isosceles

See also: isósceles

English

An isosceles triangle.

An isosceles trapezoid.

Etymology

Borrowed from Latin īsoscelēs, from Ancient Greek ἰσοσκελής (isoskelḗs, “equal-legged”), from ἴσος (ísos, “equal”) +‎ σκέλος (skélos, “leg”) +‎ -ής (-ḗs, adjective suffix).

See also iso-.

Pronunciation

• (Received Pronunciation) IPA^(key): /aɪˈsɒsəliːz/
• (General American) IPA^(key): /aɪˈsɑsəliz/

• Audio (Southern England):

  (file)

Adjective

isosceles (not comparable)

1. (geometry) Having (at least) two sides of equal length, used especially of a triangle or trapezoid.
   • 1693, Abel Swall, transl., The New Method of Fortification, as Practised by Monsieur de Vavban, Engineer General of France, 2nd edition, "A New Treatise of Fortification", page 96:

     Upon each exterior side draw an Isosceles Triangle of 480 Fathoms.

   • 1914, Henry Parker Manning, Geometry of Four Dimensions, page 204:

     A right double pyramid is isosceles when the extremities of the vertex-edge are at the same distance from the plane of the base.

   • 1945, Harold E. Wolfe, Introduction to Non-Euclidean Geometry, page 31:

     To prepare for the application of his method, Saccheri made use of a figure with which we are already acquainted. This is the isosceles quadrilateral with the two base angles right angles.

   • 1965 April 8, Newton B. Dismukes, “Multihull vessels (Patent US3316873A)”, in Google Patents‎^[1]:

     The polygon advantageously is an isosceles trapezoid or rectangle with the pivotal connections between the deck or superstructure and four hulls respectively at its corners.

   • 2019 January 23, Altered Book Lover, “Funky Flowers”, in Blogspot‎^[2]:

     The flowers were stuck inside a flower pot that was shaped like an isosceles polygon with a rectangular "edge."

Usage notes

• A trapezoid with two equal sides and two unequal sides is normally described as unequilateral, even though it can be regarded as a special case of isosceles trapezoid.
• A triangle with three equal sides is normally described as equilateral, even though it can be regarded as a special case of isosceles triangle.

Derived terms

• isosceles trapezoid
• isosceles triangle

Translations

having two sides of equal length, used especially of an isosceles triangle or trapezoid

• Armenian: հավասարասրուն (hy) (havasarasrun)
• Belarusian: раўнабедраны (rawnabjedrany)
• Bulgarian: равнобедрен (ravnobedren)
• Catalan: isòsceles (ca)
• Cebuano: duhalid
• Chinese:

  Mandarin: 等腰 (zh) (děngyāo)

• Czech: rovnoramenný
• Dutch: gelijkbenig (nl)
• Finnish: tasakylkinen (fi)
• French: isocèle (fr)
• German: gleichschenklig (de)
• Greek:

  Ancient Greek: ἰσοσκελής (isoskelḗs)

• Hebrew: שווה שוקיים m (shvé shokáim)
• Hindi: समद्विबाहु (samdvibāhu)
• Hungarian: egyenlő szárú
• Irish: comhchosach
• Italian: isoscele (it), equicrure
• Latin: īsoscelēs
• Macedonian: рамнокрак (ramnokrak)
• Manx: cochoshanagh
• Polish: równoramienny (pl)
• Portuguese: isósceles (pt), isóscele
• Romanian: isoscel (ro)
• Russian: равнобе́дренный (ru) (ravnobédrennyj)
• Spanish: isósceles (es)
• Swedish: likbent (sv)
• Tagalog: kaduhain
• Welsh: isosgeles

Further reading

• Isosceles trapezoid on Wikipedia.Wikipedia
• Isosceles triangle on Wikipedia.Wikipedia
• Isosceles (disambiguation) on Wikipedia.Wikipedia

Anagrams

• solecises

Latin

Etymology

Borrowed from Ancient Greek ῐ̓σοσκελής (ĭsoskelḗs), from ῐ̓́σος (ĭ́sos, “equal”) +‎ σκέλος (skélos, “leg”) +‎ -ής (-ḗs, adjective suffix).

Pronunciation

• (isoscelēs): (Classical Latin) IPA^(key): [ɪˈsɔs.kɛ.ɫeːs]
• (modern Italianate Ecclesiastical) IPA^(key): [iˈs̬ɔʃ.ʃe.les]
• (isosceles): (Classical Latin) IPA^(key): [ɪˈsɔs.kɛ.ɫɛs]
• (modern Italianate Ecclesiastical) IPA^(key): [iˈs̬ɔʃ.ʃe.les]

Adjective

isoscelēs (genitive isoscelis); third-declension one-termination adjective

1. (geometry) isosceles (having equal legs)

Declension

Third-declension one-termination adjective (Greek-type).

	singular			plural
	masc./fem.	neuter		masc./fem.	neuter
nominative	isoscelēs	isosceles		isoscelēs	isoscela isoscelia1
genitive	isoscelis			isoscelum isoscelium1
dative	isoscelī			isoscelibus
accusative	isoscelem	isosceles		isoscelīs isoscelēs	isoscela isoscelia1
ablative	isoscele isoscelī1			isoscelibus
vocative	isoscelēs	isosceles		isoscelēs	isoscela isoscelia1

¹It is unknown whether adjectives of this type would use i-stem or consonant-stem endings in Classical Latin: the relevant forms are not attested. Depending on the word, either ending or both may be attested in New Latin. Notes:

• The Greek masculine and feminine nominative singular is ῐ̓σοσκελής (ĭsoskelḗs), while the masculine and feminine vocative singular and the neuter nominative, accusative and vocative singular are ῐ̓σοσκελές (ĭsoskelés). Maybe Latin preserved the short length of the epsilon (ε), or maybe it did not so that the declension became similar to Latin third declension adjectives of one ending (like felix).
• This word is often used together with triangulum n and rarer with triangulus m.
• The vowel length is attested with starting īso- as well, but the Greek etymology points to ĭso- with a short vowel.

References

• “īsoscĕles”, in Charlton T. Lewis and Charles Short (1879), A Latin Dictionary, Oxford: Clarendon Press
• “īsoscĕlēs”, in Gaffiot, Félix (1934), Dictionnaire illustré latin-français, Hachette, page 860/3.