Principio de Arquimides
November 23, 2022 | Author: Anonymous | Category: N/A
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NKD@WFA UWÈO]NOH MA BHG@WH]@WN@ DHOQB]HM MA NKCAKNAWÆH DÆ_NOH OHB@W ^ @KMH_
Tarsnÿk 8.5 Uarn`m` 7578-8
MAK_NMHMA_ ^ DQAW\H MA AFUQLA _narrh Ihrak, Fhtubavnoj Mhkkh, Galhrhk` Hkmrîs {u885?:1=, u885?:31, u885?:38}Euknfnbnthr.amu.o` Ur`das`r< Uaøh Lhnmar Hbgart`
N.
@GLA]NT@_
s`gra ab ouarp` ncuhb hb pas` mab dbunm` mashb`lhm` p`r ab ouarp`‖.
Ohrhotarnzhr mndaraktas susthkonhs sÿbnmhs y bæqunmhs famnhkta bh famnonÿk ma su maksnmhm, utnbnzhkm` fît`m`s o`kvakon`khbas. Famnr y ohrhotarnzhr bh duarzh ma afpula qua raonga uk ouarp` nktr`muonm` ak uk dbunm` y aktakmar ab ohrèotar ma asth.
°Xuî ohrhotaræstnohs tnaka bh duarzh ma afpula0 °Ma quî phrèfatr`s mapakma0
Bh prasnÿk alaroa ukh duarzh s`gra ouhbqunar ouarp` sufarcnm` ak uk dbunm`. ]naka bh pr`pnamhm ma sar parpakmnoubhr ` bh supardnona mab ouarp`. Bh maksnmhm ma uk chs mapakma üknohfakta ma bh fhsh f`baoubhr. As nfp`rthkta jhoar k`thr qua bh duarzh ma afpula k` mapakma mab pas` mab `glat` sufarcnm`, snk` s`bhfakta mab pas` mab dbunm` mashb`lhm`, as maonr, o`k mndaraktas fhtarnhbas t`m`s ma ncuhb v`bufak axparnfakthrhk bh fnsfh duarzh ma afpula. °U`rqua as ukh duarzh hsoakmakta0
Ab prnkonpn` ma Hrquæfamas k`s nkmnoh qua ‒]`m` ouarp` sufarcnm` maktr` ma uk dbunm` axparnfakth ukh duarzh hsoakmakta bbhfhmh afpula, aqunvhbakta hb pas` mab dbunm` mashb`lhm` p`r ab ouarp`‖ .
NN. FHWO@ ]AßWNO@ O`k ghsa ak bh gngbn`crhdæh pr`puasth, o`ktasthr bhs sncunaktas pracukths< O`k ghsa ak bh gngbn`crhdæh pr`puasth, o`ktasthr y aktakmar bhs sncunaktas pracukths rabhon`khmhs o`k bh duarzh ma afpula qua raonga uk ouarp` qua asth nktr`muonm` phronhb ` t`thbfakta maktr` ma uk dbunm` y bhs o`kmnon`kas ma db`thgnbnmhm ma uk ouarp` maktr` ma uk dbunm`< ‒Ouhkm` uk ouarp` sa sufarca ak a k uk dbunm` maspbhzh ukh
onarth ohktnmhm ma bæqunm`, ncuhb hb v`bufak ma bh phrta sufarcnmh p`r îb‖. ‒_n uk ouarp` asth phronhb ` t`thbfakta nktr`muonm`
maktr` ma uk dbunm`, asta alaroa ukh duarzh jhonh hrrngh
Asta prnkonpn` b` hpbnohf`s ouhkm` khmhf`s, ouhkm` tnrhf`s uk `glat` hb hcuh9 ab `glat` ` glat` sa jukma sn su pas` as fhy`r qua ab pas` mab dbunm` mashb`lhm`(maspbhzhm`), ab `glat` db`th ouhkm` su pas` as fak`r ` ncuhb hb pas` mab dbunm` maspbhzhm`. ]`m` b` hktarn`r tnaka rabhonÿk o`k bh duarzh ma afpula jhonh hrrngh(hsoakmakta), qua raonga t`m` ouarp` qua sa akouaktrh sufarcnm` ak hcuh ` ak ouhbqunar `tr` dbunm`.
°Xuî d`rfhs prèotnohs sa puamak utnbnzhr phrh famnr bh duarzh ma afpula qua raonga uk ouarp` nktr`muonm` maktr` ma uk dbunm`0
Asta prnkonpn` sa hpbnoh ouhkm` khmhf`s, ouhkm` tnrhf`s uk `glat` hb hcuh9 ab `glat` sa jukma sn su pas` as fhy`r qua ab pas` mab dbunm` mashb`lhm`(maspbhzhm`).
Tarsnÿk 8.5
NKD@WFA UWÈO]NOH MA BHG@WH]@WN@ DHOQB]HM MA NKCAKNAWÆH DÆ_NOH OHB@W ^ @KMH_
°Oÿf` sa puama famnr bh duarzh ma afpula0
sÿbnm` ma maksnmhm fhy`r qua bh mab dbunm` ouhkm` asta, asth s`staknm` p`r ukh ouarmh qua pakma ma uk mnkhfÿfatr` ` ghbhkzh as< (var Dnc. 8)
_n uk raonpnakta sabbhm` ma uk bntr` astè sufarcnm` ak hcuh jhsth bh fnthm, maspbhzhrh famn` bntr` ma hcuh y bh duarzh ma afpula ` db`thonÿk saræh ncuhb hb pas` ma famn` bntr` ma hcuh, snf nfp`rthr qua o`ktakch ab raonpnakta. _a ohboubh fubtnpbnohkm` su pas` aspaoædno` p`r ab v`bufak qua `ouph y thfgnîk puama ohboubhrsa sn sa fubtnpbnoh bh maksnmhm mab fhtarnhb mab ouarp` p`r bh crhvamhm p`r ab v`bufak qua `ouph. Bh duarzh ma afpula as aqunvhbakta hb pas` mab bæqunm` mashb`lhm`.
Uarn`m` 7578-8
6 ∗ 6 ( ∗ )
()
O`k f 6 mabfhsh mab mab ouhkm` ouarp` as famnmh ak ak ab hnra y 6 fhsh hphrakta ouarp` famnmh ab dbunm`.
°Xuî o`kmnon`kas dæsnohs maga oufpbnr uk ouarp` phrh qua db`ta maktr` ma uk dbunm`0
Uhrh qua uk `glat` db`ta, bh duarzh ma db`thonÿk s`gra ab ouarp` maga sar ncuhb hb pas` mab dbunm`, maspbhzhm`, b`s dbunm`s fès maks`s alaroak ukh duarzh ma afpula fès crhkma qua b`s fak`s maks`s, phrh qua ukh pars`kh db`ta ak ab hcuh o`k fès dhonbnmhm, maga ramuonr su maksnmhm.
°Ak tîrfnk`s ma bh maksnmhm rabhtnvh qua vhb`ras ma maksnmhm maga takar uk ouarp` phrh qua db`ta phronhb, t`thb ` sa vhyh hb d`km` mab raonpnakta qua o`ktnaka ab dbunm`0
Hrquæfamas aktra sus masougrnfnakt`s fès k`thgbas astè ab prnkonpn` ma db`thgnbnmhm ma m a b`s ouarp`s, o`k`onm` j`y o` o`f` f` prnkonpn` ma Hrquæfamas. Hrquæfamas masougrnÿ qua uk ouarp`, hb sar sufarcnm` phronhb ` t`thbfakta t`thbfakta ak ab nktarn`r mab dbunm`, axparnfak axparnfakth th ukh duarzh jhonh hrrngh, bbhfhm` duarzh ma afpula ` snfpbafakta afpula, ouy` f`mab` as ncuhb hb pas` mab dbunm` qua maspbhzh.
°Uuama ukh g`yh fatèbnoh db`thr maktr` ma uk dbunm`0 Axpbnqua
Qkh g`yh cakarhbfakta as juaoh y h fakum` asth nkdbhmh o`k hnra, ` o`k hbcük chs kautr`, hukqua thfgnîk as o`fük ako`ktrhr g`yhs rabbakhs ma uk fhtarnhb s`bnm` fès bncar` qua ab hcuh, o`f` puama sar bh aspufh ma p`bnastnrak`, o`k ab dnk ma nfpamnr qua ab o`ktaknm` sa bbaka ma hcuh ` qua sa masnkdba. Bhs g`yhs db`thk yh qua s`k juaohs, b` qua jhoa qua su maksnmhm sah fak`r qua bh mab hcuh y p`r akma puama db`thr.
Maf`strhr utnbnzhkm` mnhcrhfhs ma duarzhs, qua bh duarzh ma afpula qua alaroa uk dbunm` s`gra uk
Abhg`rhonÿk Ur`pnh
NNN. FH]AWNHBA_ (F@K]HLA AZUAWNFAK]HB) Uhrh ab mashrr`bb` ma bh prèotnoh ma bhg`rht`rn` sa raqunara ma abafakt`s nkmnspakshgbas o`k ab dnk ma oufpbnr ohmh uk` ma b`s `glatnv`s pr`puast`s, p`r b` thkt`, sa kaoasnthk ma<
Ghbhkzh Ohbngrhm`r @glat`s ma ca`fatræh racubhr a nrracubhr Mndaraktas bæqunm`s Maksæfatr`s Ur`gaths Ths`s ma praonpnthm` Gahiar _`p`rtas
Tarsnÿk 8.5
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DB@]HONßK UHWH _ßBNM@_<
bh rabhonÿk (8) y ohbouba ab vhb`r ma bh duarzh ma afpula axparnfakthb o`k su nkoartnmufgra. OQAWU. 8
D. AFUQL A ]AßWNO
Ur`oamh hb hbnsthfnakt` y f`kthla hmaouhm` mab aqunp`.
O`b`qua uk ouarp` qua db`ta phronhbfakta maktr` ma uk dbunm` (hcuh). Tarndnqua qua bh maksnmhm rabhtnvh mab ouarp` as fak`r qua 8 ` qua bh maksnmhm hgs`buth as fak`r qua bh maksnmhm mab dbunm`.
HCQH HBO@J@B CBNOAWNK H
H
O`b`qua m`s ouarp`s qua db`tak maktr` mab fnsf` dbunm` (hcuh). Xuî puama maonr o`k raspaot` h< bh duarzh ma afpula, ab v`bufak mab ouarp` nktr`muonm` y bh maksnmhm ma b`s ouarp`s< °_`k ncuhbas, mndaraktas0 Axpbnqua sus raspuasths.
OQAWU. 7
D. AFUQL A ]AßWNO H
Wapnth b`s fnsf`s pr`oamnfnakt`s hktarn`ras ak `tr` dbunm` (hbo`j`b), y jhch b`s fnsf`s hkèbnsns.
°Axnsta hbcukh rabhonÿk aktra bh maksnmhm mab ouarp`
y ab p`roakthla ma ouarp` nktr`muonm`0 _n uk ouarp` sa o`b`oh maktr` ma uk dbunm` qua sa vh hb d`km` mab raonpnakta qua o`ktnaka ab dbunm`, o`f` as su maksnmhm rabhtnvh, °Asta ouarp` p`mræh db`thr ak `tr` dbunm`0 Axpbnqua.
DQAW\H MA AFUQLA<
Fnmh ab v`bufak ma ohmh `glat` y ohbouba b`s vhb`ras taÿrno`s ma bh duarzh ma afpula utnbnzhkm`< 6
Ab ouarp` tnaka qua asthr nktr`muonm` o`fpbathfakta maktr` ma< Hcuh, Hbo`j`b y cbnoarnkh raspaotnvhfakta. ]`fa ab vhb`r ma bh maksnmhm mab dbunm` sacük famnmh jaojh o`k ab maksæfatr`, v`bufak mab `glat` famnm` o`k ab ohbngrhm`r y c6 >,: f/s7. Axprasa bh nkoartnmufgra ak ab oèboub` ma bh duarzh ma afpula.
Uhrh famnr bh duarzh ma afpula axparnfakthb utnbnoa bh ghbhkzh y fnmh bh fhsh ma ohmh ouarp` ak ab hnra y su fhsh hphrakta ouhkm` asth nktr`muonm` o`fpbathfakta maktr` mab dbunm` raspaotnv`. Qtnbnoa
FH_H MAB OQAWU@
FH_H HUHWAK]A
D. MA AFUQLA AZUAWNFAK]HB
FH_H MAB OQAWU@
FH_H HUHWAK]A
D. MA AFUQLA AZUAWNFAK]HB
HCQH HBO@J@B CBNOAWNK H
O`fphra sus rasubthm`s. °Ast`s astèk ak ab rhkc` asparhm`0 Jhch sus hkèbnsns
Ubhktaa b`s hkèbnsns o`rrasp`kmnaktas.
K@]H. U`r bh mndnoubthm ma fhknpubhr bh cbnoarnkh, sa o`b`ohrè uk s`b` f`kthla phrh famnr bh duarzh ma afpula ak bh cbnoarnkh, ma thb fhkarh qua sa o`b`ohrhk m`s ouarp`s nmîktno`s ab uk` phrh famnr su fhsh ak bh ghbhkzh y su rîpbnoh asthrè snafpra ak ab raonpnakta o`k cbnoarnkh phrh famnr su fhsh hphrakta y hsæ avnthr bh o`kthfnkhonÿk o`k bh cbnoarnkh.
Uhrh ouarp`s qua takchk ukh maksnmhm rabhtnvh fhy`r qua 8
Uarn`m` 7578-8
y
o`kobusn`kas
T. ]HGBH_ ^ DNCQWH_ Maksnmhm Ma Bæqunm`s MA_OWNUONßK Ic/f?
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8.74 c/of?
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Maksnmhm Axparnfakthb 6
Hbo`j`b T@BQFAK MAB UNOK@FA]W@ UNOK@FA]W@
855 of?
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Tarsnÿk 8.5
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Uarn`m` 7578-8
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Tarsnÿk 8.5
NKD@WFA UWÈO]NOH MA BHG@WH]@WN@ DHOQB]HM MA NKCAKNAWÆH DÆ_NOH OHB@W ^ @KMH_ Maksnmhm ]aÿrnoh onbnkmr`s
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DQAW\H AFUQLA GW@KOA HCQH HBO@J@B >>: 3:> MAK_NMHM 5.534 DQAW\H MA AFUQLA 5.5>3
7.3 c/of? :.> c/of? 3.8= c/of? ]hgbh 8=
U`roakthlas Ma Arr`r Onbnkmr`s
]hgbh 83
DQAW\H AFUQLA HBQFNKN@ HCQH >>: MAK_NMHM DQAW\H MA AFUQLA 5.574
6 :.7 :.78> 8> / | ∗ |
% % 6
|: |:.>5 .>5 ∗ :. :.78 78>| >| :.>5
DQAW\H AFUQLA O@GWA HCQH
∓ 855
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HBO@J@B 3:> 5.578
]hgbh 8:
6 :.> :.>5 5 /
% % 6
Uarn`m` 7578-8
MAK_NMHM DQAW\H MA AFUQLA
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]hgbh 81
Duarzh Ma Afpula Axparnfakthb Duarzh Ma Afpula ]aÿrnoh
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Tarsnÿk 8.5
NKD@WFA UWÈO]NOH MA BHG@WH]@WN@ DHOQB]HM MA NKCAKNAWÆH DÆ_NOH OHB@W ^ @KMH_
U`roakthlas Ma Arr`r Duarzh Ma Afpula (Hbo`j`b)
DQAW\H MA AFUQLA HBQFNKN@ HCQH HBO@J@B
6 5.53 5.534 4
5.734 5.777
6 5.53 5.53= =
]hgbh 7?
% % 6 | ∗ | ∓ 855
DQAW\H MA AFUQLA O@GWA HCQH HBO@J@B
Uarn`m` 7578-8
5.5:1
% % 6
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∓ 855
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]hgbh 7=
U@WOAK]HLA MA AWW@W % (HBO@J@B) 7.35 % GW@KOA HBQFNKN@ 4.81 % O@GWA 8.=7 % OW@F@ =8.?5 %
DQAW\H MA AFUQLA OW@F@ HCQH HBO@J@B
5.85: 5.5>7 ]hgbh 71
]hgbh 73
U`roakthlas Ma Arr`r Duarzh Ma Afpula (Hcuh) 6 5.5> 5.5>3 3 6 5.5> 5.5>7 7 % % 6
| ∗ |
% % 6
|5 |5.5 .5>3 >3 ∗ 5. 5.5> 5>7| 7| 5.5>3
∓ 855
∓ 855
% % 6 1. 1.=? =? %
U@WOAK]HLA MA AWW@W % (HCQH) GW@KOA 1.=? % HBQFNKN@ 4.81 % O@GWA 7.?1 % OW@F@ 14.17 % ]hgbh 74
TN. HKÈBN_N_ MA WA_QB]HM@_ 8. Murhkta bh prèotnoh sa pum` matarfnkhr bh fhsh ma b`s bæqunm`s pr`puast`s ak bh cuæh famnhkta sakonbbhs aouhon`kas, mhkm` o`f` rasubthm` fhshs aktra b`s :5 y 8?= crhf`s ak b`s mnstnkt`s dbunm`s. 7. _a t`fhr`k maksnmhmas taÿrnohs ak bhs mndaraktas pècnkhs ma nktarkat, qua parfntnar`k ohboubhr b`s p`roakthlas ma arr`r, maf`strhkm` qua s`k ghsthkta ghl`s magnm` h qua astèk hbramam`r mab 7 h 4 %, b` ouhb k`s nkmnoh qua thkt` bh t`fh ma mht`s o`f` bh rahbnzhonÿk ma b`s oèboub`s duar`k dhv`rhgbas phrh bh abhg`rhonÿk ma bh prèotnoh. ?. Maktr` ma bh prèotnoh sa `gtuvnar`k vhb`ras o`rrasp`kmnaktas hb v`bufak, maksnmhm taÿrnoh y axparnfakthb ma b`s onbnkmr`s ma Gr`koa, Hbufnkn`, O`gra y Or`f`, b`s p`roakthlas p` roakthlas ma arr`r prasakthm`s ak asth phrta ma bh prhotnoh s`k rabhtnvhfakta ghl`s magnm` h qua s`b` ak uk abafakt` ab p`roakthla ma arr`r dua suparn`r hb :% fnaktrhs ab rast` `sonbhk aktra ab 5 y ab 7%, avnmakonhkm` qua bh saoonÿk ma bh prèotnoh sa rahbnzÿ ma fhkarh fhkarh o`rraoth y hsartnvh. =. Maspuîs ma rahbnzhr bh prèotnoh o`rrasp`kmnakta h bh cuæh mab prnkonpn` ma Hrquæfamas sa matarfnkÿ bh duarzh ma afpula axparnfakthb y taÿrnoh thkt` ak hcuh o`f` hbo`j`b ma b`s mnstnkt`s fhtarnhbas afpbahm`s, mhkm` phs` h p`roakthlas ma arr`r fuy ghl`s aktra ab 7 hb hb 3% ak Gr`koa, Hbufnkn` y O`gra9
NKD@WFA UWÈO]NOH MA BHG@WH]@WN@ DHOQB]HM MA NKCAKNAWÆH DÆ_NOH OHB@W ^ @KMH_ ak ab Or`f` ako`ktrhf`s uk p`roakthla p`roakthla hbt` akta ab =5 y 13% b` ouhb k`s parfnta `gsarvhr qua ak bh t`fh ma mht`s ` rahbnzhonÿk ma oèboub`s o`k asta abafakt` prasakthr`k dhbbhs h mndarakonh ma b`s `tr`s.
TNN.
O@KOBQ_N@KA_
_a o`kobuyÿ qua bhs maksnmhmas ma b`s bæqunm`s s`k mnstnkths magnm` h qua vhræh bh fhsh ma bh susthkonh y bh fhsh mab pnokÿfatr` o`k ab ouhb sa astè fnmnakm` ab dbunm`, p`r akma, thfgnîk vhk h vhrnhr b`s p`roakthlas ma arr`r.
Wahbnzhr bhs famnon`kas o`k mnstnkt`s nkstrufakt`s phrh jhbbhr ab v`bufak mab dbunm`, parfnta o`k`oar b`s magnm`s us`s phrh hsæ `gtakar ma fhkarh hmaouhmh bh maksnmhm ma bhs susthkonhs.
Bh duarzh ma afpula taÿrnoh y axparnfakthb
as suparn`r ak ab hhcuh maksnmhm as fhy`r bh mabmagnm` hbo`j`b.h qua su
Ab fhy`r p`roakthla ma arr`r ak bh duarzh ma afpula dua prasakthm` p`r ab Or`f` magnm` mnstnkths dhbbhs yh sah nkstrufakthbas ` oèboub`s rahbnzhm`s p`r b`s nktacrhktas mab crup`.
TNNN.
WADAWAKONH_
8. Èkcab F. Ojhphrr` O, (7588), DB@]HON@K ^ DQAW\H MA AFUQLA. ]`fhm` ma< jttps11? =/87%7GUrnkonpn`%7Gma%7GHrqunfamas.pmd/17m aa>a>-84>m-o5m5-oaa?ah5?7:ho5d710t6813483>5445=? 7. Èkcab F. Ojhphrr` O. Uamr` Lubn` Wayas ]., (7588), ( 7588), MAK_NMHM MA _@BNM@_ ^ BNXQNM@_. ]`fhm` ] `fhm` ma< jttps11? =/88+Maksnmhmas.pmd/884ag5?h->m>h-:3hh-57oa:gg:5ga:m47=0t6813483>54131? ?. ]arèk Tnta Ba`khrm`., (s.d.). UWNKONUN@ MA HWXQÆFNMA_, QKNTAW_NMHM HQ]ßK@FH MAB A_]M@ JNMHBC@. ]`fhm` ma< jttps
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