## Elements of Geometry |

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This is not Legendre's 'Elements'.

### Contents

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### Common terms and phrases

a b c ABCD adjacent angles algebraic Algebraic Quantities altitude base centre chord circ circle circumference circumscribed coefficient consequently contained Corollary cube cube root degree Demonstration denominator denoted diameter difference divided dividend equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor hence homologous sides inscribed less letters logarithm manner measure multiplied obtain OREM parallel parallelogram parallelopiped perpendicular plane polyedron preceding prism proportion proposed equation proposed number proposition pyramid quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium similar solid angle Solution sphere spherical square root straight line substituting subtract suppose surface term THEOREM third tion triangle ABC units unity unknown quantity vertex whence

### Popular passages

Page 9 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 44 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.

Page 63 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.

Page 101 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.

Page 8 - Any side of a triangle is less than the sum of the other two sides...

Page 122 - ... is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, this equation can have only imaginary roots.

Page 180 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.

Page 54 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.

Page 185 - The convex surface of a cone is equal to the circumference of the base multiplied by half the slant height.

Page 164 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.