The notes here are taken from the actual Scala, so be warned that references to the "previous" proverb refer to its order in the Scala, not its order here. You can read more about the word at the Verbosum blog: FATUM.
Agunt opus suum fata. ~ Note: The words are from Seneca's De Consolatione.
Fata viam invenient. ~ Note: Note the future tense: invenient. Here is the line from Vergil's Aeneid III where you can find this saying: Fata viam invenient aderitque vocatus Apollo.
Omnia fato fiunt. ~ Note: You can find this idea debated in Cicero's philosophical treatise De Fato.
Sic erat in fatis.
Sua quemque sequuntur fata. ~ Note: Compare the proverb you saw earlier - Trahit sua quemque voluptas - for another example of how the reflexive "sua" can sometimes be used in the nominative case.
Ratio fatum vincere nulla valet. ~ Note: Notice how the noun phrase "ratio nulla" elegantly wraps around the infinitive phrase "fatum vincere" - that kind of intertwined word order is so easy in Latin but basically impossible in English.
Multi ad fatum venere suum, dum fata timent. ~ Note: Note the use of the form venere, which is equivalent to venerunt. Notice also how the prepositional phrase ad fatum...suum wraps elegantly around that verb.
Curae cedit fatum. ~ Note: This takes the idea of the previous saying and declares the careful attention can even overcome the power of fate: Fate yields to carefulness. This is the Thomson family motto.
Fatis agimur; cedite fatis. ~ Note: Note that the first "fatis" here is ablative (we are driven by the fates), while the second is dative (yield to the fates!). You can find this fatalistic expression spoken by the chorus in Seneca's tragic play, Oedipus.
Ducunt volentem fata, nolentem trahunt. ~ Note: The proverb is built on a parallelism: ducunt/trahunt and volentem/nolentem, with a chiastic inversion. Fata is the subject of both verbs.
Ut fata trahunt. ~ Note: Note that the "ut" here simply means "as" or "how" - as you can see from the indicative verb trahunt, "ut" is not being used here to introduce a purpose or result clause.
Fata non servant ordinem inter senes et iuvenes.
Diverso tempore, diversa fata. ~ Note: This saying has been used as the title of an epigram: Tempus idem non est, vario pro tempore fata / Mutantur, pluviis proxima sole dies.
Fata regunt homines. ~ Note: You will find this observation in Juvenal's Satirae, 9.
Regitur fatis mortale genus. ~ Note: The words are from Seneca's Octavia.
Mutari fata non possunt.
Iam Troiae sic fata ferebant.
Audacem iuvant fata. ~ Note: This is a motto of the Somerville family.
Omnia fato eveniunt. ~ Note: You can find this idea discussed in Cicero's De Fato and also in his treatise De Divinatione, 2: Si omnia fato, quid mihi divinatio prodest?
Habent et sua fata libelli.
Habent sua fata libelli.
Fata si poscunt, dabo.
Dum fata deusque sinebat. ~ Note: The words are from Vergil's Aeneid, 4.
Dum fata sinunt iungamus amores.
Dum fata sinunt, vivite laeti. ~ Note: The words are from Seneca's tragedy, Hercules Furens.
Domi manendum est, fata cui sunt prospera.
Quem fata pendere volunt, non mergitur undis.
Dum fata fugimus, fata stulti incurrimus.
Fugiendo in media fata incurritur.
Melior post aspera fata resurgo. ~ Note: You can see this motto on a medallion struck in honor of Hugo Grotius here: image.
Fato prudentia maior.
Fato non repugnandum. ~ Note: This is one of the sayings Erasmus included in his Adagia, 5.1.90.
Quo fata trahunt retrahuntque sequamur.
Fatum inevitabile. ~ Note: This is one of the sayings Erasmus included in his Adagia, 3.9.86; see also 3.10.7.
Inevitabile est fatum.
Rotat omne fatum.
Fatum immutabile. ~ Note: This is one of the sayings Erasmus included in his Adagia, 3.9.53.
Transilit et fati litora magnus amor.
Tunc beatam dico vitam, cum peracta fata sunt.
Vivamus hilares, fata dum vitam ferunt. ~ Note: This is a saying by Janus Anysius (Giovanni Aniso); his sayings were sometimes published together with the ancient sayings of Publilius Syrus.