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  • Lautohi Tonu Matematē

‘Ikai ala ma‘u ha vitiō

Kātaki, ‘oku ‘ikai ma‘u ha vitiō.

  • Lautohi Tonu Matematē
  • Maʻu ʻAonga mei he Ako Fakafaifekau Fakateokalatí
  • Fakamatala Meimei Tatau
  • Ke Ke Ngāue Tōtōivi ki he Lautohí
    Maʻu ʻAonga mei he Ako Fakafaifekau Fakateokalatí
  • Mālōlō Feʻungamālie
    Maʻu ʻAonga mei he Ako Fakafaifekau Fakateokalatí
  • Ko e ʻAonga mei he Lau Tohitapu Fakaʻahó
    Ko e Taua Leʻo ʻOku Fanongonongo Ai ʻa e Puleʻanga ʻo Sihová—1995
  • Lau Tohitapú—ʻAonga mo Fakafiefia
    Ko e Taua Leʻo ʻOku Fanongonongo Ai ʻa e Puleʻanga ʻo Sihová—2000
Sio ki he Me‘a Lahi Ange
Maʻu ʻAonga mei he Ako Fakafaifekau Fakateokalatí
be ako 1 p. 83-p. 85 pal. 3

AKO 1

Lautohi Tonu Matematē

Ko e hā ʻoku fiemaʻu ke ke faí?

Lau leʻo-lahi ʻa e meʻa tofu pē ko ia ʻoku ʻi he peesi kuo pulusí. ʻOua ʻe liʻaki ha ngaahi foʻi lea, tuku ha konga ʻo e ngaahi foʻi leá, pe fetongi ha foʻi lea ʻaki ha foʻi lea ʻe taha. Puʻaki totonu ʻa e ngaahi foʻi leá. Fakatokangaʻi ʻa e ngaahi fakaʻilonga mālōloó mo e ngaahi fakaʻilonga fakamamafá.

Ko e hā ʻoku mahuʻinga aí?

Ko e lautohi lelei mo tonú ko ha konga tefito ia ʻo hono fakahaaʻi ʻa e ʻilo totonu ʻo e moʻoni faka-Tohitapú.

ʻOKU pehē ʻe he ngaahi Konga Tohitapú ko e finangalo ia ʻo e ʻOtuá ke hoko ʻa e kakai ʻi he faʻahinga kotoa pē ʻo “aʻusia ʻa e ʻilo kanokano [“totonu,” NW] ki he moʻoni.” (1 Tim. 2:4) ʻI he fakatatau ki he meʻa ko iá, ʻi he taimi ʻoku tau lautohi leʻo-lahi ai mei he Tohitapú, ko ʻetau holi ke fakahaaʻi ʻa e ʻilo totonú ʻoku totonu ke ne tākiekina ʻa e anga ʻo ʻetau lautohí.

Ko e malava ke lautohi leʻo-lahi mei he Tohitapú pea mei he ngaahi tohi ʻoku fakamatalaʻi ai ʻa e Tohitapú ʻoku mahuʻinga tatau pē ia ki he toʻutupú pea mo e faʻahinga taʻumotuʻá. ʻI he tuʻunga ko e Kau Fakamoʻoni ʻa Sihová, ʻoku tau maʻu ai ha fatongia ke vahevahe atu ki he niʻihi kehé ha ʻiloʻi ʻo Sihova mo ʻene ngaahi foungá. ʻOku faʻa kau ki ai ha lautohi ki ha tokotaha pe ki ha kiʻi kulupu. ʻOku tau toe fai ʻa e lautohi peheé ʻi he lotoʻi fāmilí. ʻI he Ako Fakafaifekau Fakateokalatí, ʻoku ʻi ai ʻa e ngaahi faingamālie feʻunga ki he fanga tokouá mo e fanga tuofāfiné, kei siʻi mo e taʻumotuʻa, ke nau tali ʻa e akonakí fakataha mo ha fakakaukau ke fakalakalaka ʻenau lautohi leʻo-lahí.

