Elements of Geometry |
From inside the book
Results 6-10 of 32
Page 57
... respect to those of only four sides , or quadrilaterals , we may alter the pro- portion of the sides without changing the angles , or change the angles without altering the sides ; thus , from the angles being equal it does not follow ...
... respect to those of only four sides , or quadrilaterals , we may alter the pro- portion of the sides without changing the angles , or change the angles without altering the sides ; thus , from the angles being equal it does not follow ...
Page 68
... respect to an inscribed quadrilateral figure . The triangle ABD being similar to BIC , BD : BC : : AB ; B1 , whence BIX BD = BC × AB . If we join CO , the triangle ICO , similar ABI , is similar to BDC , and gives the proportion BD : CO ...
... respect to an inscribed quadrilateral figure . The triangle ABD being similar to BIC , BD : BC : : AB ; B1 , whence BIX BD = BC × AB . If we join CO , the triangle ICO , similar ABI , is similar to BDC , and gives the proportion BD : CO ...
Page 81
... respect to this circumference , all the sides AB , BC , CD , & c . are equal chords ; they are accordingly equally distant from the centre ( 109 ) ; if therefore from the point O , as a centre , and with the radius OP , a circle be ...
... respect to this circumference , all the sides AB , BC , CD , & c . are equal chords ; they are accordingly equally distant from the centre ( 109 ) ; if therefore from the point O , as a centre , and with the radius OP , a circle be ...
Page 93
... respect- ively a part ; hence Ꭿ : B :: ᏟᎯ : CE . . But , on account of the parallels AD , ME , therefore CD : CM :: CA : CE ; A : A ' :: A ' : B ; that is , the polygon A ' , one of those which is sought , is a mean proportional ...
... respect- ively a part ; hence Ꭿ : B :: ᏟᎯ : CE . . But , on account of the parallels AD , ME , therefore CD : CM :: CA : CE ; A : A ' :: A ' : B ; that is , the polygon A ' , one of those which is sought , is a mean proportional ...
Page 95
... respect to the last decimal , on account of the error arising from the parts neglected ; but we have extended the calculation to one decimal more in order to be assured of the correctness of the above result to the last figure . Since ...
... respect to the last decimal , on account of the error arising from the parts neglected ; but we have extended the calculation to one decimal more in order to be assured of the correctness of the above result to the last figure . Since ...
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