Elements of Geometry |
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Page 61
... 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 62
... 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 ...
Page 63
... means , gives We have , in like manner , hence AB = BD × BC . AC DCX BC , AB + AC = BD × BC + DC × BC ; the second member , otherwise expressed , is ( BD + DC ) × BC , or BC ; consequently AB + AC = BC ; therefore the square of the ...
... means , gives We have , in like manner , hence AB = BD × BC . AC DCX BC , AB + AC = BD × BC + DC × BC ; the second member , otherwise expressed , is ( BD + DC ) × BC , or BC ; consequently AB + AC = BC ; therefore the square of the ...
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 proportional between the diameter BC and the adjacent segment BD ; or , AB = BD × BC ...
... 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
... 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 ...
... 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 ...
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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