Ko hono lau ʻa e Tohitapú ki he kakaí, pe ki he faʻahinga tāutaha pe ki ha fakatahaʻanga, ko ha meʻa ia ke vakai ki ai ʻoku mahuʻinga. Ko e Tohitapú ko e fakamānava ia ʻa e ʻOtuá. Tānaki atu ki ai, “ko e folofola ʻa e ʻOtua, ko e koto moʻui mo e koto malohi, . . . pea ʻoku ne vavangaʻi ʻa e ngaahi holi mo e fakakaukau ʻo e loto.” (Hep. 4:12) ʻOku ʻi he Folofola ʻa e ʻOtuá ʻa e ʻilo taʻehanotatau ʻa ia ʻoku ala maʻu ia ʻo ʻikai mei ha toe matavai kehe. ʻE lava ke ne tokoniʻi ha tokotaha ke ne ʻiloʻi ʻa e ʻOtua moʻoni pē tahá pea ke ne fakatupu ha vahaʻangatae lelei mo ia pea pehē foki ke fekuki lavameʻa ai mo e ngaahi palopalema ʻi he moʻuí. ʻOkú ne fakamatalaʻi ʻa e founga ki he moʻui taʻengata ʻi he māmani foʻou ʻa e ʻOtuá. ʻOku totonu ko ʻetau taumuʻá ia ke lau ʻa e Tohitapú ʻi he lelei taha ʻo ʻetau malavá.​—Sāme 119:140; Sel. 26:2.

Founga ke Lautohi Tonu Matematē Aí. ʻOku lahi ʻa e ngaahi tafaʻaki ʻi he lautohi ola leleí, ka ko hono fakatupulekina ʻa e tonu matemateé ʻa e ʻuluaki sitepú. ʻOku ʻuhinga iá ko e feinga ke lau ʻa e meʻa tofu pē ko ia ʻi he peesi kuo pulusí. Tokanga ke ʻoua ʻe liʻaki ha ngaahi foʻi lea, liʻaki ʻa e ngaahi fakaʻosinga ʻo e foʻi leá, pe lauhalaʻi ha ngaahi foʻi lea koeʻuhí ko ʻenau meimei tatau mo e ngaahi foʻi lea kehé.

Koeʻuhi ke lau totonu ʻa e ngaahi foʻi leá, ʻoku fiemaʻu ke ke mahinoʻi ʻa e potutohí. ʻE fiemaʻu ki ai ʻa e teuteu lelei. ʻI he faai atu ʻa e taimí, ʻi hoʻo fakatupulekina ʻa e malava ke sio ki muʻa ʻo vakai ki he lele lelei ʻa e foʻi fakakaukaú, ʻe fakalakalaka ai ʻa hoʻo tonu matematē ʻi he lautohí.

Ko e fakaʻilonga mālōloó mo e ngaahi fakaʻilonga fakamamafá ko e ngaahi ʻelemēniti mahuʻinga ia ʻo e lea kuo tohí. ʻE fakahaaʻi nai ʻe he fakaʻilonga mālōloó ʻa e feituʻu ke kiʻi mālōlō aí, lōloa ke mālōlō aí pea mo e fiemaʻu nai ke liliu ʻa e lahi ʻo e leʻó. ʻI he ngaahi lea ʻe niʻihi, ko e ʻikai malava ke liliu ʻa e ongo ʻo e leʻó ʻi he taimi ʻoku fiemaʻu ai ʻe he fakaʻilonga mālōloó ʻe liliu nai ai ha foʻi fehuʻi ia ʻo hoko ko ha fakamatala, pe ʻe liliu kakato nai ai ʻa e ʻuhingá. Ko e moʻoni, ʻi he taimi ʻe niʻihi, ko e ngāue ʻa e fakaʻilonga mālōloó ʻoku lahi pē ia ʻi he tuʻunga fakakalamá. ʻI he ngaahi lea lahi ʻoku faingataʻa ke lautohi tonu matematē ʻo ʻikai fai ha tokanga lelei ki he ngaahi fakaʻilonga fakamamafá—fakatouʻosi ʻa ia kuo tohí pea mo ia ʻoku mahinoʻi mei he potutohí. ʻOku tākiekina ʻe he meʻá ni ʻa e ongo ʻo e ngaahi mataʻitohi ʻa ia ʻoku kau ki aí. Fakapapauʻi ke hoko ʻo maheni mo e founga ʻoku ngāueʻaki ai ʻa e fakaʻilonga leá mo e ngaahi fakaʻilonga fakamamafá ʻi hoʻo leá. Ko ha kī eni ki he lautohi ʻi ha founga mohu ʻuhingá. Manatuʻi ʻoku totonu ko hoʻo taumuʻá ke fakahaaʻi ʻa e ngaahi fakakaukaú, ʻo ʻikai ko hono leaʻaki pē ʻa e ngaahi foʻi leá.

