By Arthur Cayley

This quantity is made out of electronic pictures from the Cornell collage Library historic arithmetic Monographs assortment.

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**Example text**

Produce AD both ways. ]. ], because the diagonal AB bisects it. ). Therefore the triangle ABC is equal to the triangle DBC. Exercises. 1. If two equal triangles be on the same base, but on opposite sides, the right line joining their vertices is bisected by the base. 2. Construct a triangle equal in area to a given quadrilateral figure. 3. Construct a triangle equal in area to a given rectilineal figure. 4. Construct a lozenge equal to a given parallelogram, and having a given side of the parallelogram for base.

State also the number of solutions. 5. If two right-angled triangles have equal hypotenuses, and an acute angle of one equal to an acute angle of the other, they are congruent. 6. If two right-angled triangles have equal hypotenuses, and a side of one equal to a side of the other, they are congruent. 7. The bisectors of the three internal angles of a triangle are concurrent. 8. The bisectors of two external angles and the bisector of the third internal angle are concurrent. 9. Through a given point draw a right line, such that perpendiculars on it from two given points on opposite sides may be equal to each other.

26. Mention all the instances of equality which are not congruence that occur in Book I. 27. What is the difference between the symbols denoting congruence and identity? 28. Classify the properties of triangles and parallelograms proved in Book I. 29. What proposition is the converse of Prop. , Part I.? 30. Define adjacent, exterior, interior, alternate angles respectively. 31. What is meant by the projection of one line on another? 32. What are meant by the medians of a triangle? 33. What is meant by the third diagonal of a quadrilateral?