User:ST47

• Proposition 1. Theorem -If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
• Proposition 2. Theorem -If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts,are together equal to the square on the whole line.
• Proposition 3. Theorem -If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square on the aforesaid part.
• Proposition 4. Theorem -If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts.
• Proposition 5. Theorem -If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section,is equal to the square on half the line.
• Proposition 6. Theorem -If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
• Proposition 7. Theorem -If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part,together with the square on the other part.
• Proposition 8. Theorem -If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts,together with the square on the other part,is equal to the square on the straight line which is made up of the whole and the part.
• Proposition 9. Theorem -If a straight line be divided into two equal, and also into two unequal parts,the squares on the two unequal parts,the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section
• Proposition 10. Theorem -If a straight line be bisected, and produced to any point, the square on the whole line thus produced and the square on the part produced, are together double of the square on half the line bisected and of the square of the line made up of the half and the part produced.
• Proposition 11. Problem -To divide a given straight line into two parts,so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
• Proposition 12. Theorem -In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced,the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which when produced, the perpendicular falls, and the straight line intercepted without the triangle,between the perpendicular, and the obtuse angle.
• Proposition 13. Theorem -In every triangle , the square on the side subtending an acute angle, is less than the square on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle and the acute angle.
• Proposition 14 - Problem -To describe a square that shall be equal to a given rectilineal figure.