## Elements of Geometry |

### From inside the book

Results 1-5 of 17

Page 62

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**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 64

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

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

**mean proportional**between the diameter BC and the adjacent segment BD ; or , AB = BD × BC ... Page 68

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**mean proportional**between the secant and the part without the circle ; that is , OC : OA :: OA : OD , or , OA = OC × OD . Demonstration . By joining AD and AC , the triangles OAD , OAC , have the angle O common ; moreover , the angle ... Page 72

... 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 indefi- nite 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 indefi- nite straight ...

**mean proportional**between two 72 Elements of Geometry . Page 73

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**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 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