Appendix:Proto-Indo-European declension

This article is not a synchronic overview of Proto-Indo-European (PIE) nominal inflection, but a comparative overview of reflexes of the reconstructed PIE paradigms in attested daughter languages of major branches.

Overview

PIE nominal words had the morphological categories of gender, number and case. The category of number was shared with verbs, while gender and case were not.

There were three numbers: singular, dual and plural. There were three genders: masculine feminine and neuter. There were eight cases: nominative, accusative, vocative, genitive, ablative, dative, locative and instrumental case.

Nominal stems, as well as verbal stems, are divided into two formal classes, thematic and athematic, the former ending in the thematic vowel. Their inflection partially differed. The following is the table of the basic inflectional endings:

number	case	athematic	thematic
singular	nominative	*-s ~ Ø (neuter Ø)	*-o-s (neuter *-o-m)
	vocative	Ø (neuter Ø)	*-e (neuter *-o-m)
	accusative	*-m (neuter Ø)	*-o-m (neuter *-o-m)
	instrumental	*-éh₁ ~ *h₁	*-o-h₁
	dative	*-éy	*-o-ey
	ablative	*és ~ *os ~ *-s	*e-ad / *o-od / o-ot
	genitive	*-és ~ *-os ~ *s	*-o-syo (?)
	locative	Ø (→ *-i)	(**-e →) *-e-y
dual	nominative / accusative / vocative	*-h₁e (neuter *-ih₁)	*-o-h₁ (neuter *-o-y(h₁))
	instrumental / dative / ablative	-bʰoh₁(m) ?	-o(y)-bʰoh₁(m) ?
	genitive / locative	*-h₁ows ?	*-o(y)-h₁ows ?
plural	nominative / vocative	*-es (neuter *-h₂ ~ Ø)	*-o-es > ōs (neuter *-e-h₂)
	accusative	*-ns (neuter *-h₂ ~ Ø)	*-o-ns (neuter *-e-h₂)
	instrumental	*-bʰí	*-ōys
	dative/ablative	*-mós	*-o-mos (*-o-y-mos?)
	genitive	*-óHom	*-o-oHom
	locative	*-sú	*-o-y-su

Some properties of PIE nominal inflection had considerable impact on the development of declensional paradigms in the daughter languages. Syncretism was one of them:

• no declension class had more than 3 different forms in dual
• neuter gender always had identical nominative, accusative and vocative forms in all three numbers
• ablative differed from genitive only in thematic stems
• in plural, ablative and dative are always identical, as well as nominative and vocative

Zero-endings in the non-neuter nominative singular chiefly arose by Szemerényi's law. Stems in -h₂, regularly feminine gender, lacked an overt nom. sg. ending for unclear reason.

PIE had several declensional patterns, fundamentally divided into mutable and fixed stems: the former changed the root and/or suffix vocalism throughout the paradigm, while the latter exhibited no such alternation. Generally, immutable stems are those on *-o- (i.e. the thematic stems), and the stems on *-eh₂, *-uh₂ and *ih₂.

Nouns

o-stems

Thematic stems or o-stems are the most important and widespread types of nouns. Paradigm is given for the masculine noun *wĺ̥kʷos (“wolf”) which was preserved in most of the daughters.

number	case	PIE	Ancient Greek	Latin	Sanskrit	Hittite	OCS	Lithuanian	Gothic
singular	nominative	*wĺ̥kʷos	λύκος (lúkos)	lupus	वृकस् (vṛkas)	𒀜𒋫𒀸 (attaš)	влькъ (vlĭkŭ)	vil̃kas	𐍅𐌿𐌻𐍆𐍃 (wulfs)
	vocative	*wĺ̥kʷe	λύκε	lupe	vṛka	atta, atti	vlьče	vil̃ke	wulf
	accusative	*wĺ̥kʷom	λύκον	lupum	vṛkam	attan	vlьkъ	vil̃ką	wulf
	instrumental	*wĺ̥kʷoh₁	-	-	vṛkā, vṛkeṇa	attit	vlьkomь	vilkù	-
	dative	*wĺ̥kʷoey > *wĺ̥kʷōy	λύκωι > λύκῳ	lupō	vṛkāya	atti	vlьku	vil̃kui	wulfa
	ablative	*wĺ̥kʷe-a[d/t], wĺ̥kʷo-o[d/t] > *wĺ̥kʷō[d/t]	-	lupōd > lupō	vṛkāt	attaz(a)	-	-	-
	genitive	*wĺ̥kʷosyo	λύκοιο > λύκου	lupī	vṛkasya	attaš	vlьka	vil̃ko	wulfis
	locative	*wĺ̥kʷey	-	lupī*	vṛke	–	vlьcě	vilkè	-
dual	nominative / accusative / vocative	*wĺ̥kʷoh₁	λύκω	-	vṛkā, vṛkau	–	vlьka	vilku	-
	genitive / locative	*wĺ̥kʷows ???	λύκοιιν, λύκοιν	-	vṛkayos	–	vlьku	-	-
	dative / ablative / instrumental	*wĺ̥kʷobʰām ???	λύκοιν	-	vṛkābhyām	–	vlьkoma	vilkam	-
plural	nominative / vocative	*wĺ̥kʷoes > *wĺ̥kʷōs	λύκοι	lupī	vṛkās	attiēš	vlьci	vilkaĩ	wulfōs
	accusative	*wĺ̥kʷons	λύκους	lupōs	vṛkān	attuš	vlьky	vilkùs	wulfans
	instrumental	*wĺ̥kʷōys	-	-	vṛkais	attit	vlьky	vilkaĩs	-
	dative / ablative	*wĺ̥kʷo(y)mos, *wĺ̥kʷobʰos, *wĺ̥kʷōys	λύκοις	lupīs	vṛkebhyas	attaš, attaz(a)	vlьkomъ	vilkáms	wulfam
	genitive	*wĺ̥kʷooHom > *wĺ̥kʷōm	λύκων	lupōrum	vṛkāṇām	attaš, attan	vlьkъ	vilkų̃	wulfē
	locative	*wĺ̥kʷoysu	-	lupīs*	vṛkeṣu	attaš	vlьcěxъ	vilkuosè	-

1. nominative singular: The ending *-os arose from the thematic vowel *-o- and the nominative singular ending *-s. It was preserved in Ancient Greek, and Old Latin (changing to Classical Latin -us). In Sanskrit, PIE */o/ changed regularly to Proto-Indo-Iranian */a/. In OCS -ъ is a regular reflex of word-final PIE *-os: *-os > -us > Proto-Slavic -u > Common Slavic *-ъ. Gothic -s is a reflex of PIE *-os -> -oz -> Proto-Germanic --az, with devoicing of /z/ and regular loss of unstressed word-final short vowels, not including diphthongs.
2. vocative singular: PIE *-e is not a real ending per se, but an e-grade of the thematic stem with zero-ending *-Ø. In Sanskrit, PIE */e/ changed regularly to Proto-Indo-Iranian */a/. Word final unstressed /e/, /a/ and /o/ was regularly lost in the development stages of Proto-Germanic and thus it is not preserved in Gothic.
3. accusative singular: The ending *-o-m arose from the thematic vowel *-o- and the accusative singular ending *-m. It was preserved as Old Latin -om yielding later Classical Latin -um. In Greek word-final PIE *-m regularly changed to -ν. OCS reflex of -ъ is regular: PIE *-om > *-um > *-un > Proto-Slavic *-u > Common Slavic -ъ. In Sanskrit, PIE */o/ changed regularly to Proto-Indo-Iranian */a/.
4. instrumental singular: The ending *-oh₁ has been preserved in Lithuanian and Vedic Sanskrit (Classical Sanskrit ending -eṇa is taken from pronominal paradigm; cf. téna, instrumental singular of तद् (tád, “it; that”)). In Latin, instrumental has undergone syntactic merger with the ablative. In Slavic the original ending has been preserved in some fossilized expressions such as Russian вчера (včerá, “yesterday”), while the OCS ending -mь has been taken from the athematic paradigm (on which see below).

   Sometimes this ending is alternatively reconstructed as -eh₁ due to the ambiguity of Indo-Iranian evidence (where Proto-Indo-Iranian */a/ could have resulted from both PIE */e/ and */o/, who merged to PII */a/), but numerous auxiliary evidence points to *-oh₁.

5. dative singular: PIE ending *-ōy resulted from the contraction of the thematic vowel *-o- and the dative singular ending *-ey. In Greek it has been preserved as -ωι, with final -ι eventually lost in the historical period yielding ῳ with iota subscript (all long dipthongs lost the final glide in the same way). Similarly in Latin: Proto-Italic *ōy was preserved in Osco-Umbrian (in Oscan as -úí), yielding eventually Latin -ō. Old Latin has some instances of the older ending: DVENOI in Duenos Inscription and NVMASIOI in Praeneste fibula (if it's not fake). In Sanskrit the expected ending -āy has some kind of a particle (or postposition) *-a appended. Standard Aukštaitian Lithuanian -ui is by analogy to ā-stems (see below), while the Žemaitian dialects have the endings -ū, -ō, which regularly correspond to OCS & Common Slavic ending -u, and can be derived from Proto-Balto-Slavic *-ōw, which could have regularly reflected PIE *-ōy.
6. ablative singular: PIE ending *-ōd or *-ōt resulting from the contraction of the thematic vowel (*-e- or *-o-) and the ablative singular ending *-od or *-ot. It has been preserved in Old Latin as -ōd (yielding Classical Latin -ō) and Sanskrit -āt. In Balto-Slavic PIE ablative has taken over the function of genitive, and OCS and Lithuanian genitive singular endings -o and -a respectively can be traced as regular reflexes of PIE -*ōd (> Balto-Slavic *-a). In Greek the ending survived in Doric adverbs of place-from-which such as ὄπω (ópō, “whence”), with the similar adverbial use as in Latin prīmō (“at first”) or tūtō (“safely; lit 'in one piece'”).
7. genitive singular: The oldest ending of PIE genitive singular is the same as nominative singular -os, and that state of affairs has been preserved in Anatolian, e.g. Hittite 𒀜𒋫𒀸 (attas, “father”), both nominative and genitive singular. On the other hand, the genitival adjective suffixes of Hittite -ašša-, Luwian -ašša/i- and Lycian -ahe/i- are all regularly derivable from PIE *-osyo, which itself, taken from originally adjectival paradigm, became the predominant genitive singular suffix of thematic nouns in the post-Anatolian period of PIE. The suffix *-osyo can be explained as the basic form of *os with suffixed relative pronoun *-yo (cf. Sanskrit यद् (yás, “who, which”)), and is attested as expected in Sanskrit -asya and Homeric Greek -οιο (later by loss of -ι- yielding first -οο and then -ου or -ω, depending on the dialect). It has been also preserved in some Old Latin inscriptions such as Lapis Satricanus (POPLIOSIO VALESIOSIO SVODALES "the accustomed associates of Publius Valerius"), while the Classical Latin ending -ī is by origin most probably a possessive adjective. Balto-Slavic genitive case ending is by origin PIE ablative (see above).
8. locative singular The ending is reconstructed as either *-ey or -*oy. In Greek both have been preserved in adverbs such as οἴκοι (oíkoi, “at home”) and ἐκεῖ (ekeî, “in that place, there”). Similary to Greek, Latin has preserved traces of locative case only in adverbs such as domī (“at home”) and humī (“on the ground”), but the Italic branch is ambiguous on which of the two PIE endings is the exact source. Sanskrit ending -e could reflect both PIE *-ey and *-oy (merging to Proto-Indo-Iranian diphthong *-ai), while OCS -ě could reflect only PIE *-oy (> Proto-Balto-Slavic diphthong *-aj, regularly reflected as Common Slavic jat *-ě). It appears that the original ending was *-ey later being ousted by *-oy, itself resulting by suffixation of the locative singular suffix *-i onto the thematic vowel *-o-.
9. dual - Dual cases are very difficult to reconstruct formally. The reconstructable ending *-oh₁ in NAV might have been originally identical the ending of instrumental singular; the meaning of dual could've evolved from instrumental (i.e. comitative) sense, i.e. in the syntagm such as "wolf with wolf" the first element could have been dropped, and the second element ("with wolf") reanalyzed as dual ("two wolves"). At any case, PIE *-oh₁ > post-PIE *ō which regularly yielded Greek -ω, Vedic Sanskrit -ā (Classical Sanskrit -au was later Indic innovation in the historical period) and OCS -a. In Latin dual is preserved in some isolated forms such as ambō (“both”). Other dual cases are difficult to reconstruct.
10. nominative plural: PIE ending *-ōs is result of the contraction of the thematic vowel *-o- end the nominative plural ending *-es. It has been preserved only in Sanskrit as -ās. Balto-Slavic, Greek and Latin have taken then ending *-i from the pronominal paradigm (cf. Sanskrit te < PIE *to-y, nominative plural of sás "who, he"). Classical Latin suffix -ī reflects Old Latin -oe and more common -ei.
11. accusative plural: PIE ending *-ons has been regularly reflected in all the languages.
12. instrumental plural: PIE ending *-ōys results from the contraction of the thematic vowel -o- and the instrumental case ending *-oys. It has been regularly reflected in all the languages
13. dative / ablative plural: the reconstruction is not certain. Latin -īs derives from Old Latin -eis, which derives from instrumental plural ending -ōys, just as Greek -οις, though via a different route. Balto-Slavic and Germanic have endings with the -m- element: In Balto-Slavic the ending was *-mus which was preserved in Old Lithuanian (modern Lithuanian -ms is by syncope). Alternative reconstructions of the ending as *-obʰos is primarily based on Sanskrit and Latin. According to Beekes 1995, the ending *-mos was originally ablative plural marker, while the ending -bʰos was dative plural marker, and these two cases were eventually syncretized but with different outputs in the daughters.
14. genitive plural: The ending *ōm resulting from the thematic vowel -o- onto which the genitive plural marker *-om was suffixed. Greek reflex -ων is regular, with the word-final change of -m to -n. Old Latin has -om, and Classical Latin -um, but which remained productive only in two obscure classes of nouns: words construing with mass nouns (e.g. passum "of paces", sēstrium, archaic gen. pl. of sēstrius, later reinterpreted as neuter singular) and certain stereotyped expressions (duumvirum "[committee] of two men", praefectus fabrum "commander of the workers"), as well as some isolated words (socium "of allies", deum "of the gods" etc.). The ending -ōrum was modeled after genitive plural of feminines -ārum, itself imported from the pronominal inflection.
15. locative plural: The ending *-oysu resulted from the base thematic vowel '-o-', onto which the locative case ending *-isu was suffixed, itself formed by agglutination of the plural ending *-su onto the locative singular ending -i. All the surviving reflexes in the daughter languages are regular.

O-stem neuters differ from the o-stem masculines only in NAV. Lithuanian has lost neuter gender so it is omitted from the table. The paradigm is given for the neuter noun *yugóm (“yoke”).

number	PIE (nominative / accusative / vocative)	Ancient Greek	Latin	Sanskrit	OCS
singular	*yugóm	ζυγόν	iugum	yugam	иго
dual	*yugóy(h₁)	ζυγώ	-	yuge	idzě
plural	*yugéh₂	ζυγά	iuga	yugāni	iga

• Most of the reflexes are by regular sound changes. In OCS the nominative ending -o cannot be directly from PIE -om (which would regularly yield OCS -ъ, cf. accusative singular ending above), so it's generally held to originate from pronominal ending in NAV neuter gender *-od (cf. Sanskrit तद् (tád, “that”)) which has been analogically transferred to nouns.
• In Ancient Greek the nominative ending -ω is of uncertain origin, probably taken from the masculine nominative dual ending.
• In Sanskrit plural form, on the original pre-form *yugā the element -n- has been added analogically to n-stems (see below), and the ending -i < *h₂ (the regular reflex of syllabic laryngeal in Sanskrit) for NAV of neuter-gender athematic nouns (see below).
• The plural ending of neuter gender formed with the suffix *-eh₂ was in PIE a collective noun which agreed with the verb in singular. That state of affairs has been preserved in Hittite and Ancient Greek, e.g. πάντα ῥεῖ "all things flow", where πᾶς (pâs, “every, each”) is in nominative plural, and ῥέω (rhéō, “I flow”) is in third-person singular.

eh₂-stems

PIE eh₂-stems or ā-stems (the traditional name) were mostly of feminine gender. Some daughter languages have masculine-gender exceptions (e.g. OCS слоуга (sluga, “servant”), Lithuanian el̃geta (“beggar, poor man”), Latin verna (“homeborn slave”)). Sometimes this inflectional type is called senā-type, after Sanskrit सेना (sénā), which also belongs to this type.

This type encompasses Greek and Latin "first declension". Of five subtypes of Greek first declension, the subtype with nominative in -ᾰ (e.g. θάλασσα (thálassa, “sea”)) is historically unrelated. The other four types all evolved from this inflectional type in PIE.

Example paradigm is given for *h₁éḱweh₂ "mare", eh₂-stem derivation of *h₁éḱwos (“horse, stallion”). For Greek, which has no such eh₂-stem derivation of the inherited word ἵππος (híppos), the inflection is provided for the word ἰδέᾱ (idéā, “look, appearance”), and in OCS for the word жєна (žena, “woman”).

number	case	PIE	Ancient Greek	Latin	Sanskrit	OCS	Lithuanian
singular	nominative	*h₁éḱweh₂	ἰδέᾱ (idéā)	equa	अश्वा (aśvā)	жєна (žena)	ašva
	vocative	*h₁éḱwe(h₂)	ἰδέᾱ	equa	aśve	ženo	ašva
	accusative	*h₁éḱweh₂m	ἰδέᾱν	equam	aśvām	ženǫ	ašvą
	instrumental	*h₁éḱweh₂(e)h₁	-	-	aśvayā	ženojǫ	ašva
	dative	*h₁éḱweh₂ey	ἰδέαι > ἰδέᾳ	equae	aśvāyai	ženě	ašvai
	ablative	*h₁éḱweh₂es	-	equā(d)	aśvāyās	-	-
	genitive	*h₁éḱweh₂es	ἰδέᾱς	equae	aśvāyās	ženy	ašvos
	locative	*h₁éḱweh₂i	-	equae*	aśvāyām	ženě	ašvoje
dual	nominative / accusative / vocative	?? *h₁éḱweh₂ih₁ ?? *h₁éḱweh₂h₁e	ἰδέᾱ	-	aśve	ženě	ašvi
	genitive / locative	??	ἰδέαιν	-	aśvayos	ženu	-
	dative / ablative / instrumental	*h₁éḱweh₂bʰām ???	ἰδέαιν	-	aśvābhyām	ženama	ašvom
plural	nominative / vocative	*h₁éḱweh₂es	ἰδέαι	equae	aśvās	ženy	ašvos
	accusative	*h₁éḱweh₂n̥s	ἰδέᾱς	equās	aśvās	ženy	ašvas
	instrumental	*h₁éḱweh₂bʰis	-	-	aśvābhis	ženami	ašvomis
	dative / ablative	*h₁éḱweh₂bʰos, *h₁éḱweh₂mos	ἰδέαις	equīs	aśvābhyas	ženamъ	ašvoms
	genitive	*h₁éḱweh₂om	ἰδεῶν	equārum	aśvānām	ženъ	ašvų
	locative	*h₁éḱweh₂su	-	equīs*	aśvāsu	ženaxъ	ašvose

