Elements of Geometry and Trigonometry |
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Page 23
... less than the sum of the sides AD , DF ( Prop . VIII . ) ; there- fore , AC , the half of the line ACF , is shorter than AD , the half of the line ADF : therefore , the oblique line , which is farther from the perpendicular , is longer ...
... less than the sum of the sides AD , DF ( Prop . VIII . ) ; there- fore , AC , the half of the line ACF , is shorter than AD , the half of the line ADF : therefore , the oblique line , which is farther from the perpendicular , is longer ...
Page 24
... less than ID + DB , and ID + DB = ID + DA = IA ; therefore , IB < IA ; therefore , every point out of the perpendicular , is unequally distant from the extremities A and B. Cor . If a straight line have two points D and F , equally dis ...
... less than ID + DB , and ID + DB = ID + DA = IA ; therefore , IB < IA ; therefore , every point out of the perpendicular , is unequally distant from the extremities A and B. Cor . If a straight line have two points D and F , equally dis ...
Page 27
... less than two right angles , the two lines will meet if sufficiently produced . Let the line EF meet the two lines CD , IH , making the sum of the interior angles OGH , A GOD , less than two right an- gles : then will IH and CD ineet if ...
... less than two right angles , the two lines will meet if sufficiently produced . Let the line EF meet the two lines CD , IH , making the sum of the interior angles OGH , A GOD , less than two right an- gles : then will IH and CD ineet if ...
Page 28
... less than two right angles PROPOSITION XXII . THEOREM . Two straight lines which are parallel to a third line , are parallel to each other . Let CD and AB be parallel to the third line EF ; then arc they parallel to each other . Draw ...
... less than two right angles PROPOSITION XXII . THEOREM . Two straight lines which are parallel to a third line , are parallel to each other . Let CD and AB be parallel to the third line EF ; then arc they parallel to each other . Draw ...
Page 30
... less , can a triangle have more than one obtuse angle . Cor . 4. In every right angled triangle , the sum of the two acute angles is equal to one right angle . Cor . 5. Since every equilateral triangle is also equiangular ( Prop . XI ...
... less , can a triangle have more than one obtuse angle . Cor . 4. In every right angled triangle , the sum of the two acute angles is equal to one right angle . Cor . 5. Since every equilateral triangle is also equiangular ( Prop . XI ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex