Overview |
Lore |
Voice-Overs |
Outfits |
Companion |
Media |
This article is about the character. For the boss, see Enter the Golden House.
Tartaglia, also known by his codename «Childe,» is a playable Hydro character in Genshin Impact.
He is the Eleventh of the Eleven Fatui Harbingers. Wherever he goes, danger follows, and Childe is always eager for a challenge, making him extremely dangerous despite being the youngest member.
Gameplay Info
Ascensions and Stats
Toggle Ascension Materials
Ascension Phase |
Level | Base HP |
Base ATK[1] |
Base DEF |
Special Stat[2] (Hydro DMG Bonus) |
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0✦ | 1/20 | 1,020 | 23 | 63 | — |
20/20 | 2,646 | 60 | 164 | ||
Ascension Cost (0 → 1)
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1✦ | 20/40 | 3,520 | 80 | 218 | — |
40/40 | 5,267 | 121 | 327 | ||
Ascension Cost (1 → 2)
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2✦ | 40/50 | 5,889 | 135 | 366 | 7.2% |
50/50 | 6,775 | 155 | 421 | ||
Ascension Cost (2 → 3)
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3✦ | 50/60 | 7,604 | 174 | 472 | 14.4% |
60/60 | 8,499 | 195 | 528 | ||
Ascension Cost (3 → 4)
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4✦ | 60/70 | 9,121 | 209 | 567 | 14.4% |
70/70 | 10,025 | 230 | 623 | ||
Ascension Cost (4 → 5)
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5✦ | 70/80 | 10,646 | 244 | 661 | 21.6% |
80/80 | 11,560 | 265 | 718 | ||
Ascension Cost (5 → 6)
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6✦ | 80/90 | 12,182 | 280 | 757 | 28.8% |
90/90 | 13,103 | 301 | 814 |
1. ↑ Does not include weapon ATK value.
2. ↑ Characters gain special stats starting with 2✦.
Total Cost (0✦ → 6✦)
Talents
Icon | Name | Type |
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Cutting Torrent | Normal Attack | |
Normal Attack Performs up to 6 consecutive shots with a bow. Charged Attack Riptide
Plunging Attack |
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Foul Legacy: Raging Tide | Elemental Skill | |
Unleashes a set of weaponry made of pure water, dealing Hydro DMG to surrounding opponents and entering Melee Stance. In this Stance, Tartaglia’s Normal and Charged Attacks are converted to Hydro DMG that cannot be overridden by any other elemental infusion and change as follows: Normal Attack Charged Attack Riptide Slash After 30s, or when the ability is unleashed again, this skill will end. Tartaglia will return to his Ranged Stance and this ability will enter CD. |
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Havoc: Obliteration | Elemental Burst | |
Performs different attacks based on what stance Tartaglia is in when casting.
Ranged Stance: Flash of Havoc Melee Stance: Light of Obliteration Riptide Blast |
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Never Ending | 1st Ascension Passive | |
Extends Riptide duration by 8s. | ||
Sword of Torrents | 4th Ascension Passive | |
When Tartaglia is in Foul Legacy: Raging Tide’s Melee stance, on dealing a CRIT hit, Normal and Charged Attacks apply the Riptide status effects to opponents. | ||
Master of Weaponry | Utility Passive | |
Increases your own party members’ Normal Attack Level by 1. |
Talent Upgrade
Talent Level |
Required Ascension |
Mora [Subtotal] |
Enhancement Materials [Subtotal] |
Character Talent Materials [Subtotal] |
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1 → 2 | 2✦ |
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2 → 3 | 3✦ |
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3 → 4 |
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4 → 5 | 4✦ |
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5 → 6 |
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6 → 7 | 5✦ |
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7 → 8 |
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8 → 9 | 6✦ |
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9 → 10 |
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Total Cost (1 → 10 for one talent)
Constellation
Icon | Name | Level |
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Foul Legacy: Tide Withholder | 1 | |
Decreases the CD of Foul Legacy: Raging Tide by 20% | ||
Foul Legacy: Understream | 2 | |
When opponents affected by Riptide are defeated, Tartaglia regenerates 4 Elemental Energy. | ||
Abyssal Mayhem: Vortex of Turmoil | 3 | |
Increases the Level of Foul Legacy: Raging Tide by 3. Maximum upgrade level is 15. |
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Abyssal Mayhem: Hydrospout | 4 | |
If Tartaglia is in Foul Legacy: Raging Tide’s Melee Stance, triggers Riptide Slash against opponents on the field affected by Riptide every 4s, otherwise, triggers Riptide Flash. Riptide Slashes and Riptide Flashes triggered by this Constellation effect are not subject to the time intervals that would typically apply to these two Riptide effects, nor do they have any effect on those time intervals. |
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Havoc: Formless Blade | 5 | |
Increases the Level of Havoc: Obliteration by 3. Maximum upgrade level is 15. |
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Havoc: Annihilation | 6 | |
When Havoc: Obliteration is cast in Melee Stance, the CD of Foul Legacy: Raging Tide is reset. This effect will only take place once Tartaglia returns to his Ranged Stance. |
Each Constellation activation requires one Tartaglia’s Stella Fortuna.
Availability
Event Wishes
Tartaglia was promoted or featured with a drop-rate boost in 4 Event Wishes:
Wish | Featured | Duration |
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Farewell of Snezhnaya 2020-11-11 |
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November 11, 2020 – December 1, 2020 |
Farewell of Snezhnaya 2021-04-06 |
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April 6, 2021 – April 27, 2021 |
Farewell of Snezhnaya 2021-10-13 |
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October 13, 2021 – November 2, 2021 |
Farewell of Snezhnaya 2022-11-18 |
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November 18, 2022 – December 6, 2022 |
Other Languages
Language | Official Name |
---|---|
English | Tartaglia |
Chinese (Simplified) |
达达利亚 Dádálìyǎ |
Chinese (Traditional) |
達達利亞 Dádálìyǎ |
Japanese | タルタリヤ Tarutariya |
Korean | 타르탈리아 Tareutallia |
Spanish | Tartaglia |
French | Tartaglia |
Russian | Тарталья Tartal’ya |
Thai | Tartaglia |
Vietnamese | Tartaglia |
German | Tartaglia |
Indonesian | Tartaglia |
Portuguese | Tartaglia |
Turkish | Tartaglia |
Italian | Tartaglia |
Change History
Version 3.0
- Updates to character voice-overs:
- Updated Audio and Text for English:
- About The Doctor:
- Old: […] Come to think of it, if I met my own prosthesis… Hah, we’d have to fight then and there to decide which one of us gets to survive.
- New: […] Well, come to think of it, if I met another version of myself… Hah, we’d have to fight then and there to decide which one of us gets to survive.
- About The Doctor:
- Updated Audio and Text for English:
Version 2.8
- Updates to character voice-overs:
- New Audio for all Languages:
- About The Jester
- About The Captain
- About The Doctor
- About Damselette
- About The Knave
- About The Rooster
- About The Marionette
- About The Regrator
- About The Fair Lady
- About The Balladeer
- New Audio for all Languages:
Version 2.7
- Updates to character voice-overs:
- Removed from all languages:
- «Disengaging Wind Glider»
- Removed from all languages:
Version 2.2
- Fixes an issue whereby the camera and attack method of Tartaglia’s Aiming Mode were abnormal under certain circumstances.
Version 1.4
- Tartaglia’s party icon was updated.
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Before
After
Version 1.3
- Updates to character voice-overs:
- Updated audio for Chinese:
- Majority of the Combat voice-overs
- Updated audio for Chinese:
Version 1.2
- Updates to character voice-overs:
- Updated audio for Korean:
- «Hello»
- All «Elemental Skill» Combat voice-overs
- All «Elemental Burst» Combat voice-overs
- Updated audio for Korean:
- December 31, 2020 — Fixes an issue whereby when Tartaglia is added to or removed from the party in the open world, the Passive Talent «Master of Weaponry» may not function as expected.
Version 1.1
- November 11, 2020 — Tartaglia was released as a playable character with the Farewell of Snezhnaya/2020-11-11 event wish.
Version 1.0
- Tartaglia was introduced as an NPC.
References
- ↑ Tartaglia’s Character Story: Character Story 3
- ↑ 2.0 2.1 Twitter: EN & JP VA Announcement
- ↑ Bilibili: 新角色「公子」预告PV-「百无禁忌」
- ↑ Twitter: KR VA Announcement
- ↑ 5.0 5.1 5.2 5.3 GenshinAcademy: Elemental Burst Frame Tests
Navigation
Eleven Fatui Harbingers | |
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Current Members |
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Former Members |
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Another World |
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Mondstadt |
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Liyue |
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Inazuma |
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Sumeru |
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Snezhnaya |
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Upcoming Characters announced by HoYoverse.
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Factions | |
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Transnational |
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Mondstadt |
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Liyue |
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Inazuma |
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Sumeru |
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Fontaine |
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Snezhnaya |
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Khaenri’ah |
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Содержание
- 5 ★ персонажи (легендарки)
- 4 ★ персонажи (эпики)
- Видео: Что значат имена героев
Так как в Геншин импакт героин напрямую связаны с регионом, олицетворяющим ту или иную реальную страну или регион, то и имена у них соответствующие.
В большинстве случаев русский вариант не является прямой транслитерацией, следовательно, очень важно знать, как правильно пишутся имена всех персонажей Genshin Impact на английском. Ведь это может в итоге много где понадобиться.
