...THREE HOURS. 1. Enunciate the propositions of Euclid dealing with the equality of triangles. 2. Prove that triangles on the same base and between the same parallels are equal. 3. If a straight line be divided into two parts, the square on the whole line is equal to the sum of...

...another. 36. Parallelograms on equal bases and between the same parallels are equal to one another. 37. Triangles on the same base and between the same parallels are equal to one another. 38. Triangles on equal bases and between the same parallels are equal to one another....

...angle LMN to the angle PQR, also the side MN equal to QR; prove that the side LMis equal to PQ. 2. Triangles on the same base and between the same parallels are equal to one another. 3. In a right-angled triangle the square on the side opposite the right angle is equal...

...the parallelogram. 36. Parallelograms on equal bases and between the same parallels are equal. 37. Triangles on the same base and between the same parallels are equal. 38. Triangles on equal bases and between the same parallels are equal. 39. Equal triangles on the same...

...quantity, treats almost exclusively of such abstract generalities; as 6=2x3; a?—y' = (x+y) (x—y); Triangles on the same base, and between the same parallels, are equal. § 128. Inference in the quantitative whole is immediate and mediate. Immediate inference from equivalent...

...triangle which has the greater contained angle shall be greater than the base of the other. I. 24. 8. Triangles on the same base and between the same parallels are equal in area. I. 37. 9 To describe a parallelogram equal to any given rectilineal figure, and having an angle equal...

...described ? In what proposition does Euclid imply the fact that there can be more than one ? 2. Prove that triangles on the same base and between the same parallels are equal to each other. Through a given point in the base of a triangle draw a straight line bisecting the triangle....

...+ 1. 5' Simplify (*+l)H (*-!)». 6. Solve the equation x + 5 x - 6 x + 3 ~ x - 9' 7. Parallelograms on the same base and between the same parallels are equal in area. 8. If a straight line is bisected and also divided unequally the sum of the squares on the unequal...

...method of casting out areas is that known as " equalising," which is based on Euclid's proposition of " triangles on the same base and between the same parallels are equal." The method consists in constructing a triangle equal to the figure, the area of which is required,...

...Give a short biographical sketch of Haydn. SINCLAIR SCHOLARSHIP EXAMINATION, 1896. MATHEMATICS. 1 Shew that triangles on the same base and between the same parallels are equal in area ; and equal triangles on the same base are between the same parallels. Shew that the straight line...