Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 44
Page 69
... equivalent . The term equal , when applied to figures , designates those which are equal in every respect , and which being applied to each other will coincide in all their parts ( Ax . 13. ) : the term equi- valent implies an equality ...
... equivalent . The term equal , when applied to figures , designates those which are equal in every respect , and which being applied to each other will coincide in all their parts ( Ax . 13. ) : the term equi- valent implies an equality ...
Page 70
... equivalent to the parallelogram ABCD ( Prop . I. Cor . ) . Cor . 2. All triangles , which have equal bases and altitudes , are equivalent , being halves of equivalent parallelograms . PROPOSITION III . THEOREM . Two rectangles having ...
... equivalent to the parallelogram ABCD ( Prop . I. Cor . ) . Cor . 2. All triangles , which have equal bases and altitudes , are equivalent , being halves of equivalent parallelograms . PROPOSITION III . THEOREM . Two rectangles having ...
Page 74
... equivalent F D to the rectangle ABEF , which has the same base AB , and the same altitude BE ( Prop . I. Cor . ) : but this rectangle is measured by AB × BE ( Prop . IV . Sch . ) ; therefore , AB × BE A is equal to the area of the ...
... equivalent F D to the rectangle ABEF , which has the same base AB , and the same altitude BE ( Prop . I. Cor . ) : but this rectangle is measured by AB × BE ( Prop . IV . Sch . ) ; therefore , AB × BE A is equal to the area of the ...
Page 75
... equivalent to the parallelogram ADKL , and is measured by EFX AL . But we have AL - DK ; and since the triangles IBL and KCI are equal , the side BL = CK : hence , AB + CD = AL + DK = 2AL ; hence AL is the half sum of the bases AB , CD ...
... equivalent to the parallelogram ADKL , and is measured by EFX AL . But we have AL - DK ; and since the triangles IBL and KCI are equal , the side BL = CK : hence , AB + CD = AL + DK = 2AL ; hence AL is the half sum of the bases AB , CD ...
Page 76
... equivalent to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . Let AC be the line , and B the point of division ; then , is AC2 or ( AB + BC ) 2 = AB2 + BC2 + 2AB × BC ...
... equivalent to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . Let AC be the line , and B the point of division ; then , is AC2 or ( AB + BC ) 2 = AB2 + BC2 + 2AB × BC ...
Other editions - View all
Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex