Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 páginas |
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Página 41
... remainder BE . Apply the remainder BE to the line CD , as many times as it will admit of , for example , once with a remainder DF . Apply the second remainder DF to the first BE , as many times as will admit of , once , for example ...
... remainder BE . Apply the remainder BE to the line CD , as many times as it will admit of , for example , once with a remainder DF . Apply the second remainder DF to the first BE , as many times as will admit of , once , for example ...
Página 78
... remainder . But , as this remainder and the following ones go on diminishing and would soon become too small to be perceived , on account of the imperfection of the mechanical operation , from which we can conclude nothing with regard ...
... remainder . But , as this remainder and the following ones go on diminishing and would soon become too small to be perceived , on account of the imperfection of the mechanical operation , from which we can conclude nothing with regard ...
Página 79
... remainder AD . Whence it is evident , that the operation will never terminate , and that accordingly there is no common measure between the diagonal and the side of a square , a truth already made known by a numerical operation , since ...
... remainder AD . Whence it is evident , that the operation will never terminate , and that accordingly there is no common measure between the diagonal and the side of a square , a truth already made known by a numerical operation , since ...
Página 168
... remainders BC , GH , will be equal . Besides the angle BCA AIG , and the angle ABC AGH . Whence the triangles ABC , AHG , have a side and the two adjacent angles of the one respectively equal to a side and the two adjacent angles of the ...
... remainders BC , GH , will be equal . Besides the angle BCA AIG , and the angle ABC AGH . Whence the triangles ABC , AHG , have a side and the two adjacent angles of the one respectively equal to a side and the two adjacent angles of the ...
Página 169
... remainder will be greater than a semi- circumference , which is the measure of two right angles ; there- fore the sum of the three angles of a spherical triangle is greater than two right angles . 490. Corollary 1. The sum of the angles ...
... remainder will be greater than a semi- circumference , which is the measure of two right angles ; there- fore the sum of the three angles of a spherical triangle is greater than two right angles . 490. Corollary 1. The sum of the angles ...
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Términos y frases comunes
ABCD adjacent angles algebraic algebraic quantities altitude angle ACB base centre chord circ circle circular sector circumference coefficient common divisor cone consequently contains Corollary cube cylinder Demonstration denominator denoted diameter divided dividend division equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor homologous sides inscribed less letters logarithm manner measure multiplied obtain parallel parallelogram parallelopiped perpendicular plane MN polyedron preceding prism proportion proposed equation proposition quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium side BC similar solid angle sphere spherical square root straight line substitute subtract suppose term THEOREM third tion triangle ABC triangular pyramids unity unknown quantity vertex whence
Pasajes populares
Página 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Página 7 - 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.
Página 151 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Página 76 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Página 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Página 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Página 160 - 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.
Página 203 - In every triangle the sum of the three angles is equal to two right angles.
Página 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Página 141 - If a pyramid is cut by a plane parallel to its base, the...