Elements of Geometry |
From inside the book
Results 6-10 of 62
Page 50
... altitude EF by half the sum of the sides AB , CD , which may be expressed in this manner ; ABCD = EF × ( B + CD ) . 179. Scholium . If , through the point I , the middle of BC , IH be drawn parallel to the base AB , the point H will ...
... altitude EF by half the sum of the sides AB , CD , which may be expressed in this manner ; ABCD = EF × ( B + CD ) . 179. Scholium . If , through the point I , the middle of BC , IH be drawn parallel to the base AB , the point H will ...
Page 52
... altitude AE is the difference of these lines ; therefore the rectangle AKLE = ( AB + BC ) × ( AB — BC ) . But this same rectangle is composed of two parts ABHE + BHLK , and the part BHLK is equal to the rectangle EDGF , for BH = DE ...
... altitude AE is the difference of these lines ; therefore the rectangle AKLE = ( AB + BC ) × ( AB — BC ) . But this same rectangle is composed of two parts ABHE + BHLK , and the part BHLK is equal to the rectangle EDGF , for BH = DE ...
Page 53
... altitude BF , the square BCGF is to the rectangle BDEF as the base BC is to the base BD ; therefore BC : AB :: BC : BD , or , the square of the hypothenuse is to the square of one of the sides of the right angle , as the hypothenuse is ...
... altitude BF , the square BCGF is to the rectangle BDEF as the base BC is to the base BD ; therefore BC : AB :: BC : BD , or , the square of the hypothenuse is to the square of one of the sides of the right angle , as the hypothenuse is ...
Page 54
... altitude DE , are to each other as their bases BD , CD . Now these rectangles are equivalent to the squares AH , AI ; therefore , AB : AC :: BD : DC , or , the squares of the two sides of a right angle are to each other as the segments ...
... altitude DE , are to each other as their bases BD , CD . Now these rectangles are equivalent to the squares AH , AI ; therefore , AB : AC :: BD : DC , or , the squares of the two sides of a right angle are to each other as the segments ...
Page 56
... altitude , since the vertices B and C are situated in a parallel to the base ; therefore the triangles are equivalent ( 170 ) . The triangles ADE , BDE , of which the common vertex is E , have the same altitude , and are to each other ...
... altitude , since the vertices B and C are situated in a parallel to the base ; therefore the triangles are equivalent ( 170 ) . The triangles ADE , BDE , of which the common vertex is E , have the same altitude , and are to each other ...
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