A COMPLETE SET OF MALE PUPIL TEACHERS' EXAMINATION QUESTIONS IN EUCLID, TO SEPTEMBER 1879 (INCLUSIVE). Compiled, Classified, and Graduated by W. J. DICKINSON, FORMERLY LECTURER ON GRAMMAR AND EUCLID AT THE BATTERSEA TRAINING COLLEGE; AUTHOR OF 'PRACTICAL ENGLISH GRAMMAR AND ANALYSIS, THE DIFFICULTIES OF GRAMMAR AND ANALYSIS SIMPLIFIED,' 'HOW TO TEACH GRAMMAR AND ANALYSIS,' AND THE DIFFICULTIES OF EUCLID SIMPLIFIED.' SECOND EDITION. LONDON: JOSEPH HUGHES, THREE TUNS PASSAGE, PATERNOSTER SQUARE, L.C. EXAMINATION QUESTIONS. EUCLID, BOOK I. CONTENTS. Definitions, Axioms, Postulates, and General Questions, Propositions I.-XV. (inclusive), 7 Propositions XXVII.-XLI. (inclusive), 9 12 13 NOTE.-The deductions given at the end are deductions which, in the Examination Papers, were given independently, not being appended to any proposition. Along with the propositions, however, many deductions will be found as they were appended to the propositions, on which they were dependent, in the Examination Papers. Although the propositions are grouped as above, for the sake of keeping the parts prescribed for the various years of apprenticeship separate (the parts formerly prescribed, as also those at present), the questions are arranged according to the propositions, and numbered accordingly. Definitions, Axioms, Postulates, and General Questions. 1. Define superficies, right angle, semicircle, acute-angled triangle, and write out the postulates. 2. Define a plane rectilineal angle, a right angle, and a perpendicular, and write out Euclid's three postulates. 3. Define parallel straight lines and a parallelogram. Write out Euclid's twelfth axiom. 4. Define point, straight line, plane angle. A boy coming. to the eleventh axiom says, 'How can right angles be equal to one another unless the lengths of the lines forming them are respectively equal?' Answer him. 5. Explain clearly why the following definition is insufficient : -'A plane rectilineal angle is the inclination of two straight lines to one another.' Define obtuse angle, isosceles triangle, rhomboid. 6. Define a plane superficies, a circle, an acute-angled triangle, parallel straight lines. What straight lines are there which though produced to any length never meet, yet are not parallel? 7. Define right-angled triangle, oblong, parallel straight lines, postulate, axiom, problem, theorem. When is one proposition said to be the converse of another? 8. Define point, plane, superficies, obtuse angle, semicircle, oblong, scalene triangle, parallelogram. 9. Draw examples of the different kinds of four-sided figures, plane rectilineal angles, and triangles. Write a definition of each. What is a postulate? Mention those of Euclid. 10. What is an axiom? Give as many of Euclid's axioms as you can. 11. Write out Euclid's definitions of parallel straight lines, a parallelogram, a right angle, and a circle. 12. Give Euclid's definitions of a circle, the centre of a circle, the radius of a circle, the diameter of a circle, a semicircle, and a segment of a circle. 13. Explain the following terms given in Euclid :-Proposition, problem, theorem, enunciation, hypothesis, axiom, postulate, and corollary. 14. Explain the difference between a problem and a theorem. What is a corollary? When is one proposition said to be the converse of another? Give examples from the First Book. Into 15. Distinguish between problems and theorems. what parts may every proposition be divided? What is an indirect demonstration? Define corollary with an example. |