Josephine M Lafay B. 31 May 1888 Cumberland, Maine to Claude J.F.Lafay & Delia Larive. I do not have the birth record for Josephine but have them for her siblings.
11 January 1904 she marries Joseph E. Deforest, Maine. Info from Maine Marriage Index.
1 December 1904 son Elias Joseph is born Connecticut. I can't find birth certificate.
20 November 1906 daughter Josephine dies age 3 months from Rhode Island Island Records
12 November 1908 son Euclide is born Rhode Island. Birthplace on census is given as Arctic, R.I.
1910 Census, Willamantic has Josie Deforest and Eli and Euclide Deforest listed with her as head of household.
1920 Census Woonsocket has Eli & Euclide Teriac in the home of Wilfred Beffre & Josephine Beffre. Wilfred and Josephine did not actually get married until 1940.
According to a Vermont court case online Euclid Theriac married Mary "Anna" Beaulieu on 1 February 1927 and a daughter Therese Theriac born 3 August 1927. It states in the court transcription that Mary "Anna" was dead when he remarries - can't find a marriage or death. Theresa is in her grandparent home in 1930 census.
22 May 1935 Euclid marries Mabel Irene Basset who was born in Canada 1915. It seems to be from this point Euclid chooses to go by the name Raymond Euclid Deforest for the rest of his life. I have many records of him from 1935 until he dies in 1983
1930 Census Woonsocket has Elias Theriac, his wife Jane and son Elias Roger.
I am unsure why Elias and Euclid's names change from Deforest to Theriac, I don't know what name they were actually registered with. On Elias Joseph's death records his father is listed as Eli Teriac.

I have tried my best to map out which names they were using at different times in their life. I'm a bit rusty at researching right now as I've only just come back to it after many years of doing none.
Thanks in advance for any suggestions on where I should focus my research on.
Jules