1. nominative singular: There is no ending, the bare eh₂-stem is used. In Greek it regularly yields -ᾱ or -η, depending on the dialect and the preceding vowel (in Attic, ᾱ changing to η except after ε, ι and ρ). The ending -ς in Greek masculine ā-stems (e.g. νεᾱνίᾱς (neāníās, “young man”) is of secondary origin. In Latin pre-form *-ā has yielded -a due to iambic shortening in disyllabic nouns, and then analogically spreading to all the other nouns of this type.
2. vocative singular: The ending is the same as nominative singular, except that the laryngeal drops without lengthening the preceding vowel, usually explained as regular loss of a laryngeal in pause, i.e. at the absolute end of words and sentences. PIE vocatives were phonologically and syntactically separate from the clauses they appeared in, with the result of laryngeal being dropped, leaving only the short vowel. This explains the short vowel in Ancient Greek vocatives such as νύμφᾰ (númpha, “Oh maid!”) and OCS -o (regularly from post-PIE *a, PIE *ā would've yielded OCS a). The rest of Greek feminines, as well as all the Latin, use the nominative singular form as vocative.
3. accusative singular: PIE *-eh₂m (with non-syllabic *-m) > post-PIE *ām, regularly yielding Greek -ᾱν, -ην (with regular Greek change of word-final -μ to -ν). In Latin the vowel is shortened due to the general shortening of all long vowels in final syllables before all consonants except -s. In OCS the ending -ǫ is a regular reflex of a sequence of a back vowel followed by a nasal, following the loss of closed syllables in Common Slavic period.
4. instrumental singular: The oldest ending has been preserved in Vedic (senā "by an army"); the same ending is used in Classical Sanskrit, but on a stem extended with -y- by analogy to i-stems. In Balto-Slavic the reconstruction is uncertain: Lithuanian has acuted -à which could be formally matched with the Vedic ending, but dialects also show the ending -u (e.g. runku "by hand"), and certain adjectives have nasal -ą (e.g. mažą́ją "with the little"), which point to the ending *-ā́m. OCS has the ending -ojǫ taken from pronominal inflection (cf. тѫѭ (tǫjǫ, “with that”)). Nasal vowel also shows a pre-form *-ām, independently reconstructible also for Baltic. In Greek and Italic the instrumental case has not been preserved, but can be traced fossilized to certain adverbs, such as κρυφᾷ (kruphâi) / κρυφῆ (kruphê) "secretly", originally *"by means of secrecy" and Latin quā (“in what manner”) (possibly ablative though).
5. dative singular: PIE *-eh₂ey > post-PIE *-āy, yielding regularly Greek -ᾱι/-ηι and the rest of attested endings, except for Sanskrit which has it suffixed onto the -y- element taken from i-stems.
6. ablative singular: In PIE ablative singular of this inflection was the same as genitive, as can be seen in Sanskrit. Classical Latin ending -ā derives from Old Latin -ād, which was formed analogically to the ending -ōd of o-stems (see above).
7. genitive singular: PIE ending *-es has been regularly reflected in most of the branches. Latin -ae has final -i < *-ī by analogy to o-stems; the inherited ending has been preserved in fossilized phrases such as pater familiās (“head of household”) and adverbs such as aliās (“at another place/time”). In Sanskrit, the interfix element -y- is taken by analogy to i-stems.
8. locative singular: PIE ending *-eh₂i > post-PIE *-ay. In Lithuanian to the inherited form postoposition *en > e has been suffixed yielding attested -oje, while Sanskrit -yām has been taken from pronominal paradigm (cf. Sanskrit instrumental singular feminine तस्याम् (tasyām, “on that”)).
9. dual: As usual, reconstruction of dual case endings is very hard; in NAV dual characteristic is the ending -ih₁, shared by eh₂-stems with the nouns of neuter gender. PIE *eh₂ih₁ > post-PIE *ai, which regularly yields all forms except for Greek -ᾱ, which is by Mycenaean evidence shown to derive from earlier *-ᾰε. The rest of Greek inflectional endings (-αιν, αιιν) arose by analogy to o-stem forms. OCS final -u in GL agrees with final -os in Sanskrit, most probably pointing to PIE *-ows.
10. nominative/vocative plural PIE *-eh₂es > post-PIE *ās, regularly reflected in most of the languages. In Latin the ending -ae was taken by analogy from o-stems, while the inherited ending was preserved in Old Latin inscriptions (e.g. QVAS > quae, HASCAE > hae, RELIQVIAS > reliquiae). Greek also independently replaced the original ending by analogy to o-stems with -ᾰι. OCS -y continues the original ending for accusative plural (see below).
11. accusative plural: PIE *-eh₂n̥s > post-PIE *ān̥s, which has been preserved in dialectal Greek forms as -ανς, whence Attic -ᾱς is derivable. In most language the word-final cluster -ns has assimilated to -s. In OCS *ā merged with *ō, which was raised to *ū before a final -s, yielding *-ūns > -y.

i-stems

Animate

number	case	PIE	Hittite	Latin	Sanskrit	Greek (attic)	Gothic	O.C.S.
singular	nominative	*mn̥tís	𒄯𒆠𒅖 (ḫarkiš)	turris	अग्निस् (agnís)	πόλῐς (pólis)	𐌵𐌴𐌽𐍃 (qēns)	kostĭ
	vocative	*mn̥téy	–	turris	अग्ने (agne)	πόλῐ	qēn	kosti
	accusative	*mn̥tím	ḫarkin	turrim	अग्निम् (agnim)	πόλῐν	qēn	kostĭ
	instrumental	*mn̥ti(y)éh₁	ḫarkit, /χarkitː/	–	páti(y)ā	–	–	kostĭjǫ
	dative	*mn̥téyey	ḫarkai < loc.sg	turrī	अग्नये (agnaye)	πόλει	qēnai	kosti
	ablative	*mn̥tóys	ḫarkaz(a) < *´-eyoti	turrē	अग्नेस् (agnes)	–	–	–
	genitive	*mn̥tóys	ḫarkaš < *´-eyos	turris	अग्नेस् (agnes)	πόλεως	qēnais	kosti
	locative	*mn̥téyi	ḫarkai	turrī	अग्ना (agnā), अग्नौ (agnau)	–	–	kosti
dual	nominative / accusative / vocative	*mn̥tíh₁	–	–	अग्नी (agnī)	πόλει	–	kosti
plural	nominative / vocative	*mn̥téyes	ḫarkaiš, ḫarkaeš	turrēs	अग्नयस् (agnayas)	πόλεις	qēneis	kosti
	accusative	*mn̥tíms	ḫarkauš, /χarkaɔs/ < *´-eym̥s	turrīs	अग्नीन् (agnīn)	πόλεις	qēnins	kosti
	instrumental	*mn̥tímis, *mn̥tíbʰis	ḫarkit	–	अग्निभिस् (agnibhis)	–	–	kostemi
	dative / ablative	*mn̥tímos, *mn̥tíbʰos	ḫarkaš	turribus	अग्निभ्यस् (agnibhyas)	πόλεσῐ(ν) < loc.	qēnim	kostemŭ
	genitive	*mn̥tyoHom, *mn̥téyoHom	*ḫarkan?, ḫarkaš	turrium	अग्नीनाम् (agnīnām)	πόλεων	qēnē	kostĭjĭ
	locative	*mn̥tísu	ḫarkaš	–	अग्निषु (agniṣu)	–	–	kostexŭ

1. nominative singular: The ending *-is comes from the zero grade of the morpheme and the nominative singular desinence *-s. It was preserved in Ancient Greek (e.g. πόλις (pólis)), in Latin turris, in Sanskrit अग्निस् (agnís), in PGmc *mundiz and Hittite ḫarkiš.
2. vocative singular: Sanskrit requires a diphthong, it could reflect either *-ey or *-oy.
3. accusative singular: The ending *-i-m comes from the zero grade and the accusative singular desinence *-m. It was preserved as Latin "-im", Sanskrit "-im". In both Greek and Hittite word-final PIE "*-m" was regularly replaced by /n/, yielding "-ῐν" and -𒅔 respectively.
4. instrumental singular: The ending *-i(y)eh₁ comes from the zero grade and the instrumental singular desinence *-éh₁.
5. dative singular: The ending "*-éyey" is securely reconstructible for PNIE. It was preserved intact in Sanskrit "-aye".
6. genitive/ablative singular: The o-grade in the ending *-oys is securely reconstructible on the basis of gothic "-ais". Anatolian however, points to "*-oyos"/ "*-eyos", which is probably a remodeling from "*-oys".
7. locative singular: PIE has the ending "*-ḗy", while Hittite has "-ai" that cannot come from a long "*ḗ", therefore the PIE ending must be "*-eyi". This would be composed from the full grade plus the locative desinence "*-i".
8. nominative/vocative plural: The ending "*-eyes" is attested in Latin "-ēs", Vedic "-ayas", and Hittite "-ēš".
9. accusative plural: "*-ims", composed by a zero grade in the root and the acc.pl ending "*-ms". Hittite in the other hand attests a full grade, but it's most likely analogical.

Neuter

number	PIE (nominative / accusative / vocative)	Latin	Sanskrit
singular	*móri	mare	vā́ri
dual	*móryih₁	-	vā́riṇī
plural	*mórih₂	maria	vā́rī

u-stems

Animate

number	case	PIE	Latin	Sanskrit	Greek (attic)	Gothic	O.C.S.
singular	nominative	*ǵéwstus	gustus	धेनुः (dhenús)	ἰχθύς (ikhthús)	𐌺𐌿𐍃𐍄𐌿𐍃 (kustus)	domъ
	vocative	*ǵéwstu	gustus	dhéno	ἰχθύ	kustu	domu
	accusative	*ǵéwstum	gustum	dhenúm	ἰχθύν	kustu	domъ
	instrumental	*ǵustúh1	–	dhenvā́	–	*kustū (c.f. Old High German sitiu)	domъmь
	dative	*ǵustéwey	gustuī	dhenáve, dhenvāí	ἰχθύϊ	kustau	domovi
	ablative	*ǵustéws	gustū	dhenós, dhenvā́s	–	–	–
	genitive	*ǵustéws	gustūs	dhenós, dhenvā́s	ἰχθύος	kustaus	domu
	locative	*ǵustéw(i)	senāti (Old Latin)	dhenāú, dhenvā́m	–	–	domu
dual	nominative / accusative / vocative	*ǵéwstuh1	–	dhenū́	ἰχθῠ́ε	–	domy
plural	nominative / vocative	*ǵéwstewes	gustūs	dhenávaḥ	ἰχθύες	kustjus	domove
	accusative	*ǵéwstuns	gustūs	dhenū́s	ἰχθῦς	kustuns	domy
	instrumental	*ǵustúbʰi	–	dhenúbhiḥ	–	–	domъmi
	dative / ablative	*ǵustúmos	gustibus	dhenúbhyaḥ	ἰχθύσι	kustum	domъmъ
	genitive	*ǵustéwoHom	gustuum	dhenūnā́m	ἰχθύων	kustiwē < kustiwō (c.f. Old High German sito)	domovъ
	locative	*ǵustúsu	–	dhenúṣu	–	–	domъxъ

Neuter

number	PIE (nominative / accusative / vocative)	Hittite	Latin	Sanskrit	Gothic (Defective, singular only)
singular	*dóru	tāru	pecū	páśu	faihu
dual	*dórwih₁	-	-	páśunī	-
plural	*dóruh₂	tāruḪI.A /taːrɔ/	pecua	páśū	-

r-stems

number	case	PIE	Latin	Sanskrit	Greek (attic)	Gothic	O.C.S.
singular	nominative	*ph₂tḗr	pater	पितृ (pitā)	πατήρ (patḗr)	𐍆𐌰𐌳𐌰𐍂 (fadar)	mati
	vocative	*ph2tér	pater	pítar	πάτερ	fadar	mati
	accusative	*ph2térm̥	patrem	pitaram	πατέρα	fadar	materь
	instrumental	*ph2tr̥éh1	–	pitrā	–	–	materьjǫ
	dative	*ph2tr̥éy	patrī	pitre	πατρί	fadr	materi
	ablative	*ph2tr̥és	patre	pitur, pitras	–	–	–
	genitive	*ph2tr̥és	patris	pitur, pitras	πατρός	fadrs	matere
	locative	*ph2tér(i)	patri*	pitari	–	–	materi
dual	nominative / accusative / vocative	*ph2térh1e	–	pitarau < piterā	πᾰτέρε	–	materi
plural	nominative / vocative	*ph2téres	patrēs	pitaras	πατέρες	fadrjus	materi
	accusative	*ph2térn̥s	patrēs	pitṝn	πατέρας	fadruns	materi
	instrumental	*ph2tr̥bʰí	–	pitṛbhis	–	–	materьmi
	dative / ablative	*ph2tr̥mós	patribus	pitṛbhyas	πατράσι	fadrum	materьmъ
	genitive	*ph2tr̥óHom	patrum	pitṝṇām	πατέρων	fadrē < fadrō (c.f. Old High German fatero)	materъ
	locative	*ph2tr̥sú	–	pitṛṣu	–	–	materьxъ

s-stems

number	case	PIE	Hittite	Latin	Sanskrit	Greek (attic)	Old English	O.C.S.
singular	nominative	*nébʰos	𒉈𒂊𒁉𒅖 (nepiš)	genus	नभः (nábhaḥ)	γένος (génos)	cælf	nebo
	vocative	*nébʰos	–	genus	nábhaḥ	γένος	–	nebo
	accusative	*nébʰos	nepiš	genus	nábhaḥ	γένος	cælf	nebo
	instrumental	*nébʰes(e)h1	nepišit	–	nábhasā	–	–	nebesьmь
	dative	*nébʰesey	nepiši	generī < *genesī	nábhase	γένει	calfur < *kalbazē (INS), *kalbazi (LOC)	nebesi
	ablative	*nébʰesos	nepišaz(a)	genere < *genese	nábhasaḥ	–	–	–
	genitive	*nébʰesos	nepišaš	generis < *genesis	nábhasaḥ	γένους < γένεος (Epic)	calfur < *kalbazaz	nebese
	locative	*nébʰes(i)	nepiši	generi* < *genesi	nábhasi	–	–	nebese
dual	nominative / accusative / vocative	*nébʰesih1	–	–	nábhasī	γένει	–	nebesě
plural	nominative / vocative	*nébʰōs	nepiša	genera < *genesa	nábhāṃsi	γένη < γένεᾰ (Epic)	calferu, calfur < *kalbaz(ō)	nebesa
	accusative	*nébʰōs	nepiša	genera < *genesa	nábhāṃsi	γένη < γένεᾰ (Epic)	calferu, calfur < *kalbaz(ō)	nebesa
	instrumental	*nébʰesbʰi	nepišit	–	nábhobhiḥ	–	–	nebesy
	dative / ablative	*nébʰesmos	nepišaš, nepišaz(a)	generibus < *genesibos	nábhobhyaḥ	γένεσῐ(ν)	calfrum < *kalbezum	nebesьmъ
	genitive	*nébʰesoHom	nepišaš	generum < *genesom	nábhasām	γενῶν < γενέων (Epic)	calfra < *kalbezo	nebesъ
	locative	*nébʰesu	nepišaš	–	nábhaḥsu	–	–	nebesьxъ

In Old English, the umlauted NOM/ACC forms are unexpected due to not being followed by a front vowel like **-iz etymologically.

n-stems

Animate

number	case	PIE	Latin	Sanskrit	Greek (attic)	Gothic	OCS
singular	nominative	*léymō	sermō	अश्मा (áśmā)	δαίμων (daímōn)	𐌲𐌿𐌼𐌰 (guma)	kamy
	vocative	*léymon	sermō	áśman	δαῖμον	guma	kamy
	accusative	*léymonm̥	sermōnem	áśmānam	δαίμονᾰ	guman	kamenь
	instrumental	*limnéh₁	–	áśmanā	–	–	kamenьmь
	dative	*limnéy	sermōnī	áśmane	δαίμονῐ	gumin	kameni
	ablative	*limnés	sermōne	áśmanaḥ	–	–	–
	genitive	*limnés	sermōnis	áśmanaḥ	δαίμονος	gumins	kamene
	locative	*limén(i)	sermōni*	áśmani	–	–	kamene
dual	nominative / accusative / vocative	*léymonh₁e	–	áśmānau < áśmānā	δαίμονε	–	kameni
plural	nominative / vocative	*léymones	sermōnēs	áśmānaḥ	δαίμονες	gumans	kamene
	accusative	*léymonn̥s	sermōnēs	áśmanaḥ	δαίμονᾰς	gumans	kameni
	instrumental	*limn̥bʰí	–	áśmabhiḥ	–	–	kamenьmi
	dative / ablative	*limn̥mós	sermōnibus	áśmabhyaḥ	δαίμοσῐ(ν)	gumam	kamenьmъ
	genitive	*limn̥óHom	sermōnum	áśmanām	δαιμόνων	gumanē < *gumanō (c.f. Old High German gomōno)	kamenъ
	locative	*limn̥sú	–	áśmasu	–	–	kamenьxъ

Neuter

number	case	PIE	Latin	Sanskrit	Greek (attic)	Gothic	OCS
singular	nominative / vocative / accusative	*h₁nḗh₃mn̥	nōmen	नाम (nā́ma)	ὄνομᾰ (ónoma)	𐌽𐌰𐌼𐍉 (namō)	imę
	instrumental	*h₁nḗh₃mn̥(e)h₁	–	nā́mnā	–	–	imenьmь
	dative	*h₁néh₃mn̥ey	nōminī	nā́mne	ὀνόμᾰτῐ	namin	imeni
	ablative / genitive	*h₁néh₃mn̥(o)s	nōminis	nā́mnaḥ	ὀνόμᾰτος	namins	imene
	locative	*h₁néh₃mn̥(i)	nomini*	nā́mni	–	–	imene
dual	nominative / accusative / vocative	*h₁nḗh₃mn̥ih₁?	–	nā́mnī	ὀνόμᾰτε	–	imeni

Note: Plurals for neuter n-stems, unlike descendant paradigms, were formed using the collective form *h₁néh₃mō, which is declined akin to the masculine n-stems (except that the nominative, accusative, and vocative forms were merged).

