## Elements of Geometry |

### From inside the book

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Page vi

... entitled the proportions of figures , contains the measure of surfaces , their comparison , the properties of a right - angled triangle , those of equiangular triangles , of

... entitled the proportions of figures , contains the measure of surfaces , their comparison , the properties of a right - angled triangle , those of equiangular triangles , of

**similar**figures , & c . We shall be found fault vi Preface . Page 3

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**similar**sense are to be understood two polygons equiangular with respect to each other . The equal sides in the first case , and the equal angles in the second , are called homologous ( A ) . 21. An Axiom is a proposition , the truth of ... Page 21

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**similar**reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig . 44 . are equal and parallel , the two other sides will ... Page 26

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**similar**reason ; it will then be in both of these lines at the same time . But two lines can cut each other in only one point ( 32 ) ; there is therefore only one circle , whose circum- ference can pass through three given points . 108 ... Page 31

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**similar**, it may be shown , that the fourth term of the proportion cannot be less than AD ; † The reference by Roman numerals is to the Introduction . therefore it is exactly AD , and we have the Of the Measure of Angles . 31.### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence