Elements of Geometry and Trigonometry |
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Page 18
... 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. A line may be ...
... 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. A line may be ...
Page 19
... given line , either from a point without , or from a point on the line . 7. A line may be drawn , making with a given line an angle equal to a given angle . 8. A line may be drawn through a given point , parallel to a given line . NOTE ...
... given line , either from a point without , or from a point on the line . 7. A line may be drawn , making with a given line an angle equal to a given angle . 8. A line may be drawn through a given point , parallel to a given line . NOTE ...
Page 20
... , CAD , DAE , EAF , formed about a given point on the same side of a straight line BF , is equal to two right an- gles . For , their sum is equal to D C E B- F A the sum of the angles EAB and EAF ; which 20 GEOMETRY . Propositions,
... , CAD , DAE , EAF , formed about a given point on the same side of a straight line BF , is equal to two right an- gles . For , their sum is equal to D C E B- F A the sum of the angles EAB and EAF ; which 20 GEOMETRY . Propositions,
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 26
... < ACBC AB ; that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may re- present the sides of a triangle , the sum of 26 GEOMETRY .
... < ACBC AB ; that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may re- present the sides of a triangle , the sum of 26 GEOMETRY .
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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...