## 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**S " figures , & c . We shall be found 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 ) . In a 21. An Axiom is a proposition , the ... Page 21

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**similar**reason AB is parallel to CD ; therefore 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 also ... 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 circumference 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 . 1 " therefore it is exactly AD , and we Of the Measure of Angles . 31.### Other editions - View all

### Common terms and phrases

ABC fig ABCD adjacent altitude angle ACB applied base called centre chord circ circle circumference circumscribed common cone consequently considered construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces figure follows formed four give given greater half hence homologous sides inclination inscribed join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment sides similar solid angle Solution sphere spherical square straight line suppose surface taken THEOREM third triangle ABC triangular pyramids vertex vertices whence