Is 'surely' the same as 'certainly'

Surely does not usually mean the same as certainly.

We use certainly when we simply tell people that something is true.

We use surely mostly to ask for people's agreement.

Compare:

• House prices are certainly rising fast at the moment. (I know this is so.)
• House prices will surely stop rising soon. (I believe this must be so (and implication of [ – wouldn't you agree?]).)

Certainly - emphatic affirmation of a truth.

'It's started snowing again'. 'It certainly has been a long hard winter'

Surely - incredulous doubting of an apparent truth.

'Surely house prices will stop rising soon' (i.e. they seem way too high already)

'You're not going to have another doughnut, surely ?' (i.e. you've had three already)

Surely can have the sense of certainly ('I surely like the way you done your hair Ma'am') - but it sounds dated and folksy to my English ears.