Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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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 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. For , suppose a second perpendicular AC to be ...
... 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. For , suppose a second perpendicular AC to be ...
Page 34
... given line at points equally distant from the foot of the perpendicular , are 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 , are 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 ...
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 im- possible ...
... 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 im- possible ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence