Ptolemy I
311-305 BCE
Alexandria
27.5 mm 14.6g 1h
Avers : Buste cornu et diadémé d’Alexandre le Grand sous les traits de Zeus-Ammon à droite, coiffé de la dépouille d’éléphant avec l’égide.
Revers : Athéna Promachos ou Alkidemos marchant à droite, brandissant une javeline de la main droite et tenant un bouclier de la gauche ; dans le champ à gauche, un casque corinthien, un monogramme et un aigle sur un foudre tourné à droite.
Sv.162 (37 ex) – Cop.29 – GC.7750 var. – BMC.- – MP.6
Ex Robert J. Myers Auction 12, lot 291 (December 4, 1975)

The Lagid (named for Ptolemy I’s father) kingdom started with Ptolemy I, who realized the advantage of a kingdom in Egypt – mainly that it was easy to defend.

Ptolemaic Kingdom of Egypt, Ptolemy II Philadelphos
AR Tetradrachm. Tyre, dated RY 30 = 256/5 BCE
14.01g, 25mm, 12h.
Diademed head of Ptolemy I to right, wearing aegis around neck / ΠΤΟΛEΜΑΙOΥ [BAΣΙΛEΩΣ], eagle standing to left; monogram of Tyre above club to left; Λ (date) above monogram to right; A between legs.
CPE 577; Svoronos 657; SNG Copenhagen 488; DCA 20
Ex collection of R. N. Draskowski;
Ex Ephesus Numismatics, North Carolina, USA

His son, Ptolemy II, is credited with finishing the Pharos (lighthouse) of Alexandria and the Library at Alexandria. He was also the first Ptolemy to marry his sister.

Ptolemaic Kings of Egypt. Ptolemy III Euergetes
AE Trihemiobol
246-222 BCE
29.18mm 16.90g
Obverse: Diademed Head of Zeus Ammon right
Reverse: Basileus Ptolemaios, statue of Aphrodite standing facing on base
CPE B447; Svoronos 1005; SNG Copenhagen 644 Paphos mint
Ex Herb Klug
Ex Marc Breitsprecher

Ptolemy III nearly defeated the Seleukid empire, but was forced to turn back due to an uprising in his own Egypt.

Ptolemaic Kingdom of Egypt. Berenike II, wife of Ptolemy III
Mint of Heraklea by the Sea or Seleukeia in Pieria
Struck circa 244-241 BCE
Tritartemorion Æ 21mm, 6,74g
Diademed and draped bust right of Berenike II /
Eagle with closed wings standing left on thunderbolt.
CPE B460; Svoronos 1055; SNG Copenhagen 460

Berenike II was the wife of Ptolemy III. She killed her first husband when she found out he was cheating on her.

Ptolemy IV Philopator
222-205/4 BCE
AE Drachm 41.4mm 66.2g
Alexandreia Mint
Obv: Head of Zeus-Ammon right, wearing tainia
Rev: Eagle standing left on thunderbolt, filleted cornucopia to left; LI between legs
Ref: Svoronos 1126

Ptolemy IV was the beginning of the lazy kings of Egypt and started its downfall.