5 ★ персонажи (легендарки)
Для начала стоит поговорить об именах персонажей Геншин на английском, которые относятся к легендарным, то есть к 5 ★:
Путешественник
Итэр (мужской вариант) — Aether
Люмин (женский вариант) — Lumine
Паймон — Paimon
Регион Мондштадт
Дилюк — Diluc
Эола — Eula
Кли — Klee
Джинн — Jean
Венти — Venti
Альбедо — Albedo
Регион Ли Юэ
Мона — Mona
Тарталья — Tartaglia
Чжун Ли — Zhongli
Гань Юй — Ganyu
Сяо — Xiao
Ху Тао — Hu Tao
Ци Ци — Qiqi
Кэ Цин — Keqing
Шэнь Хэ — Shenhe
Е Лань — Yelan
Регион Инадзума
Сёгун Райдэн — Raiden Shogun
Яэ Мико — Yae Miko
Камисато Аяка — Kamisato Ayaka
Камисато Аято — Kamisato Ayato
Сангономия Кокоми — Sangonomiya Kokomi
Ёимия — Yoimiya
Каэдэхара Кадзуха — Kaedehara Kazuha
Аратаки Итто — Arataki Itto
Регион Сумеру
Тигнари — Tighnari
Сайно — Cyno
Нилу — Nilou
Нахида — Nahida
Странник — Wanderer
Фарузан — Faruzan
Аль-Хайтам — Alhaitham
Другое
Элой — Aloy
4 ★ персонажи (эпики)
Теперь рассмотрим имена персонажей Геншин импакт на английском языке для самой многочисленной группы — эпических героев, то есть 4-звездочников:
Мондштадт
Беннет- Bennett
Эмбер — Amber
Кейа — Kaeya
Лиза — Lisa
Барбара — Barbara
Ноэлль — Noelle
Диона — Diona
Фишль — Fischl
Рэйзор — Razor
Розария — Rosaria
Сахароза — Sucrose
Регион Ли Юэ
Нин Гуан — Ningguang
Сян Лин — Xiangling
Син Цю — Xingqiu
Янь Фэй — Yanfei
Чун Юнь — Chongyun
Бэй Доу — Beidou
Юнь Цзинь — Yun Jin
Синь Янь — Xinyan
Яо Яо — Yaoyao
Инадзума
Саю — Sayu
Тома — Thoma
Горо — Gorou
Кудзё Сара — Kujou Sara
Куки Синобу — Kuki Shinobu
Сиканоин Хэйдзо — Shikanoin Heizou
Сумеру
Коллеи — Collei
Дори — Dori
Кандакия — Candace
Лайла — Layla
Видео: Что значат имена героев
На основании Вашего запроса эти примеры могут содержать грубую лексику.
На основании Вашего запроса эти примеры могут содержать разговорную лексику.
Перевод «Тарталья» на английский
Тарталья вошел в историю науки под именем «человека, сделавшего самого себя».
Tartaglia entered the history of science under the name «a man who made himself».
Тарталья с возмущением отказался — мол, не хочет даже браться за заведомо неразрешимые задачи.
Tartaglia indignantly refused — saying that he does not even want to take up the notoriously intractable problem.
Нападавший Массимо Тарталья был задержан на месте.
The attacker, Massimo Tartaglia, was arrested at the scene.
Лагранж обратил внимание, что все специальные приемы, которые использовали Кардано, Тарталья и другие, основывались на одном методе.
Lagrange had noticed that all of the special tricks employed by Cardano, Tartaglia, and others were based on one technique.
Возможно, следствием этого явилось то, что Тарталья и Кардано получили больше математической чести, чем они заслуживают.
This has possibly resulted in Tartaglia and Cardano receiving more mathematical credit than they deserve.
В 1537 году Никколо Тарталья провел несколько пробных выстрелов, чтобы определить максимальный угол и дальность полета пули.
In 1537, Niccolò Tartaglia did some test firing to determine the maximum angle and range for a shot.
Когда Кардано опубликовал его в 1545 году, Тарталья сердито обвинил его в нечестности.
When Cardano published it in 1545, Tartaglia angrily accused him of dishonesty.
Еще в 1530 г. Никколо Тарталья разработал общий способ решения кубических уравнений.
In 1535, Niccolo Tartaglia found general solutions for all cubic equations.
Заместитель мэра, Франческо Тарталья, надеется, что такое предложение побудит переселится семьи и компании друзей, а не одиноких покупателей.
Deputy Mayor Francesco Tartaglia hopes it will make families and friends move together instead of single buyers.
Имя «Тарталья» (означающее «заика»), на самом деле, было прозвищем; считается, что его настоящее имя Фонтана.
The name «Tartaglia» (meaning «stutterer») was actually a nickname; his real name is believed to have been Fontana.
Заместитель мэра города Франческо Тарталья надеется, что это заставит семьи и друзей объединиться и приехать в Бизаччу.
Deputy Mayor Francesco Tartaglia hopes it will make families and friends move together instead of single buyers.
Как правило, денег на бумагу не хватало, и Тарталья каждый день ходил на кладбище и писал упражнения и задачи углем на мраморных надгробиях.
As a rule, there was not enough money for paper, and Tartaglia went to the cemetery every day and wrote exercises and tasks on charcoal on marble tombstones.
Первой попыткой ввести какую-то оценку наведения орудия на цель было изобретение Никколо Тарталья (Tartaglia) квадранта в 1545 году.
The first recorded device to measure an elevation angle was Niccolò Tartaglia’s invention of a gunners’ quadrant circa 1545.
В этот период он начинает заниматься математическими исследованиями после знакомства с Остилио Риччи из Фермо, последователем школы Николо Тарталья.
During this period, he began his mathematical studies through the knowledge of Ostilio Ricci as a follower of the school of Niccolò Tartaglia.
Формула Кардано: Решение кубического уровнения первым нашел Никколо Фонтана Тарталья.
Cardano’s formula: The solution to the cubic function, it was discovered by Niccolò Fontana Tartaglia.
То же самое, кстати, думал о Фиоре и Тарталья, который откуда-то узнал о завещании дель Ферро.
The same, incidentally, was thinking about Fiore and Tartaglia, who learned about the will del Ferro.
Тарталья написал несколько книг, самая важная из которых была издана в Венеции в 1556 г. под названием «Общие исследования чисел и мер».
Tartaglia wrote several books, the most important of which was published in Venice in 1556 under the title «General Studies of Numbers and Measures».
«Это является гарантией того, что процесс утилизации будет быстрым и гладким, нам не нужно будет искать потомков старых владельцев, и не будет никаких проблем с третьими лицами, — говорит Тарталья.
‘This stands as a guarantee that the disposal process will be speedy and smooth, we won’t need to chase descendants of old owners nor have any issues with third parties,’ says Tartaglia.
Иное дело Роберт Тарталья (Robert Tartaglia), который, по его словам, затем только и посетит это мероприятие, чтобы рассказать всем, с какими опасностями связана поездка в Замбию.
But Robert Tartaglia says he will attend this event just to explain to everybody how unsafe it is to go to Zambia.
В возрасте примерно 14 лет он пошел к учителю, чтобы выучить алфавит, но у него закончились деньги к букве К. Многое из этого есть в собственном описании Тартальи своей жизни [Тарталья (1546), с. 69].
Around the age of 14 he went to a teacher to learn the alphabet, but he ran out of money for his lessons by the letter K. This much is in Tartaglia’s own sketch of his life, Tartaglia (1546), p.
Результатов: 34. Точных совпадений: 34. Затраченное время: 54 мс
Documents
Корпоративные решения
Спряжение
Синонимы
Корректор
Справка и о нас
Индекс слова: 1-300, 301-600, 601-900
Индекс выражения: 1-400, 401-800, 801-1200
Индекс фразы: 1-400, 401-800, 801-1200
Примеры перевода
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tartaglia
– Держите, Тарталья.
— Hold on, Tartaglia.
– А у меня – вы, Тарталья…
“And I have you, Tartaglia …”
— не удержался Тарталья.
— could not resist Tartaglia.
Тарталья, ты болван!
Tartaglia, you moron!
Тарталья промолчал.
Tartaglia said nothing.
Тарталья пожал плечами.
Tartaglia shrugged.
Тарталья моргнул — раз, другой.
Tartaglia blinked — one, another.
— Ты очнулся, Тарталья.
“You woke up, Tartaglia.”
— хотел спросить Тарталья.
— wanted to ask Tartaglia.
Тарталья вжался в угол.
Tartaglia pressed into a corner.
From Wikipedia, the free encyclopedia
Tartaglia may refer to:
- Tartaglia (commedia dell’arte), Commedia dell’arte stock character
- Angelo Tartaglia (1350 or 1370–1421), Italian condottiero
- Niccolò Fontana Tartaglia (1499/1500–1557), Venetian mathematician and engineer
- Ivo Tartaglia (1880–1949), Yugoslav politician
- Marino Tartaglia (1894–1984), Croatian painter
- Warren Tartaglia (Walid al-Taha) (born 1944), American jazz musician
- Philip Tartaglia (1951–2021), Roman Catholic Archbishop of Glasgow, Scotland
- Antonio Tartaglia (born 1968), Italian bobsledder
- John Tartaglia (born 1978), American singer, actor, dancer and puppeteer
- Tartaglia (Chinese: 达达利亚), a playable character in Genshin Impact
From Wikipedia, the free encyclopedia
Tartaglia may refer to:
- Tartaglia (commedia dell’arte), Commedia dell’arte stock character
- Angelo Tartaglia (1350 or 1370–1421), Italian condottiero
- Niccolò Fontana Tartaglia (1499/1500–1557), Venetian mathematician and engineer
- Ivo Tartaglia (1880–1949), Yugoslav politician
- Marino Tartaglia (1894–1984), Croatian painter
- Warren Tartaglia (Walid al-Taha) (born 1944), American jazz musician
- Philip Tartaglia (1951–2021), Roman Catholic Archbishop of Glasgow, Scotland
- Antonio Tartaglia (born 1968), Italian bobsledder
- John Tartaglia (born 1978), American singer, actor, dancer and puppeteer
- Tartaglia (Chinese: 达达利亚), a playable character in Genshin Impact
From Wikipedia, the free encyclopedia
Niccolò Fontana Tartaglia |
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Born |
Niccolò Fontana 1499/1500 Brescia, Republic of Venice |
Died | 13 December 1557
Venice, Republic of Venice |
Nationality | Italian |
Known for | Cardano–Tartaglia formula Early research into ballistics Tartaglia’s triangle |
Scientific career | |
Fields | Mathematics, engineering |
Notable students | Ostilio Ricci[1] |
Niccolò Fontana Tartaglia (Italian: [nikkoˈlɔ ffonˈtaːna tarˈtaʎʎa]; 1499/1500 – 13 December 1557) was an Italian mathematician, engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the then Republic of Venice. He published many books, including the first Italian translations of Archimedes and Euclid, and an acclaimed compilation of mathematics. Tartaglia was the first to apply mathematics to the investigation of the paths of cannonballs, known as ballistics, in his Nova Scientia (A New Science, 1537); his work was later partially validated and partially superseded by Galileo’s studies on falling bodies. He also published a treatise on retrieving sunken ships.
Personal life[edit]
Niccolò Fontana was born in Brescia, the son of Michele Fontana, a dispatch rider who travelled to neighbouring towns to deliver mail. In 1506, Michele was murdered by robbers, and Niccolò, his two siblings, and his mother were left impoverished. Niccolò experienced further tragedy in 1512 when King Louis XII’s troops invaded Brescia during the War of the League of Cambrai against Venice. The militia of Brescia defended their city for seven days. When the French finally broke through, they took their revenge by massacring the inhabitants of Brescia. By the end of battle, over 45,000 residents were killed. During the massacre, Niccolò and his family sought sanctuary in the local cathedral. But the French entered and a soldier sliced Niccolò’s jaw and palate with a saber and left him for dead. His mother nursed him back to health but the young boy was left with a speech impediment, prompting the nickname «Tartaglia» («stammerer»). After this he would never shave, and grew a beard to camouflage his scars.[2]
Tartaglia’s biographer Arnoldo Masotti writes that:
At the age of about fourteen, he [Tartaglia] went to a Master Francesco to learn to write the alphabet; but by the time he reached “k,” he was no longer able to pay the teacher. “From that day,” he later wrote in a moving autobiographical sketch, “I never returned to a tutor, but continued to labour by myself over the works of dead men, accompanied only by the daughter of poverty that is called industry” (Quesiti, bk. VI, question 8).[3]
Tartaglia moved to Verona around 1517, then to Venice in 1534, a major European commercial hub and one of the great centres of the Italian renaissance at this time. Also relevant is Venice’s place at the forefront of European printing culture in the sixteenth century, making early printed texts available even to poor scholars if sufficiently motivated or well-connected — Tartaglia knew of Archimedes’ work on the quadrature of the parabola, for example, from Guarico’s Latin edition of 1503, which he had found «in the hands of a sausage-seller in Verona in 1531» (in mano di un salzizaro in Verona, l’anno 1531 in his words).[4]
Tartaglia eked out a living teaching practical mathematics in abacus schools and earned a penny where he could:
This remarkable man [Tartaglia] was a self-educated mathematics teacher who sold mathematical advice to gunners and architects, ten pennies one question, and had to litigate with his customers when they gave him a worn-out cloak for his lectures on Euclid instead of the payment agreed on.[5]
He died in Venice.
Ballistics[edit]
Nova Scientia (1537) was Tartaglia’s first published work, described by Matteo Valleriani as:
… one of the most fundamental works on mechanics of the Renaissance, indeed, the first to transform aspects of practical knowledge accumulated by the early modern artillerists into a theoretical and mathematical framework.[6]
Then dominant Aristotelian physics preferred categories like «heavy» and «natural» and «violent» to describe motion, generally eschewing mathematical explanations. Tartaglia brought mathematical models to the fore, «eviscerat[ing] Aristotelian terms of projectile movement» in the words of Mary J. Henninger-Voss.[7] One of his findings was that the maximum range of a projectile was achieved by directing the cannon at a 45° angle to the horizon.
