A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
From inside the book
Results 6-10 of 32
Page 58
... similar . S 4. Draw T'AT the common tangent to the two at A. [ Ex . 3 , p . 181. ] Let AX be between AP and AT . Then L TAX = LAPX [ III . 32 ] . L TAX = L AQY : And , in ( i ) , in ( ii ) , L TAX = LT'AY = L AQY . .. PX is par1 . to QY ...
... similar . S 4. Draw T'AT the common tangent to the two at A. [ Ex . 3 , p . 181. ] Let AX be between AP and AT . Then L TAX = LAPX [ III . 32 ] . L TAX = L AQY : And , in ( i ) , in ( ii ) , L TAX = LT'AY = L AQY . .. PX is par1 . to QY ...
Page 68
... similar manner with the second circle , we see that the points common to the two locus - circles satisfy the conditions . There are two solutions , one solution or no solution according as the loci - circles intersect , touch one ...
... similar manner with the second circle , we see that the points common to the two locus - circles satisfy the conditions . There are two solutions , one solution or no solution according as the loci - circles intersect , touch one ...
Page 79
... similar manner . 8 23. For , with the fig . of p . 227 , since the AFO , AEO are rt . angles ( hyp . ) , .. the four points A , F , O , E are concyclic . ..the FAE , FOE together two rt . angles [ III . 22 ] . That is , the BAC , BOC ...
... similar manner . 8 23. For , with the fig . of p . 227 , since the AFO , AEO are rt . angles ( hyp . ) , .. the four points A , F , O , E are concyclic . ..the FAE , FOE together two rt . angles [ III . 22 ] . That is , the BAC , BOC ...
Page 84
... similar to the segment ACB . 46. Let A be the point of intersection of the rulers . Then PXQA is a rectangle . ..AX = PQ , which is constant , and the point A is fixed . Hence the locus of X is the quadrant of a circle described from ...
... similar to the segment ACB . 46. Let A be the point of intersection of the rulers . Then PXQA is a rectangle . ..AX = PQ , which is constant , and the point A is fixed . Hence the locus of X is the quadrant of a circle described from ...
Page 87
... similar . 59. Let ABX , ABY be the two equal 3 , and let the C de- scribed from centre A cut the ABY at C and the ABX at D , the points C , D being on the same side of AB . S Then the arc AC = the arc AD , for they are cut off from ...
... similar . 59. Let ABX , ABY be the two equal 3 , and let the C de- scribed from centre A cut the ABY at C and the ABX at D , the points C , D being on the same side of AB . S Then the arc AC = the arc AD , for they are cut off from ...
Other editions - View all
A Key to the Exercises and Examples Contained in a Text-Book of Euclid's ... H S 1848-1934 Hall No preview available - 2018 |
A Key to the Exercises and Examples Contained in a Text-Book of Euclid's ... H. S. Hall No preview available - 2017 |
Common terms and phrases
A. W. VERRALL AABC AB² ABCD AC² angles Assistant Master AX² BC² bisector bisects Cambridge centre chord circle circum College concyclic constant describe diam diameter diff draw ELEMENTARY equiangular equilat FASNACHT Fcap fixed point G. E. FASNACHT given base given point given ratio given st GREEK Hence identically equal inscribed intersect Introduction and Notes ISAAC TODHUNTER isosceles Join Let ABC LL.D locus M.A. BOOK meet middle point middle pt orthocentre Owens College par¹ parm pedal triangle perp plane produced Prof Professor Radical Axis radius equal rect respectively segment shewn sides Similarly sum of sqq tangent touch Translated triangle Trinity College vert vols
Popular passages
Page 6 - BLACKIE— GREEK AND ENGLISH DIALOGUES FOR USE IN SCHOOLS AND COLLEGES. By JOHN STUART BLACKIE, Professor of Greek in the University of Edinburgh.
Page 13 - THE THIRD AND FOURTH COURSES, consisting of Long Vowels, and all the Double Vowels in the Language. 6d. 1 " These are admirable books, because they are constructed on a principle, and that the simplest principle on which it is possible to learn to read English."— SPECTATOR.
Page 13 - TAYLOR— WORDS AND PLACES; or, Etymological Illustrations of History, Ethnology, and Geography. By the Rev. ISAAC TAYLOR, MA Third and cheaper Edition, revised and compressed. With Maps. Globe 8vo. 6s.
Page 7 - FIRST GREEK READER. Edited after KARL HALM, with Corrections and large Additions by Professor JOHN EB MAYOR, MA, Fellow of St. John's College, Cambridge. New Edition, revised.
Page 26 - Crown 8vo. gr. 6d. GRAVITATION: an Elementary Explanation of the Principal Perturbations in the Solar System.
Page 17 - Also a Small Chart on a Card, price id. EASY LESSONS IN ARITHMETIC, combining Exercises in Reading, Writing, Spelling, and Dictation. Part I. for Standard I. in National Schools. Crown 8vo.
Page 25 - SHANN— AN ELEMENTARY TREATISE ON HEAT, IN RELATION TO STEAM AND THE STEAM-ENGINE. By G. SHANN, MA With Illustrations. Crown 8vo.
Page 10 - Hales.— LONGER ENGLISH POEMS. With Notes, Philological and Explanatory, and an Introduction on the Teaching of English. Chiefly for use in Schools. Edited by JW HALES, MA, Professor of English Literature at King's College, London, &c. &c. Fifth Edition. Extra fcap. 8vo. 4*.
Page 33 - Conflicts of Capital and Labour Historically and Economically considered. Being a History and Review of the Trade Unions of Great Britain, showing their Origin, Progress, Constitution, and Objects, in their Political, Social, Economical, and Industrial Aspects.
Page 13 - THE ENGLISH METHOD OF TEACHING TO READ. By A. SONNENSCHEIN and JMD MEIKLEJOHN, MA Fcap. 8vo. COMPRISING : THE NURSERY BOOK, containing all the Two-Letter Words in the Language, id. (Also in Large Type on Sheets for School Walls. 5*.) THE FIRST COURSE, consisting of Short Vowels with Single Consonants.