city to
cut off stragglers. At one point quite a charge was made, wherein several Spaniards were wounded and four carried off alive. This event did more to cast a gloom over the army than many defeats, for all knew the fate of prisoners.[1099]
After a stay of three days, all fraught with hard fighting, the army filed out from Xochimilco, presenting the appearance of a dilapidated caravan rather than of a reconnoitring and fighting expedition, so much so that Cortés thought it necessary to remonstrate, but in vain. The enemy hovered about like vultures, to harass them in what they regarded as a retreat. The march was made in regular fighting order, with cavalry distributed in three sections, in van, rear, and on flank. In order to complete the reconnoissance, a north-westerly route was taken to Coyuhuacan, the centre of a series of inner towns which lay clustered within a radius of a league and a half, along the shores or upon islands in the lake, all picturesque in their pyramidal temples and their white walls, which gleamed amidst blooming orchards and shady groves. Coyuhuacan itself was a beautiful town, and Cortés felt so captivated with it that he afterward made it for some time his favorite residence.[1100] It had been evacuated, but toward and beyond Mexico the lake teemed with canoes, while in every direction spread one continuous extent of farms and hamlets, connected by causeways and roads with busy traffic. To Alderete and friar Melgarejo this was a novel scene, and they could not refrain from expressing their admiration at the enterprise and prowess of Cortés and his followers in undertaking so vast a conquest. God’s aid alone could have enabled them to succeed as they had done.[1101]
The army remained here over the following day, chiefly to examine the place as intended head-quarters of a besieging force. It was found satisfactory; and while arrows were prepared and the wounded tended, the general advanced along the causeway leading to Mexico and expended his remaining ammunition in the useless
capture of the temple fortress of Xoloc,[1102] during which a number of soldiers were wounded, though the enemy suffered considerably. After offering to heaven the fiery sacrifice of pagan temple, the army proceeded through Tlacopan without halting, for they had no ammunition, and this place had been examined on the previous expedition. This unexpected haste encouraged the Mexicans to come forth in great numbers and attack the baggage train and rear. Owing to the level nature of the ground the cavalry found no difficulty in repelling them, yet they caused more trouble, and succeeded even in carrying off two of the favorite equerries[1103] of Cortés. He was deeply grieved at the loss, and partly with a view to avenge them, partly to inflict a lesson which should save the army from such annoyance, he formed an ambuscade beside the road with twenty horse. Seeing the other ten horses engaged as formerly in covering the rear, the Mexicans continued their pursuit. At a favorable moment the hidden horsemen appeared, and soon over a hundred of the flower of the Mexicans lay dead upon the ground,[1104] their rich panoplies, dresses, and arms offering a pleasing addition to the already heavy plunder. Freed from further molestation, the army proceeded through Azcapuzalco and Tenayocan to Quauhtitlan, all deserted. Here the army clustered round camp fires of green wood, wet from a recent shower and supperless. Next morning they followed the route already pursued during the flight from Mexico, round Zumpango Lake through Citlaltepec, and thence through Acolman to Tezcuco.[1105]
A mass of booty and slaves being now at hand, a general distribution was ordered, the second in Tezcuco. Again, says Bernal Diaz, Cortés disregarded his promises and secured not only for himself the objectionable fifth, but allowed his favorites to carry off the prettiest women before they were brought forward at auction. Many who remembered the former tricks hid their women and said they had escaped, or they declared them free servants from allied
tribes; while a few managed to obtain a private branding, paying the fifth required. A large proportion of the soldiers were so heavily in debt for stores and fifths that their booty left them no surplus.[1106]
While the reconnoitring expeditions had on the whole been fraught with pecuniary benefit and glory, they had nevertheless served to open the eyes of many to the difficulty of the great purpose, the capture of Mexico. This was particularly the case with the Velazquez party, whose adhesion before the Tepeaca campaign had been compulsory, and after it mercenary in its motives. Every obstacle to them appeared terrible, magnified through constant fear of the dreaded stone of sacrifice, on which so many comrades had already been laid. And this they were encountering for what? the advancement of an envied usurper and a pecuniary reward far beneath their expectations. The failure at Iztapalapan, the repeated inroads of the Mexicans, unabashed by constant repulses, and the hardships of the campaigns, particularly the last, all tended to support their arguments against Cortés’ plans as chimerical, involving long delays, constant toil, and waste of life, and with poor recompense save for Cortés and his favorites.
Presently the affair assumed the color of conspiracy, headed by Antonio de Villafañe, a common soldier from Zamora, who is claimed by Herrera to have had the active or passive sympathy of some three hundred malcontents, nearly one third of the army. The professed object was to secure a pliable leader who would consult the wishes of the soldiers, even those desirous of returning. Such a man, and withal of great influence and valor, was Verdugo, the brother-in-law of the all-powerful patron Velazquez, and him the conspirators chose as the new captain-general, unknown to himself, since he might prove too honorable to engage in plots against the commander. As a reward for his own efforts Villafañe claimed the position of alguacil mayor, while other friends and influential men of Narvaez were assured of the remaining offices, from alcalde mayor
and maestre de campo downward, now held by the retainers of Cortés, as well as a share in the arms and other effects of the doomed number.[1107] It was arranged that when Cortés was seated at table with his intimate friends, as Alvarado, Sandoval, Olid, and Tápia, a letter was to be handed him, as if coming from his father, and while he was reading, the conspirators should fall on and stab him and his supporters, since all must be removed who might prove troublesome. The new officers were thereupon to be proclaimed, together with the liberal plan agreed on, by which it was hoped to allure even the friends of Cortés.
There were too many in the secret, however, and Cortés was a man of magnetic influence. At the eleventh hour, two days after the return from Xochimilco, says Diaz, an accomplice, struck with compunction, rushed distractedly to the feet of Cortés and implored pardon for having even dared to listen to the vile machinations. He thereupon revealed the plot and stated that Villafañe carried the names and details on a list in his breast-pocket. Cortés quietly summoned his captains. He represented the need for a “remedy, since, besides the scandal, it was evident that all the Spaniards must perish if once they turned one against the other; and to this end not only declared foes but allies would join.”[1108]
Attended by Sandoval and others, Cortés hastened to the house of the accused and found several persons assembled. Some were secured as they sought escape. Villafañe found time to take a paper from his breast and tear it in pieces, but Cortés gathered and arranged them,[1109] and was grieved to read the names of quite a number of promising persons whom he had honored and regarded as friends. Villafañe confessed the details of the plot, which had been forming since the Tepeaca campaign. A court-martial was held, presided over by Cortés himself, and there being no doubt of his
guilt, the accused was condemned to death and promptly hanged from the window of his dwelling.[1110]
Cortés had probably no doubt regarding the guilt of the persons named on the list, but the prosecution of so many notable men might not be prudent, and would only widen the breach between himself and the malcontents and gain them sympathy. The day following the execution the general called a meeting. Many were the consciences that pricked their possessors to trembling on that occasion. But the sage Cortés preferred the traitors should risk their necks in winning for him Mexico, rather than himself to break them with a rope.
Napoleon, who in national warfare could open with his sword the veins of the people until there poured forth torrents of blood, shrank in horror from blood shed in civil broils. It was policy with Cortés, however. So, after finishing his narration of the conspiracy, he coolly informed them that Villafañe had refused to reveal his accomplices, and he could not therefore name the guilty. There were no doubt men amongst them with real or fancied grievances which may have induced them to harbor resentment; but let them frankly state their wrongs and he would seek to right them. If he had erred, let the error be named. The conclusion of the affair created general satisfaction. Thankful for their escape, the guilty sought both by words and deeds to prove their devotion, and although Cortés kept his eye upon them, there was no indication that he suspected any. He rather sought to win them back with favors.[1111] So impressed were his intimate followers by the risk to which so valuable a life had been exposed that they insisted on his accepting a body-guard of twelve select men, under the command of Antonio de Quiñones, an hidalgo of Zamora,[1112] who watched over him day and night.
[1062] This is according to Cortés; others differ slightly, and Ixtlilxochitl increases the Tezcucan force to 60,000. Hor. Crueldades, 13.
