## Modern Methods in Elementary Geometry |

### From inside the book

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**THEOREM VII**. If the exterior angle EGB be equal to the interior angle GHD ; then shall AB be paral- lel to CD . then For if EGB = GHD , FHCHGA . A E B H C- D F Hence HC is situated with regard to GA precisely as GB with regard to HD ... Page 42

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**THEOREM VII**. The circumferences of two circles O and I cannot cut one another in more than two points ; nor touch in more than one . 0 0 For every point on the circumference of I is equally dis- tant from the centre I. But only two ... Page 43

... THEOREM VIII . The straight line AB which joins the points of intersec- tion A , B , is bisected at right angles by OI , which joins the centres O and I. ( Fig . ,

... THEOREM VIII . The straight line AB which joins the points of intersec- tion A , B , is bisected at right angles by OI , which joins the centres O and I. ( Fig . ,

**Theorem VII**. ) For if AB be bisected at right angles the centre of ... Page 65

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**THEOREM VII**. The measure of a triangle is half the product of its base multiplied by its altitude . COR . 1. Triangles of the same or equal altitude are to one another as their bases . COR . 2. Triangles on the same or equal bases are ... Page 87

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**THEOREM VII**. Similar triangles are to one another as PROPORTIONAL LINES . SIMILAR FIGURES . 87.### 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

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