Over the next few months, Alvintzi menacingly hovered in the Bassano
region, gathering up reinforcements from the Trieste region that increased his
army’s strength to 45,000 men. Napoleon had roughly the same number of men but
10,000 of them were committed to the continuing siege of Mantova. Prior to
Alvintzi’s last attack, the French army was in the best possible defensive
position. Joubert’s division was garrisoned between La Corona and Rivoli on
the eastern side of Lake Garda, in close support of Massena’s division in
Verona. Augereau was positioned on the Adige River, south of Ronco, while
General Rey occupied the western shores of Lake Garda. Sérurier, recently
recuperated, took over command of the Mantova siege from a now ill Kilmaine.
On the 8th of January 1797, the first contact was made between
Austrian and French forces and Augereau was driven back by an Austrian advance
at Bassano. Augereau, believing that this was the main Austrian advance, sought
reinforcements. Napoleon believed that this Austrian advance was only a
diversion and that the main attack was still to come. Napoleon was soon proven
correct. Joubert was attacked by a sizeable force and had to retreat from La
Madonna di Corona, the small village just north of Rivoli. 
Alvintzi had revealed
his plan. His Lake Garda column was sizeable, totaling 28,000 men. Bonaparte
acted quickly, ordering Joubert to hold his position at all costs while he
summoned Massena and Rey to move to Rivoli at once.
The battlefield at Rivoli favoured the French. There were several routes
to move along between Verona and Rivoli all leading to a horseshoe-shaped ridge
called the Trombalore Heights, between the Adige and Tasso Rivers. The Austrian
army had less to work with, as there were only two mountain roads along which
the troops could move southward.
The key to French victory would be the speed at which the reinforcements
could be brought to battle. At 6:00am on the 14th, Napoleon ordered
Joubert to position his division on the eastern flank of the plateau and to hold
off the Austrian forces under Koblos and Liptay. Massena arrived shortly
thereafter and was ordered to position his division on the western flank. By
10:00am, the French had 17,700 men on the field. This number would increase to
23,000 with the arrival of Rey’s division.
The crucial point in the battle came later that day as the Austrians
flanked the French forces by seizing the Osteria Gorge to the east of the
Trombalore Heights. Napoleon quickly ordered Joubert’s forces to move east to
counter the Austrian advance. The French commander trained his artillery on the
densely packed enemy from above and decimated the Austrian force, bringing about
a full retreat. 
The Austrians were defeated. Over the two days
of fighting, Alvintzi’s army sustained 14,000 casualties and 11,000 prisoners.
The remainder of the Austrian army retreated up the Adige signaling the end of
the Austrian offensive of 1796-7 in Northern Italy.
All that remained was the siege of Mantova. Würmser held out until the 2nd
of February 1797, when the fortress was turned over peacefully to the French. Of
the garrison of 30,000 men, only 16,000 were able to walk out of the fortress
without assistance. The fall of Mantova completed Napoleon’s conquest of
Northern Italy. Napoleon may have won the battles but the war was not over. The
Austrian Government refused to capitulate to the French Government and made
preparations to create another army under their best commander, the Archduke
Charles.
Sources:
Chandler, David G. (1966). The Campaigns of Napoleon. New York: MacMillan
Publishing Co., Inc.
Britt, Albert Sydney (1986). Atlas for Wars of Napoleon. Wayne, N.J. : Avery Publishing Group.