ʻOku fiemaʻu ʻa e ʻahiʻahiʻi kapau ʻokú ke teu ke fakatupulekina ʻa e malava ke lautohi tonu matemateé. Lau ha palakalafi pē ʻe taha, pea toutou fai leva ia kae ʻoua kuó ke lava ke lau ia ʻo ʻikai ha fehālaaki. Hoko atu leva ki he palakalafi hokó. Fakaʻosí, feinga ke lau ʻa e ngaahi peesi ʻo e fakamatalá ʻo ʻikai liʻaki, toe leaʻaki, pe lauhalaʻi ha ngaahi foʻi lea. Hili hoʻo fou ʻi he ngaahi sitepu ko iá, kole ki ha taha ke ne vakaiʻi ʻa hoʻo lautohí pea fakahaaʻi ha ngaahi fehālaaki pē nai te ke fai.

ʻI he ngaahi tapa ʻe niʻihi ʻo e māmaní, ko e kovi ʻa e sió mo e ʻikai feʻunga ʻa e māmá ʻoku toe fakalahi ai ʻa e faingataʻaʻia ʻi he lautohí. Kapau ʻe ala lava ke fai ha tokanga ki he meʻá ni, ʻe iku taʻetoeveiveiua ai ki he fakalakalaka ʻi he lautohí.

ʻI he faai mai ʻa e taimí, ko e fanga tokoua ʻoku nau lautohi leleí ʻe fakaafeʻi nai ke nau kau ʻi he lautohi fakahāhā ʻo e fakamatala ki he akó ʻi he Ako Tohi ʻa e Fakatahaʻangá pea mo e Ako Taua Leʻo. Ka ke tokangaʻi lelei ha monū pehē, ʻoku fiemaʻu ʻa e meʻa lahi ange ia ʻi he malava pē ke leaʻaki totonu ʻa e ngaahi foʻi leá. Ke hoko ko ha tokotaha lautohi fakahāhā ola lelei ʻi he fakatahaʻangá, ʻe fiemaʻu ke ke fakatupulekina ʻa e ngaahi tōʻonga lelei ʻi he lautohi fakafoʻituituí. ʻOku kau ki heni ʻa hono ʻiloʻi ko e foʻi lea taki taha ʻi ha sētesi ʻokú ne fakahoko ha ngafa. ʻE ʻikai lava ke ke tukunoaʻi ha niʻihi ʻo e ngaahi foʻi lea ko iá pea maʻu ha mahino kakato ki he meʻa ʻoku leaʻakí. Kapau ʻokú ke lau halaʻi ha ngaahi foʻi lea, naʻa mo e taimi ʻokú ke lautohi pē ai kiate koé, ʻe mioʻi ai ʻa e ʻuhinga ia ʻo e sētesí. Ko e lau halá ʻoku tupu nai ia mei he ʻikai lava ke fakakaukau ki he ngaahi fakaʻilonga fakamamafá pe ko e potutohi ʻa ia ʻoku ngāueʻaki ai ʻa e ngaahi foʻi leá. Fai ha feinga ke mahinoʻi ʻa e ʻuhinga ʻo e foʻi lea taki taha ʻi he fokotuʻutuʻu ko ia ʻoku ʻasi aí. Toe fakakaukau foki ki he anga ʻo e kaunga ʻa e fakaʻilonga mālōloó ki he ʻuhinga ʻo e sētesí. Manatuʻi ko e ngaahi fakakaukaú ʻoku faʻa fakahaaʻi ia ʻe ha pupunga lea. Fakatokangaʻi ʻa e ngaahi meʻá ni koeʻuhi ʻi he taimi ʻo e lautohi leʻo-lahí ʻokú ke lau ʻa e ngaahi pupunga leá—ko e ngaahi kupuʻi lea mo e ngaahi kupuʻi sētesi—ʻo ʻikai ko e ngaahi foʻi lea pē. Ko hono mahinoʻi lelei ʻa e meʻa ʻokú ke laú ko ha sitepu mahuʻinga ia ki he hoko ʻo malava ke fakahaaʻi ʻa e ʻilo totonú ki he niʻihi kehé ʻi he lautohi fakahāhaá.

