Latin Cases - 3) Dative

The Grammar section of Collins Latin Dictionary And Grammar explains as follows:

Dative Case

1. Indirect object (ie to or for whom an action is performed)
pecuniam domino debit (he gave the money to his master)

2. used with verbs of obeying (parere), resisting (resitere), pleasing (placere), ordering (imperare), etc
maria terraque Deo parent (land and sea obey God)

3. verb compounds (beginning ad-, ob-, prae-, sub-) denoting helping or hindering take dative
adesse  -  come to help
subvenire  -  help 
Prompeius hostibus obstitit (Pomey opposed the enemy)

4. indicates possession
Poppaea amica est Marciae (Pappaea is Marcica's friend)

5. is used with adjectives meaning "like" (similis), "fit" (aptus), "near" (proximus)
feles tigri similis est (the cat is like a tiger)

6. indicates a purpose (known as predicative dative)
nemo mihi auxilio est (there is no-one to help me)

7. shows the agent of genrund /gerundive
omnia erant agenda nobis (everything had to be done by us)

-----

New Latin Grammar (Charles E. Bennett) explains

186. The Dative case, in general, expresses relations which are designated in English by the prepositions to and for.

This definition differs from the definition of the Accusative case (172. The Accusative is the Case of the Direct Object) and uses the prepositions to and for even English can uses the concept of the Indirect Object.

I think that the Dative case is to be defined as ＜the Case of the Indirect Object＞. And actually the explanation starts with  Dative of Indirect Object as the commonest use of the Dative

Dative of Indirect Object
 
187. The commonest use of the Dative is to denote the person to whom something is given, said, or done. Thus:—

I. With transitive verbs in connection with the Accusative; as,—

hanc pecūniam mihi dat, he gives me this money;
haec nōbīs dīxit, he said this to us.

a. Some verbs which take this construction (particularly dōnō and circumdō) admit also the Accusative of the person along with the Ablative of the thing. Thus:—

Either Themistoclī mūnera dōnāvit, he presented gifts to Themistocles, or
Themistoclem mūneribus dōnāvit, he presented Themistocles with gifts;
urbī mūrōs circumdat, he builds walls around the city, or
urbem mūrīs circumdat, he surrounds the city with walls

dōnō = to donate, to give

In English - "Give him some food" - him is regarded as an indirect object and food is as a direct object.

However, the verbs like to supply, to provide, to equip, to furnish are used as

to supply (to provide) someone with something (1)
to equip (to furnish) something (2) with something (3)

In the above someone and something (2) are regarded as a direct object. But something (1) and something (3) look like or can be considered as an direct object even they have with before them.


II. With many intransitive verbs; as,—

nūllī labōrī cēdit, he yields to no labor.

a. Here belong many verbs signifying favor,^[48] help, injure, please, displease, trust, distrust, command, obey, serve, resist, indulge, spare, pardon, envy, threaten, be angry, believe, persuade, and the like; as,—

Caesar populāribus favet, Caesar favors (i.e. is favorable to) the popular party;
amīcīs cōnfīdō, I trust (to) my friends;
Orgetorīx Helvētiīs persuāsit, Orgetorix persuaded (made it acceptable to) the Helvetians;
bonīs nocet quī malīs parcit, he injures (does harm to) the good, who spares the bad.

NOTE.—It is to be borne in mind that these verbs do not take the Dative by virtue of their apparent English equivalence, but simply because they are intransitive, and adapted to an indirect object. Some verbs of the same apparent English equivalence are transitive and govern the Accusative; as, juvō, laedō, dēlectō. Thus: audentēs deus juvat, God helps the bold; nēminem laesit he injured no one.

b. Verbs of this class are used in the passive only impersonally; as,—

tibi parcitur, you are spared;
mihi persuādētur, I am being persuaded;
eī invidētur, he is envied.

c. Some of the foregoing verbs admit also a Direct Object in connection with the Dative; as,—

mihi mortem minitātur, he threatens me with death (threatens death to me).

The comment in the above ＜NOTE.—It is to be borne in mind that these verbs do not take the Dative by virtue of their apparent English equivalence, but simply because they are intransitive, and adapted to an indirect object.＞ is the auther's comment and reminder for the readers. ＜simply because they are intransitive＞does not explain why intransitive in Latin and transitive in English.

This is an interesting part to investigate why,  and there are some easy ways to do so.

1. What these intransitive verbs (favor,^[48] help, injure, please, displease, trust, distrust, command, obey, serve, resist, indulge, spare, pardon, envy, threaten, be angry, believe, persuade) have in common ?

a) opposite meaning
help - injure
please - displease
trust - distrust 
command - obey,  serve

not exactly the opposite

resist - indulge (cannot resist)
believe (by oneself) - persuade (someone else persuades someone to believe)

favor, spare, pardon, envy, threaten, be angry should be treated separately as these are rather special verbs although commonly used. The opposite meaning words to these may take the Dative.

b) Most these verbs describe human psychological behaviors or just feelings and therefore directly or indirectly involve or are related with  a person or persons.

The Accusative Case section of New Latin Grammar (Charles E. Bennett) says:

b) Many Verbs expressing emotions, regularly Intransitive, have also a Transitive use; as,—

queror fātum, I lament my fate;
doleō ejus mortem, I grieve at his death;
rīdeō tuam stultitiam, I laugh at your folly.

So also lūgeō, maereō, mourn; gemō, bemoan; horreō, shudder, and others.

2. How these verbs used in German ?  German still keeps the Dative.


III. With many verbs compounded with the prepositions: ad, ante, circum, com,^[49] in, inter, ob, post, prae, prō, sub, super.
These verbs fall into two main classes,—
1. Many simple verbs which cannot take a Dative of the indirect object become capable of doing so when compounded with a preposition; as,—

afflīctīs succurrit, he helps the aflicted;
exercituī praefuit, he was in command of the army;
intersum cōnsiliīs, I share in the deliberations.

2. Many transitive verbs which take only a direct object become capable, when compounded, of taking a dative also as indirect object; as,—

pecūniae pudōrem antepōnit, he puts honor before money;
inicere spem amīcīs, to inspire hope in one's friends;
mūnītiōni Labiēnum praefēcit, he put Labienus in charge of the fortifications.

As Dative of Indirect Object is the commonest use of the Dative no my comment on the rest of this section right now.