Acts 1:3

οἷς καὶ παρέστησεν ἑαυτὸν ζῶντα μετὰ τὸ παθεῖν αὐτὸν ἐν πολλοῖς τεκμηρίοις, δι᾽ ἡμερῶν τεσσαράκοντα ὀπτανόμενος αὐτοῖς, καὶ λέγων τὰ περὶ τῆς βασιλείας τοῦ Θεοῦ.

RBT Greek Interlinear:

Strongs 3739; hois; οἷς; which/whichever; RelPro-DMP

Strongs 2532; kai; καὶ; and; Conj

Strongs 3936; parestēsen; παρέστησεν; he presented; V-AIA-3S

Strongs 1438; heauton; ἑαυτὸν; his own self; RefPro-AM3S

Strongs 2198; zōnta; ζῶντα; he who is living; V-PPA-AMS

Strongs 3326; meta; μετὰ; in company with/after; Prep

Strongs 3588; to; τὸ; the; Art-ANS

Strongs 3958; pathein; παθεῖν; to have been acted upon; V-ANA

Strongs 846; auton; αὐτὸν; himself; PPro-AM3S

Strongs 1722; en; ἐν; within; Prep

Strongs 4183; pollois; πολλοῖς; many; Adj-DNP

Strongs 5039; tekmēriois; τεκμηρίοις; proofs; N-DNP

Strongs 1223; di’; δι’; across; Prep

Strongs 2250; hēmerōn; ἡμερῶν; days; N-GFP

Strongs 5062; tesserakonta; τεσσεράκοντα; forty; Adj-GFP

Strongs 3700; optanomenos; ὀπτανόμενος; he who is being seen; V-PPM/P-NMS

Strongs 846; autois; αὐτοῖς; to themselves; PPro-DM3P

Strongs 2532; kai; καὶ; and; Conj

Strongs 3004; legōn; λέγων; he who is saying; V-PPA-NMS

Strongs 3588; ta; τὰ; the; Art-ANP

Strongs 4012; peri; περὶ; around; Prep

Strongs 3588; tēs; τῆς; the; Art-GFS

Strongs 932; basileias; βασιλείας; queen/kingdom; N-GFS

Strongs 3588; tou; τοῦ; the; Art-GMS

Strongs 2316; Theou; Θεοῦ; God; N-GMS

RBT Hebrew Literal:

τεκμηρίοις - Indubitable proofs, token signs

to those whom he also presented his own self, he who is living, beyond the Afflicting of Himself, within multitudes of token proofs¹ across through days of forty, he who is being seen by themselves and he who is speaking around the Queen of the God.

Julia Smith Literal 1876 Translation:
To them also he presented himself living, after he suffered, by many infallible signs, through forty days seen to them, and speaking the things of the kingdom of God:

LITV Translation:
to whom also He presented Himself living after His suffering, by many infallible proofs, being seen by them through forty days, and speaking the things concerning the kingdom of God.

ESV Translation:
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Footnotes

1

τεκμήριον, ου (τό)

1. Sign of recognition (signe de reconnaissance):
Originally, the term referred to a distinctive mark or sign by which something could be recognized or identified. Examples include uses in Herodotus (Hdt. 2,13) and tragedy such as Aeschylus (Agamemnon 1366), Sophocles (Electra 744). It carries the sense of a visible or noticeable indication — a symptom or token that serves as evidence of something.

2. Mark, testimony, evidence, proof (marque, témoignage, preuve):
By extension, τεκμήριον came to mean any form of proof or demonstration — an argument or piece of evidence presented to establish a fact or truth. It can be something that provides or yields proof (παρέχεσθαι, διδόναι), as seen in Xenophon (Agesilaus 6.1) or the philosophical dialogues of Plato (Theaetetus 185b, 158b).

• It can mean to demonstrate or prove something by logical or empirical means (ἀποδεικνύναι, ἀποφαίνειν).

• In rhetoric and logic, τεκμήριον is understood as a conclusive proof, distinguished from less certain signs such as σημεῖον (sign) or εἰκός (probability). Aristotle treats it as a form of proof that yields certainty, contrasting with these other types of evidence that might be fallible or probabilistic (see Aristotle, Analytica Posteriora 2.27.7; Rhetoric 1.2.16 and 2.25.8).

Typical usage in discourse:
It is common for a speaker or writer to introduce a τεκμήριον with the phrase τεκμήριον δέ τούτο (“and here is the proof for this”), sometimes followed by the particle γάρ to explain or justify the assertion with evidence, as seen in Herodotus (2.58), Thucydides (2.50), or Demosthenes (459, 28).

Etymology:
The word derives from τέκμαρ, which also denotes a fixed, established sign or limit, something that marks certainty or serves as a criterion.

Summary:

• τεκμήριον began as a recognizable sign or mark, a symptom or distinctive token.

• It evolved to signify a piece of evidence, proof, or testimony that can establish the truth of a claim.

• Philosophically and rhetorically, it indicates conclusive proof (as opposed to probable signs).

• Often introduced in argumentation as a clear and authoritative demonstration of the point under discussion.

(cf. LSJ, Bailley)