## Elements of Geometry |

### From inside the book

Results 1-5 of 15

Page 60

...

...

**mean proportional**between the hypothenuse BC and the adjacent segment BD or DC ; 3. The perpendicular AD will be a**mean proportional**between the two segments BD , DC . Demonstration . 1. The triangles BAD , BAC , have the angle B common ... Page 62

... mean propor- tional between the segments BD , DC , of the diameter , or , which amounts to the same thing , --2 AD BD x DC . 2. The chord AB is a

... mean propor- tional between the segments BD , DC , of the diameter , or , which amounts to the same thing , --2 AD BD x DC . 2. The chord AB is a

**mean proportional**between the diameter BC and the adjacent segment BD ; or , --2 AB ... Page 66

...

...

**mean proportional**between the secant and the part without the circle ; that is , OC : OA :: OA : OD , or , OA = OC × OD . --2 Demonstration . By joining AD and AC , the triangles OAD , OAC , have the angle O common ; moreover , the ... Page 70

... proportional to any given lines . Solution . 1. Let it be proposed to divide the line AB ( fig . 137 ) into five equal parts ; through the extremity A draw the inde- finite straight ...

... proportional to any given lines . Solution . 1. Let it be proposed to divide the line AB ( fig . 137 ) into five equal parts ; through the extremity A draw the inde- finite straight ...

**mean proportional**between two 70 Elements of Geometry . Page 71

...

...

**mean proportional**sought . For the perpendicular GE , let fall from the point in the cir- cumference upon the diameter , is a**mean proportional**between the two segments of the diameter DE , EF ( 215 ) , and these two segments are equal ...### 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