Tartaglia’s model for a cannonball’s flight was that it proceeded from the cannon in a straight line, then after a while started to arc towards the earth along a circular path, then finally dropped in another straight line directly towards the earth.[8] At the end of Book 2 of Nova Scientia, Tartaglia proposes to find the length of that initial rectilinear path for a projectile fired at an elevation of 45°, engaging in a Euclidean-style argument, but one with numbers attached to line segments and areas, and eventually proceeds algebraically to find the desired quantity (procederemo per algebra in his words).[9]
Mary J. Henninger-Voss notes that «Tartaglia’s work on military science had an enormous circulation throughout Europe», being a reference for common gunners into the eighteenth century, sometimes through unattributed translations. He influenced Galileo as well, who owned «richly annotated» copies of his works on ballistics as he set about solving the projectile problem once and for all.[10]
Translations[edit]
Archimedes’ works began to be studied outside the universities in Tartaglia’s day as exemplary of the notion that mathematics is the key to understanding physics, Federigo Commandino reflecting this notion when saying in 1558 that «with respect to geometry no one of sound mind could deny that Archimedes was some god».[11] Tartaglia published a 71-page Latin edition of Archimedes in 1543, Opera Archimedis Syracusani philosophi et mathematici ingeniosissimi, containing Archimedes’ works on the parabola, the circle, centres of gravity, and floating bodies. Guarico had published Latin editions of the first two in 1503, but the works on centres of gravity and floating bodies had not been published before. Tartaglia published Italian versions of some Archimedean texts later in life, his executor continuing to publish his translations after his death. Galileo probably learned of Archimedes’ work through these widely disseminated editions.[12]
Tartaglia’s Italian edition of Euclid in 1543, Euclide Megarense philosopho, was especially significant as the first translation of the Elements into any modern European language. For two centuries Euclid had been taught from two Latin translations taken from an Arabic source; these contained errors in Book V, the Eudoxian theory of proportion, which rendered it unusable. Tartaglia’s edition was based on Zamberti’s Latin translation of an uncorrupted Greek text, and rendered Book V correctly. He also wrote the first modern and useful commentary on the theory.[13] This work went through many editions in the sixteenth century and helped diffuse knowledge of mathematics to a non-academic but increasingly well-informed literate and numerate public in Italy. The theory became an essential tool for Galileo, as it had been for Archimedes.
General Trattato di Numeri et Misure[edit]
General trattato di numeri et misure, 1556
Tartaglia exemplified and eventually transcended the abaco tradition that had flourished in Italy since the twelfth century, a tradition of concrete commercial mathematics taught at abacus schools maintained by communities of merchants. Maestros d’abaco like Tartaglia taught not with the abacus but with paper-and-pen, inculcating algorithms of the type found in grade schools today.
Tartaglia’s masterpiece was the General Trattato di Numeri et Misure (General Treatise on Number and Measure),[14] a 1500-page encyclopedia in six parts written in the Venetian dialect, the first three coming out in 1556 about the time of Tartaglia’s death and the last three published posthumously by his literary executor and publisher Curtio Troiano in 1560. David Eugene Smith wrote of the General Trattato that it was:
the best treatise on arithmetic that appeared in Italy in his century, containing a very full discussion of the numerical operations and the commercial rules of the Italian arithmeticians. The life of the people, the customs of the merchants, and the efforts at improving arithmetic in the 16th century are all set forth in this remarkable work.[15]
Part I is 554 pages long and constitutes essentially commercial arithmetic, taking up such topics as basic operations with the complex currencies of the day (ducats, soldi, pizolli, and so on), exchanging currencies, calculating interest, and dividing profits into joint companies. The book is replete with worked examples with much emphasis on methods and rules (that is, algorithms), all ready to use virtually as is.[16]
Part II takes up more general arithmetic problems, including progressions, powers, binomial expansions, Tartaglia’s triangle (also known as «Pascal’s triangle»), calculations with roots, and proportions / fractions.[17]
Part IV concerns triangles, regular polygons, the Platonic solids, and Archimedean topics like the quadrature of the circle and circumscribing a cylinder around a sphere.[18]
Tartaglia’s triangle[edit]
Tartaglia was proficient with binomial expansions and included many worked examples in Part II of the General Trattato, one a detailed explanation of how to calculate the summands of , including the appropriate binomial coefficients.[19]
Tartaglia knew of Pascal’s triangle one hundred years before Pascal, as shown in this image from the General Trattato. His examples are numeric, but he thinks about it geometrically, the horizontal line at the top of the triangle being broken into two segments
and
, where point
is the apex of the triangle. Binomial expansions amount to taking
for exponents
as you go down the triangle. The symbols along the outside represent powers at this early stage of algebraic notation:
, and so on. He writes explicitly about the additive formation rule, that (for example) the adjacent 15 and 20 in the fifth row add up to 35, which appears beneath them in the sixth row.[20]
Solution to cubic equations[edit]
Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano. In 1539, Cardano cajoled Tartaglia into revealing his solution to the cubic equations by promising not to publish them. Tartaglia divulged the secrets of the solutions of three different forms of the cubic equation in verse.[21] Several years later, Cardano happened to see unpublished work by Scipione del Ferro who independently came up with the same solution as Tartaglia. (Tartaglia had previously been challenged by del Ferro’s student Fiore, which made Tartaglia aware that a solution existed.)[22]
As the unpublished work was dated before Tartaglia’s, Cardano decided his promise could be broken and included Tartaglia’s solution in his next publication. Even though Cardano credited his discovery, Tartaglia was extremely upset and a famous public challenge match resulted between himself and Cardano’s student, Ludovico Ferrari. Widespread stories that Tartaglia devoted the rest of his life to ruining Cardano, however, appear to be completely fabricated.[23] Mathematical historians now credit both Cardano and Tartaglia with the formula to solve cubic equations, referring to it as the «Cardano–Tartaglia formula».
Volume of a tetrahedron[edit]
Tartaglia was a prodigious calculator and master of solid geometry. In Part IV of the General Trattato he shows by example how to calculate the height of a pyramid on a triangular base, that is, an irregular tetrahedron.[24]
The base of the pyramid is a triangle
, with edges of length
, and
rising up to the apex
from points
,
, and
respectively. Base triangle
partitions into
and
triangles by dropping the perpendicular from point
to side
. He proceeds to erect a triangle in the plane perpendicular to line
through the pyramid’s apex, point
, calculating all three sides of this triangle and noting that its height is the height of the pyramid. At the last step, he applies what amounts to this formula for the height
of a triangle in terms of its sides
(the height from side
to its opposite vertex):
a formula deriving from the Law of Cosines (not that he cites any justification in this section of the General Trattato).
Tartaglia drops a digit early in the calculation, taking as
, but his method is sound. The final (correct) answer is:
The volume of the pyramid is easily gotten after that (not that Tartaglia gives it):
Simon Stevin invented decimal fractions later in the sixteenth century, so the last figure would have been foreign to Tartaglia, who always used fractions. All the same, his approach is in some ways a modern one, suggesting by example an algorithm for calculating the height of most or all irregular tetrahedra, but (as usual for him) he gives no explicit formula.
Notes[edit]
- ^ Stillman Drake, Galileo at Work: His Scientific Biography, Dover, 1978, p. 3.
- ^ Strathern 2013, p. 189
- ^ Masotti, Arnoldo, Niccolò Tartaglia in the Dictionary of Scientific Biography.
- ^ See Tartaglia, Niccolò. General Trattato di Numeri et Misure, Part IV, Book 3, p. 43v for the sausage seller.
- ^ Zilsel, Edgar, The Social Origins of Modern Science, p. 35.
- ^ See Valleriani, Matteo, Metallurgy, Ballistics and Epistemic Instruments: The Nova Scientia of Nicolò Tartaglia, 2013, p. 1.
- ^ Henninger-Voss, Mary J., «How the ‘New Science’ of Cannons Shook up the Aristotelian Cosmos», Journal of the History of Ideas 63, 3 (July 2002), pp. 371-397. «eviscerated»: p. 376.
- ^ See Valleriani, Matteo, Metallurgy, Ballistics and Epistemic Instruments: The Nova Scientia of Nicolò Tartaglia, 2013, pp. 169-181.
- ^ See Valleriani, Matteo, Metallurgy, Ballistics and Epistemic Instruments: The Nova Scientia of Nicolò Tartaglia, 2013, pp. 176-177.
- ^ See Henninger-Voss, Mary J., «How the ‘New Science’ of Cannons Shook up the Aristotelian Cosmos», Journal of the History of Ideas 63, 3 (July 2002), pp. 391-393 for discussion and quotes.
- ^ Clagett, Marshall, «William of Moerbeke: Translator of Archimedes», pp. 356-366.
- ^ Henninger-Voss, Mary J., «‘New Science’ of Cannons», p. 392.
- ^ See Malet, Antoni, «Euclid’s Swan Song: Euclid’s Elements in Early Modern Europe», where Tartaglia’s work on Euclid is described as «mathematically cogent, innovative, and influential» (p. 207).
- ^ Tartaglia, Niccolò, 1556-1560
- ^ Smith 1985, p. 298.
- ^ Tartaglia, Niccolò. General Trattato di Numeri et Misure, Part I.
- ^ Tartaglia, Niccolò. General Trattato di Numeri et Misure, Part II.
- ^ Tartaglia, Niccolò. General Trattato di Numeri et Misure, Part IV.
- ^ See Tartaglia, Niccolò. General Trattato di Numeri et Misure, Part II, Book 2, p. 51v for expanding
.
