Siemens AG, Europe’s largest engineering company, has agreed to buy Los Angeles-based Diagnostic Products Corp. for about $1.86 billion in cash, the companies announced Thursday.

The acquisition would expand Siemens’ medical division, which now is strongest in medical imaging and healthcare information technology. Diagnostic Products, which makes test kits to detect diseases such as cancer and allergies, will give Siemens an immediate presense in the in-vitro diagnostics market.

Siemens will pay $58.50, 21 percent more than Wednesday’s close, for each share of Diagnostic Products, whose shares jumped 19 percent to $57.89 in Thursday trading.

Diagnostic Products had 2005 sales of $481 million and operating income of $96 million. The company announced Thursday that its first-quarter net income increased 12 percent on sales of its Immulite automated diagnostic systems. Earnings rose to $18 million, or 60 cents per share, from $16.1 million, or 54 cents, in the same period a year ago. The results included a stock option compensation expense of $1.4 million in compliance with new reporting rules.