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

### From inside the book

Results 1-5 of 97

Page 22

...

...

**proved**. Cor . 1. If one of the angles about C all of the others will be right angles also . each of its adjacent angles will be a right angle ; and from the proposition just demonstrated , its opposite angle will also be a right angle ... Page 23

...

...

**proved**, and then continuing the reasoning until the assumed hypothesis is shown to be false . Its contradictory is thus**proved**to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a ... Page 26

...

...

**proved**. PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side AC . For , the ... Page 30

...

...

**proved**. Scholium . In triangles , equal in all their parts , the equal sides lie opposite the equal angles ; and conversely . PROPOSITION XI . THEOREM . In an isosceles triangle the angles opposite the equal sides are equal . Let BAC ... Page 31

...

...

**proved**. B D Cor . 1. An equilateral triangle is equiangular . AD Cor . 2. The angle BAD is equal to DAC , and BDA to CDA hence , the last two are right angles . Conse- quently , a straight line drawn from the vertex of an isosceles ...### 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.