## An Encyclopaedia of Architecture, Historical, Theoretical, and Practical |

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Page 264

Fig . 235 Let AB ( fig . 235 . ) be the given line upon which it is required to

describe a triangle whose three sides shall be

the radius AB , describe the circumference BCD , and from the point B , with the

radius ...

Fig . 235 Let AB ( fig . 235 . ) be the given line upon which it is required to

describe a triangle whose three sides shall be

**equal**. D _ From the point A , withthe radius AB , describe the circumference BCD , and from the point B , with the

radius ...

Page 268

the alternate angle C . Therefore , substituting B for x , and C for y , the three

angles B , A , C are together

...

**equal**. c D But the angle = is**equal**to the alternate angle B , and the angle y tothe alternate angle C . Therefore , substituting B for x , and C for y , the three

angles B , A , C are together

**equal**to two right angles . CorollARY . Hence , if two...

Page 269

Hence , the diagonal bisects the parallelogram ; for the triangles BAD , BCD ,

having the three sides

which are between the same parallels , and have the same base , are

the ...

Hence , the diagonal bisects the parallelogram ; for the triangles BAD , BCD ,

having the three sides

**equal**, are identical . 903 . Prop . XXVIII . Parallelogramswhich are between the same parallels , and have the same base , are

**equal**. Letthe ...

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