Ko ha tokotaha mātuʻa Kalisitiane taukei naʻe tohi ki ai ʻa e ʻapositolo ko Paulá: “Hokohoko atu ʻa hoʻo ngāue tonu ki he lautohi fakahāhaá.” (1 Tim. 4:​13, NW) ʻOku hā mahino ko ha tafaʻaki eni ʻe lava ke tau fai kotoa ai ha fakalakalaka.

FAKAʻILONGA MĀLŌLŌ

Piliote (.) fakahaaʻi ha mālōlō.

Koma (,) faʻa fiemaʻu ai ha kiʻi mālōlō, he ʻe hoko atu ai ki ha konga lahi ange.

Semikoloni (;) fakaʻilongaʻi ha mālōlō vaivai ange ʻi ha piliote kae mālohi ange ʻi ha koma.

Koloni (:) ʻomai ha lisi pe ko ha lea; ʻoku fiemaʻu ai ha mālōlō ʻo ʻikai ke tō ʻa e lahi ʻo e leʻó.

Fakaʻilonga ofo (!) fakaʻilongaʻi ʻa e ngaahi ongo mālohi ʻi he anga ʻo e leʻó.

Fakaʻilonga fehuʻi (?) faʻa fiemaʻu ke lau ʻa e sētesí ʻi ha leʻo ʻoku kiʻi māʻolunga ange pe hikiʻi ʻa e lahi ʻo e leʻó.

Fakaʻilonga ʻo e lea hiki (“ ” pe ‘ ’) fakahaaʻi nai ko e ngaahi foʻi lea ʻoku kau ki aí ʻoku totonu ke kamata ia ʻaki ʻa e ngaahi mālōlō (mātuʻaki siʻisiʻi kapau ko ha konga ʻo e potutohí; mālohi ange kapau ko ha fakamatala kakato).

Ngaahi tesi (​—), ʻi he taimi ʻoku ngāueʻaki ai ke kamata ha ngaahi foʻi lea, ʻoku faʻa fiemaʻu ki ai ha kiʻi liliu ʻo e anga ʻo e leʻó pe vave ʻo e leʻó.

Ngaahi haʻi ( ) mo e ngaahi haʻi sikuea [ ] te ne fakamavaheʻi nai ʻa e ngaahi foʻi leá ke lau ʻaki ha leʻo ʻoku kiʻi māʻulalo ange. Ko e ngaahi maʻuʻanga fakamatala ʻi he haʻí ʻoku ʻikai fiemaʻu ia ke lau, pea ko e ngaahi foʻi lea haʻi sikuea ʻoku fiemaʻu ke fakakakatoʻaki ʻa e ʻuhinga ʻo e meʻa ʻoku laú, ʻoku ʻikai fiemaʻu ai ha liliu ia ʻi he anga ʻo e leʻó.

FOUNGA KE LAVAʻI AI IÁ

  • ʻAhiʻahiʻi! ʻAhiʻahiʻi! ʻAhiʻahiʻi! Pea fai leʻo-lahi ia.

  • Kole ki ha taha ke ne vakaiʻi ʻa hoʻo lautohí pea fakahaaʻi ʻa e ngaahi fehālaakí.

  • ʻI hono fai ʻo e ako fakafoʻituituí, akonakiʻi koe ke lau tokanga.

  • ʻI he ʻikai ke lau pē ʻa e ngaahi foʻi leá, ako ke lau ʻa e ngaahi pupunga leá.

MEʻA KE FAI: Hili ʻa e teuteu leleí, kole ki ha kaumeʻa pe ki ha mēmipa ʻi he fāmilí ke muimui ʻi he Tohitapú ʻi hoʻo lau leʻo-lahi ha konga mei he Mātiu vahe 5 ki he 7. Kole kiate ia ke ne taʻofi koe ʻi he taimi kotoa pē ʻokú ke (1) liʻaki ai ha foʻi leá, (2) lau taʻetotonu ha foʻi lea pe liliu ʻa e hokohoko ʻo e foʻi leá, pe (3) tukunoaʻi ha fakaʻilonga fakamamafa pe ko ha fakaʻilonga mālōlō, ʻa ia ʻoku fiemaʻu ai ha mālōlō pe ko ha liliu ʻa e lahi ʻo e leʻó. ʻE lelei ke fai eni ʻo ʻikai siʻi hifo ʻi he miniti ʻe hongofulú ʻo tuʻo ua pe tuʻo tolu.

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