Elements of Geometry and Trigonometry |
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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 and rhomboids . two varieties of parallelograms : rectangles 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 and rhomboids . two varieties of parallelograms : rectangles 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 4 ...
... 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 4 ...
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 ; I. for Introduction ; P. for Proposition ; P. for ...
... 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 ; I. for Introduction ; P. for Proposition ; P. for ...
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 B point 0 , there would be two perpendiculars OA , OB , drawn A D -O C from the same point to the same straight ...
... parallel . Let the two lines AC , BD , be perpendicular to AB : then will they be parallel . For , if they could meet in a B point 0 , there would be two perpendiculars OA , OB , drawn A D -O C from the same point to the same straight ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
AB² ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...