Ásgeir æðikollur átti fimm börn.
Asgeir “Hothead” had five children.

Son hans hét Auðun faðir Ásgeirs, föður Auðunar, föður Egils er átti Úlfeiði dóttur Eyjólfs hins halta.
His son was named Audun, father of Asgeir, father of Audan, father of Egil who married Ulfeid, daughter of Eyjolf the lame.

Þeirra son var Eyjólfur er veginn var á alþingi.
Their son was Eyjolfr who was killed at the All-Thing.

Annar son Ásgeirs hét Þorvaldur.
Another son of Asgeir was named Thorvald.

Hans dóttir var Dalla er átti Ísleifur biskup.
His daughter was Dalla whom bishop Isleifr married.

Þeirra son var Gissur biskup.
Their son was bishop Gissur.

Hinn þriðji son Ásgeirs hét Kálfur.
Asgeir's third son was named Kalfr.

Allir voru synir Ásgeirs vænlegir menn.
All Asgeir's sons were fine men.

Kálfur Ásgeirsson var þann tíma í förum og þótti hinn nýsti maður.
Kalfr Asgeirson was at that time travelling (?) and thought the most (nýsti?) man. (Z. has 'í þann tíma, at that time,' my assumption is that the word order is flexible, per what is in the passage)

Dóttir Ásgeirs hét Þuríður.
A daughter of Asgeir was named Thurid.

Hún var gift Þorkeli kugga syni Þórðar gellis.
She was married to Thorel the cog, Thord Gellis's son.

Þeirra son var Þorsteinn.
Their son was Thorstein.

Önnur dóttir Ásgeirs hét Hrefna.
Another daughter of Asgeir was named Hrefna.

Hún var vænst kvenna norður þar í sveitum og vel vinsæl.
She was the most beautiful woman to the north there in the district and very popular.

Ásgeir var mikill maður fyrir sér.
Asgeir was a powerful man. (Z. fyrir 13 - mikill f. sér, strong, powerful)

Það er sagt eitt sinn, að Kjartan Ã"lafsson byrjaði ferð sína suður til Borgarfjarðar.
It is said one time that Kjartan Olafson began his journey south to Borgarfjard.

Ekki er getið um ferð hans fyrr en hann kom til Borgar.
It is not told concerning his journey (i.e., there is nothing to say of his journey) before he came to Borgar.

Þar bjó þá Þorsteinn Egilsson móðurbróðir hans.
His uncle Thorstein Egilson lived there then.

Bolli var í ferð með honum því að svo var ástúðigt með þeim fóstbræðrum að hvorgi þóttist nýta mega að þeir væru eigi ásamt.
Bolli was travelling with him because (he) was so friendly with the foster brothers that everywhere was thought to be able to endure that they were not together.

Þorsteinn tók við Kjartani með allri blíðu, kvaðst þökk kunna að hann væri þar lengur en skemur.
Thorstein received Kjartan with all friendliness, stated for himself to be thankful that he would be there longer or shorter.

Kjartan dvelst að Borg um hríð.
Kjartan remained at Borg a while.

Þetta sumar stóð skip uppi í Gufuárósi.
This summer a ship was laid up ashore at Gufuarosi.

Það skip átti Kálfur Ásgeirsson.
Kalfr Asgeirson owned that ship.

Hann hafði verið um veturinn á vist með Þorsteini Egilssyni.
During the winter he had been staying with Thorstein Egilson.

Kjartan segir Þorsteini í hljóði að það var mest erindi hans suður þangað að hann vildi kaupa skip hálft að Kálfi, "er mér á því hugur að fara utan" og spyr Þorstein hversu honum virðist Kálfur.
Kjartan says to Thorstein in all quietness that that was most his mission southwards there that he wanted to buy a ship in halves with Kafl, “I have in mind to go abroad” and asks Thorstein how he, Kalfr, would think.

Þorsteinn kvaðst hyggja að hann væri góður drengur "er það vorkunn mikil frændi," segir Þorsteinn, "að þig fýsi að kanna annarra manna siðu.
Thorstein stated for himself to think that he was a nobleminded man, “that is an excuse for a great relative,” says Thorstein, “that you are eager to search for another well-bred man. (not sure if this applies: Z. siða-maðr, m. a well-bred man)

Mun þín ferð verða merkileg með nokkuru móti.
Your journey would be noteworthy with someone against. (?)

Eiga frændur þínir mikið í hættu hversu þér tekst ferðin."
Your relative runs a great risk how you take the journey.”

Kjartan kvað vel takast munu.
Kjartan stated (it) would be well received.