The sum and difference of two simple terms were applied to the ETC search triangle (6,9,13). The resulting numerical coordinates were sought in the ETC tables and then they were checked algebraically.
SA, SB, SC, SW are the standard variables for Conway notation.
S=2*area(ABC), R=circumradius, r=inradius and s=semiperimeter of triangle.
| X(7) | (b*c-SA)/a | X(610) | SB*SC-a^2*SA | X(2223) | a^2*(a*s-SW) |
| X(8) | (b*c+SA)/a | X(612) | b*c+SW | X(2285) | SB*SC+a^2*b*c |
| X(9) | a-s | X(614) | b*c-SW | X(2300) | a^2*(a*s+SA) |
| X(19) | a^2*SA-S^2 | X(615) | a*R-b*c | X(2308) | a*(a*r+S) |
| X(37) | a*r-S | X(661) | SB-SC | X(2548) | a^3*R+b*c*S |
| X(38) | SA+SW | X(672) | a*(a*s-SW) | X(2964) | a^2-R^2 |
| X(41) | a^2*(a-s) | X(748) | a^2*r*s-b*c*S | X(2965) | a*(a^2-R^2) |
| X(42) | a*(a*r-S) | X(750) | a^2*r*s+b*c*S | X(2999) | b*c-s^2 |
| X(47) | a^2*r*s-S*R^2 | X(798) | SB^2-SC^2 | X(3053) | a*(a^2-SA) |
| X(48) | SB*SC-S^2 | X(894) | (b*c+a^2)/a | X(3068) | (S+a^2)/a |
| X(55) | a*(a-s) | X(940) | a*s+b*c | X(3069) | (S-a^2)/a |
| X(57) | SA-b*c | X(968) | a^2*r-S*s | X(3083) | b*c+S |
| X(58) | a^2*s+S*R | X(1100) | a*r+S | X(3084) | b*c-S |
| X(63) | SA | X(1124) | a*(S+b*c) | X(3299) | a+R |
| X(75) | SA^2+S^2 | X(1193) | a*(a*s+SA) | X(3301) | a-R |
| X(77) | SA*(SA-b*c) | X(1203) | a*s-R*r | X(3553) | a*R+r*s |
| X(78) | SA*(SA+b*c) | X(1267) | (b*c+S)/a | X(3553) | a^2*b*c+S^2 |
| X(171) | a^2+b*c | X(1335) | a*(S-b*c) | X(3554) | a*R-r*s |
| X(191) | SA+R*r | X(1386) | a*s+SW | X(3554) | a^2*b*c-S^2 |
| X(193) | (SA-a^2)/a | X(1449) | a+s | X(3624) | b*c+R*r |
| X(213) | a^2*(a*r-S) | X(1468) | a*(a*s+b*c) | X(3666) | SA+a*s |
| X(238) | a^2-b*c | X(1572) | a^3*s+S^2 | X(3751) | a*S-SW*r |
| X(239) | (b*c-a^2)/a | X(1580) | a^4-b^2*c^2 | X(3915) | a*(a*s-b*c) |
| X(326) | b^2*c^2-S^2 | X(1582) | a^4+b^2*c^2 | X(4258) | a*(a^2-s^2) |
| X(405) | b*c*S+SA*r*a | X(1698) | b*c-R*r | X(4383) | a*s-b*c |
| X(474) | b*c*S-SA*r*a | X(1707) | a^2-SA | X(4512) | a^2-s^2 |
| X(491) | (SA-S)/a | X(1743) | a*S-s^2*r | X(4641) | SA-a*s |
| X(492) | (SA+S)/a | X(1953) | SB*SC+S^2 | X(5019) | a^2*(a*s+b*c) |
| X(518) | a*s-SW | X(1958) | SA^2+SB*SC | X(5058) | a^2*(a*R-b*c) |
| X(560) | a^2*(SA-SW) | X(1958) | a^2*SA-b^2*c^2 | X(5062) | a^2*(a*R+b*c) |
| X(590) | a*R+b*c | X(1959) | SA^2-SB*SC | X(5266) | SA*r*a-S*SW |
| X(595) | a^2*s-S*R | X(1964) | SA^2-SW^2 | X(5277) | a^3*r+b*c*S |
| X(604) | a^2*(SA-b*c) | X(1964) | a^2*(SA+SW) | X(5280) | a*SW+S*R |
| X(605) | a^2*(S+b*c) | X(2082) | SB*SC-a^2*b*c | X(5299) | a*SW-S*R |
| X(606) | a^2*(S-b*c) | X(2175) | a^3*(a-s) | X(5336) | SB*SC-a^3*s |
| X(609) | a^3+S*R | X(2210) | a^2*(a^2-b*c) | X(5391) | (b*c-S)/a |
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