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Proposition 8.

If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they will also have the angles equal which are contained by the equal straight lines.

Let ABC, DEF be two triangles having the two sides AB, AC equal to the two sides DE, DF respectively, namely AB to DE, and AC to DF; and let them have the base BC equal
to the base EF;

I say that the angle BAC is also equal to the angle EDF.

For, if the triangle ABC be applied to the triangle DEF, and if the point B be placed on
the point E and the straight line BC on EF,

the point C will also coincide with F, because BC is equal to EF.

1 “to relate his trifles at full length,” to which Taylor retorts “But Mr Simson was no philosopher; and therefore the greatest part of these Commentaries must be considered by him as trifles, from the want of a philosophic genius to comprehend their meaning, and a taste superior to that of a mere mathematician, to discover their beauty and elegance.”

2 It would be natural to insert here the step “but the angle ACD is greater than the angle BCD. [C.N. 5].”

3 much greater, literally “greater by much” (πολλῷ μεἰζων). Simson and those who follow him translate: “much more then is the angle BDC greater than the angle BCD,” but the Greek for this would have to be πολλῷ (or πολὺ[ρπαρ ] μᾶλλόν ἐστι...μείζων. πολλῷ μᾶλλον, however, though used by Apollonius, is not, apparently, found in Euclid or Archimedes.

Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.

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