Elements of Geometry and Trigonometry |
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Page 91
... extremity , and is therefore tangent to the circle . Scholium . The lines that bisect the three angles of a triangle all meet in one point . PROBLEM XVI . On a given line , to construct a segment that shall contain a given angle . Let ...
... extremity , and is therefore tangent to the circle . Scholium . The lines that bisect the three angles of a triangle all meet in one point . PROBLEM XVI . On a given line , to construct a segment that shall contain a given angle . Let ...
Page 121
... extremities B and C of the diam- eter BC , and a perpendicular AD be drawn to the diameter : then will ABC be a right - angled tri- angle , right - angled at A ; and from what was proved above , each chord will be a mean proportional ...
... extremities B and C of the diam- eter BC , and a perpendicular AD be drawn to the diameter : then will ABC be a right - angled tri- angle , right - angled at A ; and from what was proved above , each chord will be a mean proportional ...
Page 129
... extremity A , 1 F B draw the indefinite line AG , making any angle with AB ; A P lay off AC equal to P , CD equal to Q , and DE equal Q R Ꭱ ; to draw EB , and from the points C and D , Ε ENG draw CI and DF parallel to EB : then will AI ...
... extremity A , 1 F B draw the indefinite line AG , making any angle with AB ; A P lay off AC equal to P , CD equal to Q , and DE equal Q R Ꭱ ; to draw EB , and from the points C and D , Ε ENG draw CI and DF parallel to EB : then will AI ...
Page 130
... extremity A , draw the indefinite line AG ; take AI equal to any convenient line , and lay off IK , KL , LM , and MB , each equal to AI . Draw C D E F H A K L M B G BH , and from I , K , L , and M , draw the lines IC , KD , LE , and MF ...
... extremity A , draw the indefinite line AG ; take AI equal to any convenient line , and lay off IK , KL , LM , and MB , each equal to AI . Draw C D E F H A K L M B G BH , and from I , K , L , and M , draw the lines IC , KD , LE , and MF ...
Page 131
... extremity B , draw BC perpendicular to AB , and make it equal to half of AB . With C as a centre , and CB as a radius , describe the are A DBE ; draw AC , and produce it till it terminates in the concave arc at E ; centre and AD as ...
... extremity B , draw BC perpendicular to AB , and make it equal to half of AB . With C as a centre , and CB as a radius , describe the are A DBE ; draw AC , and produce it till it terminates in the concave arc at E ; centre and AD as ...
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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...