Elements of Geometry and Trigonometry |
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Page 35
... given point to a given straight line , only two equal straight lines can be drawn ; for , if there could be more , there would be at least two equal oblique lines on the same side of the perpendicular ; which is impossible . PROPOSITION ...
... given point to a given straight line , only two equal straight lines can be drawn ; for , if there could be more , there would be at least two equal oblique lines on the same side of the perpendicular ; which is impossible . PROPOSITION ...
Page 44
... given , the third will be found by subtracting their sum from two right angles . Cor . 2. If two angles of one triangle are respectively equal to two angles of another , the two triangles are mutually equiangular . Cor . 3. In any ...
... given , the third will be found by subtracting their sum from two right angles . Cor . 2. If two angles of one triangle are respectively equal to two angles of another , the two triangles are mutually equiangular . Cor . 3. In any ...
Page 49
... given straight line , and on the same side of it , the straight line joining them will be parallel to the given line . PROPOSITION XXXI . THEOREM . The diagonals of a parallelogram divide each other into equal parts , or mutually bisect ...
... given straight line , and on the same side of it , the straight line joining them will be parallel to the given line . PROPOSITION XXXI . THEOREM . The diagonals of a parallelogram divide each other into equal parts , or mutually bisect ...
Page 82
... given straight line . From A and B , as centres , with a radius greater than one half of AB , describe arcs intersecting at E and F : join E and F , by the straight line EF . Then will EF bisect the given line AB . For , E and F are ...
... given straight line . From A and B , as centres , with a radius greater than one half of AB , describe arcs intersecting at E and F : join E and F , by the straight line EF . Then will EF bisect the given line AB . For , E and F are ...
Page 83
... given straight line , from a given point without that line . and A Let BD be the given line , and A the given point . From A , as a centre , with a ra dius sufficiently great , describe an arc cutting BD in two points , B D ; with B and ...
... given straight line , from a given point without that line . and A Let BD be the given line , and A the given point . From A , as a centre , with a ra dius sufficiently great , describe an arc cutting BD in two points , B D ; with B and ...
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Common terms and phrases
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence