Elements of Geometry and Trigonometry |
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Page 18
... given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1 ...
... given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1 ...
Page 19
... given straight line an angle equal to a given angle . 8. A straight line may be drawn through a given point , parallel to a given line . NOTE . In making references , the following abbreviations are employed , viz .: A. for Axiom ; B ...
... given straight line an angle equal to a given angle . 8. A straight line may be drawn through a given point , parallel to a given line . NOTE . In making references , the following abbreviations are employed , viz .: A. for Axiom ; B ...
Page 23
... given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III . THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one ...
... given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III . THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one ...
Page 33
... given point only one perpendicular can be drawn to a given straight line . Let A be a given point , and AB a perpendicular to DE : then can no other perpendicular to DE be drawn from A. A D B E F For , suppose a second perpendicular AC ...
... given point only one perpendicular can be drawn to a given straight line . Let A be a given point , and AB a perpendicular to DE : then can no other perpendicular to DE be drawn from A. A D B E F For , suppose a second perpendicular AC ...
Page 34
... given line at points equally distant from the foot of the perpendicular , will be equal : 3 ° . Of two oblique lines that meet the given line at points unequally distant from the foot of the perpendicular , the one which meets it at the ...
... given line at points equally distant from the foot of the perpendicular , will be equal : 3 ° . Of two oblique lines that meet the given line at points unequally distant from the foot of the perpendicular , the one which meets it at the ...
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Common terms and phrases
ABCD AC² 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