## Modern Methods in Elementary Geometry |

### From inside the book

Page 9

... exterior and interior angles . The angles ( 3 ) and ( I ) are called alternate angles . The angles ( 2 ) and ( I ) are called interior angles on the same side of EF . I THEOREM VII . If the

... exterior and interior angles . The angles ( 3 ) and ( I ) are called alternate angles . The angles ( 2 ) and ( I ) are called interior angles on the same side of EF . I THEOREM VII . If the

**exterior angle**EGB be equal to the interior angle ... Page 11

... angle ACE the alternate angle A , = and the

... angle ACE the alternate angle A , = and the

**exterior angle**ECD = the interior angle B. Therefore the whole ACD = A + B. > Again , A + B = ACD . 12 Add to each C , then A + B THE STRAIGHT LINE . 11. Page 12

... angles of one triangle be equal to two angles of another , the third angle of the first is equal to the third angle of the second . 1 COR . 2. The

... angles of one triangle be equal to two angles of another , the third angle of the first is equal to the third angle of the second . 1 COR . 2. The

**exterior angle**is greater than either of the interior and opposite angles . THEOREM XI ... Page 13

... angle B. Let AD be the perpendicular . Then since AB is greater than AC , it is more remote from the perpen- dicular . A B C Ꭰ Hence if ADC be turned about AD , C will fall between D and B , as at C ' . Then the

... angle B. Let AD be the perpendicular . Then since AB is greater than AC , it is more remote from the perpen- dicular . A B C Ꭰ Hence if ADC be turned about AD , C will fall between D and B , as at C ' . Then the

**exterior angle**AC'D ... Page 20

... angle ABD = the alternate angle CDB . Hence in the triangles ABD , CDB , AB = CD , BD is common , and ABD = CDB ...

... angle ABD = the alternate angle CDB . Hence in the triangles ABD , CDB , AB = CD , BD is common , and ABD = CDB ...

**exterior angles**of any convex polygon are together equal to four right angles , and the interior angles to twice as ...### Other editions - View all

### Common terms and phrases

Algebra alternate angle altitude ARITHMETIC base BC² BEGINNERS bisect BROOKE FOSS WESTCOTT Cambridge centre chord Christ's College circle touching circumference Clifton College cloth coincide congruent CONIC SECTIONS construct contains convex angle Crown 8vo describe a circle diagonals diameter dicular distance divide Edward Thring ELEMENTARY TREATISE equal angles equally distant equiangular equilateral triangle Examination Papers Exercises exterior angle Fcap Fellow of St GEOMETRY given circle given line given point given square given straight line greater Greek Text Head Master Hence inscribe intersect John's College Join JOSEPH WOLSTENHOLME Jugurtha late Fellow Latin Let ABCD line drawn locus Mathematical Lecturer measure meet middle point MIXED MATHEMATICS numerous parallel to BC parallelogram perpen perpendicular polygon problems quadrilateral figure radius rectangle right angles Second Edition Shew similar triangles student tangent THEOREM VII Third Edition trapezium triangle ABC vertex

### Popular passages

Page 7 - 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.

Page 6 - 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 16 - New Edition. Crown 8vo. $s. KEY TO PLANE TRIGONOMETRY. Crown 8vo. los. 6d. A TREATISE ON SPHERICAL TRIGONOMETRY. New Edition, enlarged. Crown 8vo. 4-?. 6d. PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples.

Page 5 - 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. 410. cloth. 25*. YONGE (CHARLOTTE M.)— SCRIPTURE READINGS FOR SCHOOLS AND FAMILIES. By CHARLOTTE M. YONGE, Author of "The Heir of Redclyffe.

Page 5 - 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 4 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.

Page 16 - ... 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 7 - 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 5 - THE BIBLE IN THE CHURCH. A Popular Account of the Collection and Reception of the Holy Scriptures in the Christian Churches.

Page 11 - AN ELEMENTARY TREATISE ON THE LUNAR THEORY, with a Brief Sketch of the Problem up to the time of Newton. Second Edition, revised. Crown 8vo. cloth. 5*. 6d. Hemming. — AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use; of Colleges and Schools.