Elements of Geometry |
From inside the book
Results 6-10 of 31
Page 59
... 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 70
... respect to an inscribed quadrilateral figure . The triangle ABD being similar to BIC , BD : BC : : AB : BI , whence BIX BD = BC × AB . If we join CO , the triangle ICO , similar to ABI , is similar to BDC , and gives the proportion BD ...
... respect to an inscribed quadrilateral figure . The triangle ABD being similar to BIC , BD : BC : : AB : BI , whence BIX BD = BC × AB . If we join CO , the triangle ICO , similar to ABI , is similar to BDC , and gives the proportion BD ...
Page 83
... 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 95
... respect- ively a part ; hence AB : CA : 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 between the ...
... respect- ively a part ; hence AB : CA : 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 between the ...
Page 97
... 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 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