Elements of Geometry and Trigonometry |
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Page 114
... reason of these same parallels , we have GH : AB :: OH : OB , and HI : BC : : OH : OB ; therefore GH : AB :: HI : BC . But AB = BC , therefore GH - HI . For the same reason , HI = IK , & c .; hence the sides of the circum- scribed ...
... reason of these same parallels , we have GH : AB :: OH : OB , and HI : BC : : OH : OB ; therefore GH : AB :: HI : BC . But AB = BC , therefore GH - HI . For the same reason , HI = IK , & c .; hence the sides of the circum- scribed ...
Page 145
... reason , we have SB : Sb :: SC : Sc ; and so on . Hence the edges SA , SB , SC , & c . are cut proportionally in a ... reason of the similar trian- gles SAB , Sab , we have AB : ab :: SB : Sb ; and by reason of the similar triangles SBC ...
... reason , we have SB : Sb :: SC : Sc ; and so on . Hence the edges SA , SB , SC , & c . are cut proportionally in a ... reason of the similar trian- gles SAB , Sab , we have AB : ab :: SB : Sb ; and by reason of the similar triangles SBC ...
Page 148
... reason of the equal parallelograms ABGF , abgf , the side GF will fall on its equal gf , and in the same manner GH on gh ; hence , the plane of the upper base , FGHIK will coincide with the plane fghik ( Book VI . Prop . II ...
... reason of the equal parallelograms ABGF , abgf , the side GF will fall on its equal gf , and in the same manner GH on gh ; hence , the plane of the upper base , FGHIK will coincide with the plane fghik ( Book VI . Prop . II ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
14 other sections not shown
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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 consequently convex surface cosine Cotang 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex