From BiblePortal Wikipedia

King James Dictionary [1]

PROP'ER, a. L. proprius, supposed to be allied to prope, near.

1. Peculiar naturally or essentially belonging to a person or thing not common. That is not proper, which is common to many. Every animal has his proper instincts and inclinations, appetites and habits. Every muscle and vessel of the body has its proper office. Every art has it proper rules. Creation is the proper work of an Almighty Being. 2. Particularly suited to. Every animal lives in his proper element. 3. One's own. It may be joined with any possessive pronoun as our proper son.

Our proper conceptions.

Now learn the difference at your proper cost.

Note. Own is often used in such phrases "at your own proper cost." This is really tautological, but sanctioned by usage, and expressive of emphasis.

4. Noting an individual pertaining to one of a species, but not common to the whole as a proper name. Dublin is the proper name of a city. 5. Fit suitable adapted accommodated. A thin dress is not proper for clothing in a cold climate. Stimulants are proper remedies for debility. Gravity of manners is very proper for persons of advanced age.

In Athens, all was pleasure,mirth and play

All proper to the spring and sprightly May.

6. Correct just as a proper word a proper expression. 7. Not figurative. 8. Well formed handsome.

Moses was a proper child.  Hebrews 11

9. Tall lusty handsome with bulk. Low and not used. 10. In vulgar language, very as proper good proper sweet. This is very improper, as well as vulgar.

Proper receptacle, in botany, that which supports only a single flower or fructification proper perianth or involucre, that which incloses only a single flower proper flower or corol, one of the single florets or corollets in an aggregate or compound flower proper nectary, separate form the petals and other parts of the flower.

Vine's Expository Dictionary of NT Words [2]

1: Ἀστεῖος (Strong'S #791 — Adjective — asteios — as-ti'-os )

is translated "proper" in  Hebrews 11:23 , RV, "goodly:" see Beautiful , No. 2.

2: Ἴδιος (Strong'S #2398 — Adjective — idios — id'-ee-os )

"one's own," is found in some mss. in  Acts 1:19 , AV, "proper;" in  1—Corinthians 7:7 , RV, "own" (AV, "proper"); in  Jude 1:6 , RV, "their proper (habitation)," AV, "their own."

Webster's Dictionary [3]

(1): ( a.) Belonging to one; one's own; individual.

(2): ( a.) Befitting one's nature, qualities, etc.; suitable in all respect; appropriate; right; fit; decent; as, water is the proper element for fish; a proper dress.

(3): ( a.) Belonging to the natural or essential constitution; peculiar; not common; particular; as, every animal has his proper instincts and appetites.

(4): ( a.) Becoming in appearance; well formed; handsome.

(5): ( a.) Pertaining to one of a species, but not common to the whole; not appellative; - opposed to common; as, a proper name; Dublin is the proper name of a city.

(6): ( a.) Rightly so called; strictly considered; as, Greece proper; the garden proper.

(7): ( a.) Represented in its natural color; - said of any object used as a charge.

(8): ( adv.) Properly; hence, to a great degree; very; as, proper good.

International Standard Bible Encyclopedia [4]

prop´ẽr  : For the King James Version "proper" (child), in   Hebrews 11:23 , the Revised Version (British and American) substitutes "goodly"; in  1 Chronicles 29:3;  1 Corinthians 7:7 , the Revised Version (British and American) "own" is employed, and for the too emphatic "their proper tongue" in  Acts 1:19 "their language" is written. But none of the King James Version forms are really obsolete.