## Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |

### From inside the book

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Page 12

... unit an equal number of times . 15. Magnitudes are equal in all their parts , when they may be so placed as to

... unit an equal number of times . 15. Magnitudes are equal in all their parts , when they may be so placed as to

**coincide**throughout their whole extent . ELEMENTS OF OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . 12 GEOMETRY . Page 23

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**coincide**throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines**coincide**throughout . E A B -D Between A and B they must**coincide**( A. 11 ) . Suppose , now ... Page 25

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**coincide**with the vertex F ; consequently , the side BC will**coincide**with the side EF ( A. 11 ) . The two triangles , therefore ,**coincide**throughout , and are consequently equal in all their parts ( I. , D. 14 ) ; which was to be ... Page 26

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**coincide**with the vertex F ; and because the angle C is equal to the angle F , the side CA will take the direction FD . Now , the vertex A being at the same time on the lines ED and FD , it must be at their intersection D ( P. III . , C ... Page 61

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**coincide**; otherwise there would be some points in either one or the other of the curves unequally distant from the centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its circumference , into two equal ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa 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 polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence

### Popular passages

Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.

Page 59 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.

Page 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.

Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.

Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 28 - If two triangles have two sides of the one equal to two sides of the...

Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 99 - The area of a parallelogram is equal to the product of its base and altitude.

Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.

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.