Elementary geometry |
From inside the book
Results 1-5 of 16
Page 20
... angle will be equal to the two interior and opposite angles , and the three interior angles of any triangle will be ... ACB be added to these , the two angles ACD + ACB = the three angles ABC + ВСА + САВ . But ACD + ACB = two right ...
... angle will be equal to the two interior and opposite angles , and the three interior angles of any triangle will be ... ACB be added to these , the two angles ACD + ACB = the three angles ABC + ВСА + САВ . But ACD + ACB = two right ...
Page 21
... angle B = the angle C. Proof . For conceive the triangle ABC taken up and put down in its former po- sition , with ... ACB be greater than the angle ABC . Proof . Conceive the triangle BAC taken up and put down with the arms of Ꭺ B B ...
... angle B = the angle C. Proof . For conceive the triangle ABC taken up and put down in its former po- sition , with ... ACB be greater than the angle ABC . Proof . Conceive the triangle BAC taken up and put down with the arms of Ꭺ B B ...
Page 22
... angle ACB is the same as the angle AC'B ; but AC'B ' is greater than ABC , because it is the exterior angle of the triangle OC'B ( Th . 7 , Cor . 4 ) ; and therefore ACB is greater than ABC . THEOREM IO . Conversely . A triangle which has ...
... angle ACB is the same as the angle AC'B ; but AC'B ' is greater than ABC , because it is the exterior angle of the triangle OC'B ( Th . 7 , Cor . 4 ) ; and therefore ACB is greater than ABC . THEOREM IO . Conversely . A triangle which has ...
Page 24
... angle POS = the angle POR , that is , OS and OR are equally inclined to the perpendicular OP on opposite sides of it ... ACB , AB is the straight line join- ing A and B , and is therefore shorter than the broken line ACB , Ax . I. A C B ...
... angle POS = the angle POR , that is , OS and OR are equally inclined to the perpendicular OP on opposite sides of it ... ACB , AB is the straight line join- ing A and B , and is therefore shorter than the broken line ACB , Ax . I. A C B ...
Page 33
... angles of a triangle meet in one point . Let ABC be a triangle and let the bisectors of the angles ABC , ACB be BO , CO , meeting in O ; then the theorem will be proved if we can shew that AO is the bisector of the angle BAC . Let ...
... angles of a triangle meet in one point . Let ABC be a triangle and let the bisectors of the angles ABC , ACB be BO , CO , meeting in O ; then the theorem will be proved if we can shew that AO is the bisector of the angle BAC . Let ...
Other editions - View all
Common terms and phrases
AB² ABCD ALGEBRA altitude angle ABC angle AOB ARITHMETIC bisectors bisects the angle BROOKE FOSS WESTCOTT Cambridge centre chord circumference cloth coincide common measure corresponding angles Crown 8vo decagon describe a circle diagonals diameter divided ELEMENTARY equal angles equiangular equivalent Euclid exterior angles Fcap Find the locus four right angles Geometry given angle given circle given line given point given ratio given straight line greater Hence hypothenuse inscribed intersect isosceles triangle less Let ABC magnitudes Mathematical meet middle points opposite sides parallel parallelogram perpendicular PROBLEM Proof proportional prove quadrilateral radius rectangle contained regular polygon respectively equal rhombus right angles right-angled triangle Schools Second Edition segments shew shewn similar similar triangles square subtend tangent Theorem 15 three sides touch TREATISE triangle ABC unequal vertical angle
Popular passages
Page 11 - 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.
Page 178 - Thucydides. — THE SICILIAN EXPEDITION. Being Books VI. and VII. of Thucydides, with Notes. A New Edition, revised and enlarged, with a Map. By the Rev. PERCIVAL FROST, MA. late Fellow of St. John's College, Cambridge. Fcap. 8vo.
Page 182 - NM FERRERS, MA, Fellow and Tutor of Gonville and Caius College, Cambridge. AN ELEMENTARY TREATISE ON TRILINEAR ' CO-ORDINATES, the Method of Reciprocal Polars, and the Theory of Projectors.
Page 11 - WILSON— THE BIBLE STUDENT'S GUIDE to the more Correct Understanding of the English Translation of the Old Testament, by reference to the original Hebrew. By WILLIAM WILSON, DD, Canon of Winchester, late Fellow of Queen's College, Oxford. Second Edition, carefully revised. 4to. cloth. 25*. YONGE (CHARLOTTE M.)— SCRIPTURE READINGS FOR SCHOOLS AND FAMILIES. By CHARLOTTE M. YONGE, Author of "The Heir of Redclyffe.
Page 175 - ARISTOTLE.— AN INTRODUCTION TO ARISTOTLE'S RHETORIC. With Analysis, Notes, and Appendices. By EM COPE, Senior Fellow and Tutor of Trinity College, Cambridge. 8vo.
Page 175 - ARISTOTLE ON FALLACIES ; OR, THE SOPHISTICI ELENCHI. With a Translation and Notes by EDWARD POSTE, MA, Fellow of Oriel College, Oxford. 8vo.
Page 182 - 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.
Page 179 - HELLENICA; OR, A HISTORY OF GREECE IN GREEK, as related by Diodorus and Thucydides ; being a First Greek Reading Book, with explanatory Notes, Critical and Historical.
Page 4 - ... obtaining all the information which he will require on this branch of Mathematics. Each chapter is followed by a set of Examples : those which are entitled Miscellaneous Examples, together with a few in some of the other sets, may be advantageously reserved by the student for exercist after he has made some progress in the subject.
Page 179 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.