Elementary Geometry ... |
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Σελίδα 23
... Join BE , and produce it to F , making EF = EB . And join FC . Then in the triangles AEB , CEF we have AE = EC , BE = EF , ( Constr . ) ( Constr . ) and the contained angles AEB , CEF are equal ; ( Th . 4. ) , therefore the triangles ...
... Join BE , and produce it to F , making EF = EB . And join FC . Then in the triangles AEB , CEF we have AE = EC , BE = EF , ( Constr . ) ( Constr . ) and the contained angles AEB , CEF are equal ; ( Th . 4. ) , therefore the triangles ...
Σελίδα 24
... join DB . Because AD = AB ; therefore the angle ABD = the angle ADB . ( Constr . ) ( Th . 6. ) But because ADB is the exterior angle of the triangle BDC , therefore the angle ADB is greater than the angle ACB ; ( Th . 9. ) therefore ...
... join DB . Because AD = AB ; therefore the angle ABD = the angle ADB . ( Constr . ) ( Th . 6. ) But because ADB is the exterior angle of the triangle BDC , therefore the angle ADB is greater than the angle ACB ; ( Th . 9. ) therefore ...
Σελίδα 25
... join DC . Then because BD = BC , therefore the angle BCD = the angle BDC . ( Constr . ) ( Th . 6. ) But the angle ACD is greater than the angle BCD ; therefore the angle ACD is greater than the angle ADC ; and therefore AD is greater ...
... join DC . Then because BD = BC , therefore the angle BCD = the angle BDC . ( Constr . ) ( Th . 6. ) But the angle ACD is greater than the angle BCD ; therefore the angle ACD is greater than the angle ADC ; and therefore AD is greater ...
Σελίδα 27
... as DG ; and BC will fall as EG . ( Hyp . ) Let DH be the bisector of the angle FDG , ( Ax . 4. ) meeting EG in H. * Euclid , I. 21. + Euclid , I. 24 . Join FH . Then because in the triangles FDH , SECT . II . ] 27 TRIANGLES .
... as DG ; and BC will fall as EG . ( Hyp . ) Let DH be the bisector of the angle FDG , ( Ax . 4. ) meeting EG in H. * Euclid , I. 21. + Euclid , I. 24 . Join FH . Then because in the triangles FDH , SECT . II . ] 27 TRIANGLES .
Σελίδα 29
... Join DG . Then because and because EG = ED , therefore the angle EDG = the angle EGD : FG = FD , therefore the angle FDG = the angle FGD : ( Hyp . ) ( Th . 6. ) ( Hyp . ) ( Th . 6. ) ( Constr . ) therefore the whole angle EDF = the ...
... Join DG . Then because and because EG = ED , therefore the angle EDG = the angle EGD : FG = FD , therefore the angle FDG = the angle FGD : ( Hyp . ) ( Th . 6. ) ( Hyp . ) ( Th . 6. ) ( Constr . ) therefore the whole angle EDF = the ...
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AB² ABCD alternate angles angle ABC angle APB angle BAC angles are equal angles equal bisector centre chord circumference coincide College Constr construct contrapositive Crown 8vo describe a circle diagonals diameter divided draw Edition equal angles equal circles equiangular Euclid exterior angle fcap Find the locus four right angles Geometry given angle given circle given line given point given rectilineal figure given straight line hypotenuse included angle inscribed intersect isosceles triangle less Let AB Let ABC locus magnitudes meet middle point minor arc opposite angles opposite sides parallel parallelogram perpendicular polygon PROBLEM produced Proof Q. E. D. THEOREM quadrilateral radius rectangle contained reflex angle required to prove rhombus right angles segment semicircle Shew square subtend supplementary supplementary angles tangent THEOREM trapezium triangle ABC triangles are equal unequal
Δημοφιλή αποσπάσματα
Σελίδα 185 - MORTE D'ARTHUR. Sir Thomas Malory's Book of King Arthur, and of his Noble Knights of the Round Table. The Edition of Caxton, revised for Modern Use. With an Introduction, Notes, and Glossary, by Sir EDWARD STRACHEY. *' It is with perfect confidence that we recommend this edition of the old romance to every class of readers.
Σελίδα 173 - 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.
Σελίδα 172 - Book VI. is fitted for higher Classes, and as an Introduction to English Literature. "They are far above any others that have appeared both in form and substance. . . . The editor of the present series has rightly seen that reading books must ' aim chiefly at giving to the pupils the power of accurate, and, if possible, apt and skilful expression ; at cultivating in them ^a good literary taste, and at arousing a desire of further reading.
Σελίδα 143 - ROBY— A GRAMMAR OF THE LATIN LANGUAGE, from Plautus to Suetonius. By HJ ROBY, MA, late Fellow of St. John's College, Cambridge. In Two Parts. Third Edition. Part I. containing : — Book I. Sounds. Book II. Inflexions. Book III. Word-formation. Appendices. Crown 8vo.
Σελίδα 161 - Flower (WH) — AN INTRODUCTION TO THE OSTEOLOGY OF THE MAMMALIA. Being the Substance of the Course of Lectures delivered at the Royal College of Surgeons of England in 1870.
Σελίδα 183 - A GENERAL SURVEY OF THE HISTORY OF THE CANON OF THE NEW TESTAMENT DURING THE fIRST FOUR CENTURIES. Fourth Edition. With Preface on "Supernatural Religion.
Σελίδα 173 - Sonnenschein and Meiklejohn. — 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.
Σελίδα 145 - MATHEMATICS. AIRY — Works by Sir GB AIRY, KCB, Astronomer Royal : — ELEMENTARY TREATISE ON PARTIAL DIFFERENTIAL EQUATIONS. Designed for the Use of Students in the Universities. With Diagrams.
Σελίδα 148 - CHRISTIE— A COLLECTION OF ELEMENTARY TESTQUESTIONS IN PURE AND MIXED MATHEMATICS; with Answers and Appendices on Synthetic Division, and on the Solution of Numerical Equations by Homer's Method. By JAMES R. CHRISTIE, FRS, Royal Military Academy, Woolwich. Crown 8vo. 8s. 6d. CLIFFORD— THE ELEMENTS OF DYNAMIC.
Σελίδα 150 - GODFRAY — Works by HUGH GODFRAY, MA, Mathematical Lecturer at Pembroke College, Cambridge. A TREATISE ON ASTRONOMY, for the Use of Colleges and Schools. New Edition.