- ^ See Tartaglia, Niccolò. General Trattato di Numeri et Misure, Part II, Book 2, p. 72 for discussion of the additive rule in «Pascal’s triangle».
- ^ Katz 1998, p. 359
- ^ Feldmann, Richard W. (1961). «The Cardano-Tartaglia dispute». The Mathematics Teacher. 54 (3): 160–163. ISSN 0025-5769. JSTOR 27956338.
His student, Antonio Maria Fiore, knew the solution and attempted to gain a reputation by exploiting his master’s discovery. He challenged Tartaglia with thirty questions, all of which reduced to the solution of x3 + ax = b.
- ^ Tony Rothman, Cardano v Tartaglia: The Great Feud Goes Supernatural.
- ^ See Tartaglia, Niccolò. General Trattato di Numeri et Misure, Part IV, Book 2, p. 35r for the calculation of the height of a 13-14-15-20-18-16 pyramid.
References[edit]
- Chisholm, Hugh, ed. (1911). «Tartaglia, Niccolò» . Encyclopædia Britannica. Vol. 26 (11th ed.). Cambridge University Press.
- Clagett, Marshall (1982). «William of Moerbeke: Translator of Archimedes». Proceedings of the American Philosophical Society. 126 (5): 356–366..
- Henninger-Voss, Mary J. (July 2002). «How the ‘New Science’ of Cannons Shook up the Aristotelian Cosmos». Journal of the History of Ideas. 63 (3): 371–397. doi:10.1353/jhi.2002.0029. S2CID 170464547.
- Herbermann, Charles, ed. (1913). «Nicolò Tartaglia» . Catholic Encyclopedia. New York: Robert Appleton Company.
- Charles Hutton (1815). «Tartaglia or Tartaglia (Nicholas)». A philosophical and mathematical dictionary. Printed for the author. p. 482.
- Katz, Victor J. (1998), A History of Mathematics: An Introduction (2nd ed.), Reading: Addison Wesley Longman, ISBN 0-321-01618-1.
- Malet, Antoni (2012). «Euclid’s Swan Song: Euclid’s Elements in Early Modern Europe». In Olmos, Paula (ed.). Greek Science in the Long Run: Essays on the Greek Scientific Tradition (4th c. BCE-17th c. CE). Cambridge Scholars Publishing. pp. 205–234. ISBN 978-1-4438-3775-0..
- Masotti, Arnoldo (1970). «Niccolò Tartaglia». In Gillispie, Charles (ed.). Dictionary of Scientific Biography. New York: Scribner & American Council of Learned Societies.
- Smith, D.E. (1958), History of Mathematics, vol. I, New York: Dover Publications, ISBN 0-486-20429-4.
- Strathern, Paul (2013), Venetians, New York, NY: Pegasus Books.
- Tartaglia, Niccolò (1543). Opera Archimedis Syracusani philosophi et mathematici ingeniosissimi. Venice.
- Tartaglia, Niccolò (1543). Euclide Megarense philosopho. Venice.
- Tartaglia, Niccolò (1556–1560), General Trattato di Numeri et Misure, Venice: Curtio Troiano.
- Valleriani, Matteo (2013), Metallurgy, Ballistics and Epistemic Instruments: The Nova Scientia of Nicolò Tartaglia, Berlin: Edition Open Access / Max Planck Research Library, ISBN 978-3-8442-5258-3.
- Zilsel, Edgar (2000), Raven, Diederick; Krohn, Wolfgang; Cohen, Robert S. (eds.), The Social Origins of Modern Science, Springer Netherlands, ISBN 0-7923-6457-0.
External links[edit]
- History Today Archived 22 January 2012 at the Wayback Machine
- The Galileo Project
- O’Connor, John J.; Robertson, Edmund F., «Niccolò Fontana Tartaglia», MacTutor History of Mathematics archive, University of St Andrews
- Tartaglia’s work (and poetry) on the solution of the Cubic Equation at Convergence
- La Nova Scientia (Venice, 1550)
- Tartaglia, Niccolò, General Trattato di Numeri et Misure, Part I (Venice, 1556)
- Tartaglia, Niccolò, General Trattato di Numeri et Misure, Part II (Venice, 1556)
- Tartaglia, Niccolò, General Trattato di Numeri et Misure, Part III (Venice, 1556)
- Tartaglia, Niccolò, General Trattato di Numeri et Misure, Part IV (Venice, 1560)
- Tartaglia, Niccolò, General Trattato di Numeri et Misure, Part V (Venice, 1560)
- Tartaglia, Niccolò, General Trattato di Numeri et Misure, Part VI (Venice, 1560)
- Valleriani, Matteo, Metallurgy, Ballistics and Epistemic Instruments: The Nova scientia of Nicolò Tartaglia)