Heteroclitic Stems

number	case	PIE	Latin	Sanskrit	Greek (attic)	Gothic	Hittite
singular	nominative / vocative / accusative	*wódr̥	femur	यकृत् (yakṛt)	ἧπᾰρ (hêpar)	𐍅𐌰𐍄𐍉 (watō) < *watōr (c.f. OSX/ODT watar)	𒉿𒀀𒋻 (wātar)
	instrumental	*udénh₁	–	yaknā	–	–	witenit
	dative	*udéney	feminī	yakne	ἥπᾰτῐ	watin	witeni
	ablative / genitive	*udéns	feminis	yaknaḥ	ἥπᾰτος	watins	witenaš
	locative	*udén(i)	femini*	yakni	–	–	witeni

Note: Plurals were formed using the collective form *wédōr, which is also a heteroclitic stem. Furthermore, there is evidence that this declension paradigm was originally acrostatic, but descendants point to a proterokinetic paradigm by late PIE.

Root Consonant Declension

number	case	PIE	Latin	Sanskrit	Greek (attic)	Gothic
singular	nominative	*pṓds	pes	पात् (pā́t)	πούς (poús)	𐍂𐌴𐌹𐌺𐍃 (reiks)
	vocative	*pṓd	pes	pā́t	πούς	reik*
	accusative	*pódm̥	pedem	pā́dam	πόδᾰ	reik*
	instrumental	*pedéh₁	–	pā́dā	–	–
	dative	*pedéy	pedī	páde	ποδῐ́	reik
	ablative	*pedés	pede	pádaḥ	–	–
	genitive	*pedés	pedis	pádaḥ	ποδός	reikis
	locative	*péd(i)	pedi*	pádi	–	–
dual	nominative / accusative / vocative	*pódh₁e	–	pā́dau < pā́dā	πόδε	–
plural	nominative / vocative	*pódes	pedēs	pā́daḥ	πόδες	reiks
	accusative	*pódn̥s	pedēs	pádaḥ	πόδᾰς	reiks*
	instrumental	*pedbʰí	–	pádbhiḥ	–	–
	dative / ablative	*pedmós	pedibus	pádbhyaḥ	ποσῐ́ (ν)	reikam
	genitive	*pedóHom	pedum	pádām	ποδῶν	reikē < *reikō (c.f. Old High German nahto)
	locative	*pedsú	–	patsú	–	–

Adjectives

u/wih₂-stems

Masculine

number	case	PIE	Ancient Greek	Latin	Sanskrit	Hittite	Gothic	Lithuanian
singular	nominative	*ténh₂us(m)	ἡδῠ́ς (hēdús)	suāvis	स्वादु (svādúḥ)	𒉺𒀭𒆪𒍑 (pankuš)	𐌺𐌰𐌿𐍂𐌿𐍃 (kaurus)	platùs
	vocative	*ténh₂u	ἡδῠ́	suāvis	svā́do	–	–	–
	accusative	*ténh₂um	ἡδῠ́ν	suāvem	svādúm	pankun	kaurjana	platų
	instrumental	*tn̥h₂úh₁	-	-	svādvā̀	pankawit	-	plačiu
	dative	*tn̥h₂éwey	ἡδεῖ	suāvī	svādáve	pankawi	*kaurjamma	plačiam
	ablative	*tn̥h₂éws	-	suāvī	svādóḥ	pankawaz	-	-
	genitive	*tn̥h₂éws	ἡδέως	suāvis	svādóḥ	pankawaš	*kauraus	plataus
	locative	*tn̥h₂éw(i)	-	suavī*	svādaú	pankawi	–	plačiame
dual	nominative / accusative / vocative	*ténh₂uh₁(e)	ἡδέε	-	svādū́	–	–	–
plural	nominative / vocative	*ténh₂ewes	ἡδεῖς	suāvēs	svādávaḥ	pankweš	kaurjai	platūs
	accusative	*ténh₂ums	ἡδέων	suāvīs	svādū́n	pankamuš	kaurjans	plačius
	instrumental	*tn̥h₂úbʰi	-	-	svādúbhiḥ	pankawit	-	plačiais
	dative / ablative	*tn̥h₂úmos	ἡδέσῐ(ν)	suāvibus	svādúbhyaḥ	pankawaš	kaurjaim	platiems
	genitive	*tn̥h₂éwoHom	ἡδέων	suāvium	svādūnā́m	pankawaš	kaurjaizē	plačių
	locative	*tn̥h₂úsu	-	-	svādúṣu	pankawaš	-	plačiuose

Neuter

number (nominative / accusative / vocative)	PIE	Ancient Greek	Latin	Sanskrit	Hittite	Gothic	Lithuanian
singular	*ténh₂u	ἡδῠ́	suāve	svādú	panku	kauru	platù
dual	*ténh₂uh₁(e)	ἡδέε	-	svādū́	–	–	–
plural	*ténh₂uh₂	ἡδέᾰ	suāvia	svādū́	panku	*kaurja	–

Note: The Masculine and Neuter paradigms are identical except in the Nominative/Accusative/Vocative forms. In addition, Lithuanian's neuter adjective is defective and uses the ancestral Nominative/Vocative/Accusative singular form for all of its cases.

