Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 15
... parallel , when they lie in the same plane and can- not meet , how far soever , either way , both may be produced . They then have the same direction . 17. A PLANE FIGURE is a portion of a plane bounded by lines , either straight or ...
... parallel , when they lie in the same plane and can- not meet , how far soever , either way , both may be produced . They then have the same direction . 17. A PLANE FIGURE is a portion of a plane bounded by lines , either straight or ...
Page 17
... parallel . 28. A PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all ...
... parallel . 28. A PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all ...
Page 18
... parallel to a given line .. POSTULATES . 1. A straight line can be drawn between any two points . 2. A straight line may be prolonged to any length . 3. If two lines are unequal , the length of the less may be laid off on the greater ...
... parallel to a given line .. POSTULATES . 1. A straight line can be drawn between any two points . 2. A straight line may be prolonged to any length . 3. If two lines are unequal , the length of the less may be laid off on the greater ...
Page 19
... parallel to a given line . NOTE . In making references , the following abbreviations are employed , viz . A. for Axiom ; B. for Book ; C. for Corollary ; D. for Definition ; 1 . for Introduction ; P. for Proposition ; Prob . for Problem ...
... parallel to a given line . NOTE . In making references , the following abbreviations are employed , viz . A. for Axiom ; B. for Book ; C. for Corollary ; D. for Definition ; 1 . for Introduction ; P. for Proposition ; Prob . for Problem ...
Page 37
... parallel . Let the two lines AC , BD , be perpendicular to AB : then will they be parallel . For , if they could meet in a point 0 , there would be two perpendiculars OA , OB , drawn from the same point to the same B D C straight line ...
... parallel . Let the two lines AC , BD , be perpendicular to AB : then will they be parallel . For , if they could meet in a point 0 , there would be two perpendiculars OA , OB , drawn from the same point to the same B D C straight line ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following