Elements of Geometry |
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Page xi
... means , these proportions will be- come A : CBD , A : CEF ; B : D :: E : F whence or B : E :: D : F. IV . Other changes , besides the transposition of terms , may be made among proportionals without destroying the equality of the ...
... means , these proportions will be- come A : CBD , A : CEF ; B : D :: E : F whence or B : E :: D : F. IV . Other changes , besides the transposition of terms , may be made among proportionals without destroying the equality of the ...
Page xii
... means in these results , they will become B + A : D + C :: A : C , B - AD - C :: A : C ; but , by the same change , the proportion gives also A : B :: C : D A : C :: B : D , and , since the ratios A : C , B : D , are equal , we obtain B ...
... means in these results , they will become B + A : D + C :: A : C , B - AD - C :: A : C ; but , by the same change , the proportion gives also A : B :: C : D A : C :: B : D , and , since the ratios A : C , B : D , are equal , we obtain B ...
Page 32
... means of them , the direct and absolute measure ; for , if we compare the arc , which is used as the measure of an angle , with the fourth part of the circumference , we have the ratio of the given angle to a right angle , which is the ...
... means of them , the direct and absolute measure ; for , if we compare the arc , which is used as the measure of an angle , with the fourth part of the circumference , we have the ratio of the given angle to a right angle , which is the ...
Page 59
... means of quadrilaterals , such as AIDH , which have two right angles , or by comparing two triangles which , beside the vertical angles , have each a right angle ; or we can always suppose , within the triangle ABC , a triangle DEF ...
... means of quadrilaterals , such as AIDH , which have two right angles , or by comparing two triangles which , beside the vertical angles , have each a right angle ; or we can always suppose , within the triangle ABC , a triangle DEF ...
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 ...
... 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 ...
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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