Feminine

number	case	PIE	Ancient Greek	Latin	Sanskrit	Hittite	Gothic	Lithuanian
singular	nominative	*tn̥h₂éwih₂	ἡδεῖᾰ	suāvis	svādvī́	pankuš	kaurus	platì
	vocative	*tn̥h₂éwih₂	ἡδεῖᾰ	suāvis	svā́dvi	–	–	–
	accusative	*tn̥h₂éwih₂m̥	ἡδεῖᾰν	suāvem	svādvī́m	pankun	kaurja	plačią
	instrumental	*tn̥h₂uyéh₂h₁	-	-	svādvyā̀	pankawit	-	plačia
	dative	*tn̥h₂uyéh₂ey	ἡδείᾳ	suāvī	svādvyaì	pankawi	*kaurjai	plačiai
	ablative	*tn̥h₂uyéh₂s	-	suāvī	svādvyā̀ḥ	pankawaz	-	-
	genitive	*tn̥h₂uyéh₂s	ἡδείᾱς	suāvis	svādvyā̀ḥ	pankawaš	*kaurjaizōs	plačios
	locative	*tn̥h₂uyéh₂(i)	-	suavī*	svādvyā̀m	pankawi	–	plačioje
dual	nominative / accusative / vocative	*tn̥h₂éwih₂h₁(e)	ἡδείᾱ	-	svādvī́	–	–	–
plural	nominative / vocative	*tn̥h₂éwih₂es	ἡδεῖαι	suāvēs	svādvī́ḥ	pankweš	kaurjōs	plačios
	accusative	*tn̥h₂éwih₂m̥s	ἡδειῶν	suāvīs	svādvī́ḥ	pankamuš	kaurjōs	plačias
	instrumental	*tn̥h₂uyéh₂bʰi	-	-	svādvī́bhiḥ	pankawit	-	plačiomis
	dative / ablative	*tn̥h₂uyéh₂mos	ἡδείαις	suāvibus	svādúbhyaḥ	pankawaš	kaurjaim	plačioms
	genitive	*tn̥h₂uyéh₂oHom	ἡδειῶν	suāvium	svādvī́nām	pankawaš	kaurjaizō	plačių
	locative	*tn̥h₂uyéh₂su	-	-	svādvī́ṣu	pankawaš	-	plačiose

Note: Technically, Hittite has no feminine gender, as Feminine and Masculine nouns in other PIE languages are grouped together as "common" nouns.

nt-stems

number	case	PIE	Hittite	Latin	Sanskrit	Greek	Gothic
singular	nominative	*h₁sónts	𒀀𒊭𒀀𒀭𒍝 (asānza)	sōns	सत् (sát)	ἐών (eṓn)	𐍆𐍂𐌹𐌾𐍉𐌽𐌳𐍃 (frijōnds)
	accusative	*h₁sóntm̥	𒀀𒊭𒀀𒀭𒋫𒀭 (asāntan)	sontem	santam	ἐόντᾰ	frijōnd
	instrumental	*h₁sn̥téh₁	𒀀𒊭𒀀𒀭𒋾𒀉 (asāntit)	–	sátā	–	–
	dative	*h₁sn̥téy	𒀀𒊭𒀀𒀭𒋾 (asānti) < loc.sg	sontī	sate	ἐόντῐ	frijōnd < *frijōndi (c.f. Old High German friunte)
	ablative	*h₁sn̥tós	𒀀𒊭𒀀𒀭𒋫𒊍 (asāntaz(a))	sontī	satas	–	–
	genitive	*h₁sn̥tós	𒀀𒊭𒀀𒀭𒋫𒀸 (asāntaš)	sontis	satas	ἐόντος	frijōndis
	locative	*h₁sénti	𒀀𒊭𒀀𒀭𒋾 (asānti)	monte	satí	–	–
dual	nominative / accusative / vocative	*h₁sónth₁(e)	–	–	sántāu < sántā	–	–
plural	nominative / vocative	*h₁sóntes	𒀀𒊭𒀀𒀭𒋾𒅖 (asāntis)	sontēs	sántas	ἐόντες	frijōnds
	accusative	*h₁sn̥tḿ̥s	𒀀𒊭𒀀𒀭𒌅𒍑 (asāntus /⁠ʔsaːntːɔs⁠/)	sontēs	satás	ἐόντᾰς	frijōnds
	instrumental	*h₁sn̥tmís, *h₁sn̥tbʰís	𒀀𒊭𒀀𒀭𒋾𒀉 (asāntit)	–	sádbhis	–	*frijōndam
	dative / ablative	*h₁sn̥tmós, *h₁sn̥tbʰós	asāntaš	sontibus	sádbhyas	ἐοῦσῐ(ν) < loc.pl	frijōndam
	genitive	*h₁sn̥tóHom	𒀀𒊭𒀀𒀭𒋫𒀭 (asāntan), 𒀀𒊭𒀀𒀭𒋫𒀸 (asāntaš)	sontium	satā́m	ἐόντων	frijōndē < *frijōndō (c.f. Old High German friunto)
	locative	*h₁sn̥(t)sú?	–	–	satsu	ἐοῦσῐ(ν)	–

1. nominative singular: For this case the ending is composed by the full grade of the morpheme and the nominative singular morpheme "*-s". The ending is *-onts the basis of Latin -ēns/āns < Proto-Italic *-onts/ānts as well as Gothic -onds < Proto-Germanic *-ondz.
2. accusative singular: The ending *-ónt-m̥ comes from the full grade and the accusative singular desinence *-m. It was preserved as Latin "-ontem", Sanskrit "-antam". Hittite generalized the thematic ending "*-om" at the expense of the original "-m̥", yeilding "-𒀭𒌅𒀭 " ("-antan").
3. instrumental singular: The ending *-n̥téh₁ comes from the zero grade and the instrumental singular desinence *-éh₁. It's supported by both Sanskrit and PGmc.
4. dative singular: The ending "*-n̥téy" is securely reconstructible for PIE. The accentuation is perfectly reflected in PGmc by Verner's law.
5. locative singular: The ending "*-énti" is reconstructible for PIE, Hittite "-anti" must be a recomposition of an earlier "*-ant͡s". The grade of the suffix vowel is uncertain.
6. nominative/vocative plural: For both PIE and PNIE the ending "*-ontes" is attested in Greek "-όντες", Vedic "-antas", and Hittite "-antiš".
7. accusative plural: The ending "*-n̥tḿ̥s" must be reconstructed, the zero grade in the suffix attested in Vedic.

References

• Alwin Kloekhorst (2008) Etymological Dictionary of the Hittite Inherited Lexicon, Brill Publishers
• Ranko Matasović (2008) Poredbenopovijesna gramatika hrvatskoga jezika, Zagreb: Matica hrvatska
• Andrew Sihler (1995) New Comparative Grammar of Greek and Latin, Oxford University Pres