## Elements of Geometry |

### From inside the book

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Page xi

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**consequently**a new proportion . Let there be , for example , the proportion we shall have or 46 12 : 18 6 + 44 18+ 12 : 12 , 10 : 4 : 30 : 12 . 2. If from the consequent of a ratio we subtract the antece- dent , and compare the ... Page xii

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**consequently**B + A : D + C :: B - A : D - C , or , by changing the place of the means , BA : BA :: D + C : D - C ; that is , the sum of the two first terms of a proportion is to their dif- ference , as the sum of the two last is to ... Page 15

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**consequently**less than the oblique line , AK ; whence in the triangle AEK the angle AKE , opposite to the side AE , is less than the right angle AEK , opposite to the side AK ( 49 ) . Therefore the angle IKF , equal to the angle AKE ... Page 17

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**Consequently**AB and CD are perpen- dicular to the same straight line PQ , therefore they are par- allel ( 57 ) . THEOREM . 69. Two parallel lines are throughout at the same distance from each other . Demonstration . The two parallels AB ... Page 18

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**consequently**the three angles of the triangle ABC make the same sum as the three angles CAB , BAE , EAD ; therefore this sum is equal to two right augles ( 31 ) . 73. Corollary I. Two angles of a triangle being given , or only their sum ...### 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