[1063] From tocatl and xal, spider and sand. Chimalpain, Hist. Conq., ii. 29. The lake in which it lies is divided about the centre by an artificial causeway about one league long, running from east to west, the southern water being now known as San Cristóbal Ecatepec, from the town of that name, and the northern water as Xaltocan or Tomanitla, San Cristóbal being also the general term for both waters
[1064] See Native Races, ii v
[1065] Bachiller Alonso Perez, afterward fiscal of Mexico Bernal Diaz, Hist Verdad , 135
[1066] This incident was commemorated by some poetic follower in a ballad which became a favorite with the conquerors:
En Tacuba está Cortés, Con su esquadron esforçado, Triste estaua, y muy penoso, Triste, y con gran cuidado, La vna mano en la mexilla, Y la otra en el costado
Which may be translated literally:
In Tacuba stands Cortés, With his troopers strong and brave: Sad he was and deeply grave; Sad, and heavily oppressed With one hand his cheek he pressed; Against his side, the other
[1067] So runs Bernal Diaz’ account, which appears a little exaggerated, for recently Cortés had shown the greatest caution, and would hardly have allowed himself to be so readily trapped on so memorable a spot Hist Verdad , 126 Cortés states that not a Spaniard was lost, though several Mexicans fell Cartas, 187
[1068] Herrera, dec iii lib i cap vii
[1069] They begged permission to return home, says Chimalpain, Hist Conq , i 31 Herrera relates that the efforts of Ojeda, by Cortés’ order, to take from the
Tlascaltecs the gold part of their booty so offended them that they began to desert. The extortion was accordingly stopped, dec. iii. lib. i. cap. vii. Clavigero doubts the story Prescott regards the departure of the allies as distasteful to Cortés; but we have seen that he did not care at present to encumber himself with too many unruly auxiliaries to prey upon the peaceful provinces The Tlascaltecs would willingly have remained to share in raiding expeditions
[1070] Including 8000 Tezcucans under Chichinquatzin Ixtlilxochitl, Hor Crueldades, 15 On March 12th, says Vetancurt, Teatro Mex , pt iii 154
[1071] Also known as Chimalhuacan-Chalco, to distinguish it from Chimalhuacan on Tezcuco Lake
[1072] Lorenzana inspected the position in later times Cortés, Hist N Esp , 214
[1073] ‘Que todos los que allí se hallaron afirman ’ Cortés, Cartas, 190 The general lauds the achievement with rare fervor for him Bernal Diaz sneers at the river of blood story; but then he was not present to share the glory The Roman Mario was less dainty than these Spaniards under a similar circumstance, commemorated by Plutarch; or as Floro more prosaically puts it: ‘Ut victor Romanus de cruento flumine non plus aquæ biberit quam sanguinis barbarorum ’ Epitome, lib. iii. cap. iii.
[1074] Fifteen, says Bernal Diaz Chimalpain, the Chalcan narrator, states that his tribe lost 350 men, but killed 1500 foes, capturing the captain-general, Chimalpopocatzin, a relative of the emperor, who now became a captain among the Tezcucans, and was killed during the siege. Hist. Conq., ii. 34. Some of these facts are evidently not very reliable. He also assumes that Sandoval lost eight soldiers on again returning to Tezcuco.
[1075] The ‘comissario’ or clerk in charge of the bulls was Gerónimo Lopez, afterward secretary at Mexico. Bernal Diaz, Hist. Verdad., 129. This author names several of the arrivals, some of whom became captains of vessels. A number also arrived during the following week, he adds, notably in Juan de Búrgos’ vessel, which brought much material.
[1076] Gomara mentions also Maxcaltzinco as a distant place. Hist. Mex., 186.
[1077] The chiefs were awaiting orders to appear before Cortés. The general told them to wait till tranquillity was more fully restored. The name of the other soldier was Nicolás. Cortés, Cartas, 203-5. Herrera assumes that Barrientos arrived in camp during the late Tepeaca campaign, dec. ii. lib. x. cap. xvii.
[1078] Of the rank and file none suffered penalty on returning, for captivity was regarded as disgraceful only to a noble. Native Races, ii. 419.
[1079] Bernal Diaz states that the soldiers were tired of these repeated calls, many being also on the sick-list, but Cortés had now a large fresh force only too eager for a fray attended with spoliation
[1080] According to a native painting the army entered here April 5th, which is a day or two too early, and received a reënforcement of 20,000. See copy in Carbajal Espinosa, Hist Mex , ii 523
[1081] So says Bernal Diaz, Hist Verdad , 130, who names four Cortés allows only two killed and twenty wounded; how many fatally so, he carefully omits to mention Cartas, 194
[1082] Twenty fell, says Bernal Diaz He speaks of two futile attempts on the previous evening to scale the central hill It seems unlikely for soldiers, tired by repulse and march, to undertake so difficult a feat, and that at the least assailable point
[1083] Yet Bernal Diaz relates a story to show that the order was a mere pretence
[1084] Cartas, 196; Torquemada, i 536
[1085] Some write Xilotepec Bernal Diaz mentions Tepoxtlan, which may have been visited by a detachment
[1086] Place of the Eagle Corrupted into the present Cuernavaca, which singularly enough means cow’s horn
[1087] See Native Races, v
[1088] Cortés was so captivated by the alluring clime and scenery that he made the town his favorite residence in later years It was included in the domains granted to him, and descended to his heirs Madame Calderon speaks of his ruined palace and church Life in Mexico, ii 50
[1089] Ixtlilxochitl, Hist Chich , 311 Brasseur de Bourbourg calls him Yaomahuitl
[1090] ‘El vno se quebró la pierna y se me desvanecia la cabeça, y todavia pasè yo, y otros veinte, ô trienta soldados ’ Bernal Diaz, Hist Verdad , 132 Solis misinterprets the passage, and gives this author credit for leading the party Hist Mex , ii 362 Vetancurt calls the district toward this spot Amanalco Teatro Mex , pt iii 155
