## 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 22

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**similar**reason , AB is parallel to CD ; therefore the quadrilateral ABCD is a parallelogram . THEOREM . 84. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral are equal and parallel , the two other sides will also be equal ... Page 28

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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 ... Page 33

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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 . GEOM . 5 therefore it is exactly AD , and we have the Of the Measure of Angles . 33.### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence