The Gerund and Gerundive

Outside the finite forms of the verb, and akin to the noun, are a number of verbal forms: the infinitive, the supine, the lparticiple, the gerund, and the gerundive.

FORMATION: The GERUND is formed by taking the verb stem and adding (1) the infix -ND- and (2) masculine singular
           second-declension endings:

Notice:

(1) There is no nominative singular. If you have a nominative form in a sentence, it is not the GERUND.
(2) There are no feminine or neuter forms whatever. If you have a feminine form or a neuter form in a sentence, it is not the GERUND.
(3) There is no plural at all. If you have a plural form, it is not the GERUND.
(4) The gerund looks like the future passive participle to some extent (so does the gerundive).

FORMATION:

GRAMMAR:

The infinitive, used as a noun, is used only in the nominative and accusative cases. The gerund is used in the cases where the infinitive is not used (genitive, dative and ablative), and it can be used in the accusative as an alternative to the infinitive. Since it lacks a nominative form, it cannot be used in the nominative case as an alternative for the infinitive.

The gerund obeys the same rules for cases used with it as the verb would, since (obviously) it is a verb as well as a noun.

The gerund is virtually always active in meaning, while the gerundive (a verbal adjective) is passive in meaning. Note that the gerundive and the perfect passive participles are often translated in the same way.

The genitive:

The genitive of the gerund (and gerundive) is used chiefly after nouns and adjectives which would require a complement:

SAPIENTIA ARS VIVENDI PUTANDA EST.
"Wisdom is to be considered the art of living." (Cicero de Finibus 1.13.42)

(Titus) EQUITANDI PERITISSIMUS FUIT.
"(The Emperor Titus) was quite expert in horse riding." (Suetoonius Titus 9)

Prepositions:

AD (and occasionally ante, circa, in, inter, ob, propter)) frequently takes the gerund and the gerundive with the accusative.

ATTICUS PHILOSOPHORUM PRAECEPTIS AD VITAM AGENDAM NON AD OSTENTATIONEM UTEBATUR.
"Atticus used the precepts of the philosophers for living life not for showing off." (Nepos, Atticus 17.3)

AB (and de, ex, in, pro) takes the ablative of the gerund and gerundive:

PROHIBENDA EST MAXIME IRA IN PUNIENDO. "Anger must be prohibited above all in punishing."

EX DISCENDO CAPIUNT VOLUPTATEM. "They get their pleasure from learning."

Instead of the gerund + an accusative, Latin much prefers to put the object into the case of the gerund, and to turn the gerund into a gerundive (i.e. make the gerund-noun into an adjective) ; the gerundive, as an adjective, is then obligated to agree with its noun in number, gender and case.

AD PLACANDUM DEOS becomes AD DEOS PLACANDOS.