Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 páginas |
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Página xiv
... whole , and to be taken for unity ; then A , B , C , D , will each represent a certain number of units , entire or fractional , commen- surable or incommensurable , and the proportion among the lines Xiv Introduction .
... whole , and to be taken for unity ; then A , B , C , D , will each represent a certain number of units , entire or fractional , commen- surable or incommensurable , and the proportion among the lines Xiv Introduction .
Página xv
... units , C and D in superficial units , and the product Ax D will be a number , as also the product B x C. Indeed , in all the operations , which are made upon proportional quantities , it is necessary to regard the terms of the ...
... units , C and D in superficial units , and the product Ax D will be a number , as also the product B x C. Indeed , in all the operations , which are made upon proportional quantities , it is necessary to regard the terms of the ...
Página 19
... units in the number of sides minus two . Demonstration . Let ABCDE & c . ( fig . 42 ) be the proposed Fig . 42 . polygon ; if from the vertex of the angle A we draw to the vertices of the opposite angles the diagonals AC , AD , AE , & c ...
... units in the number of sides minus two . Demonstration . Let ABCDE & c . ( fig . 42 ) be the proposed Fig . 42 . polygon ; if from the vertex of the angle A we draw to the vertices of the opposite angles the diagonals AC , AD , AE , & c ...
Página 32
... unit of measure , the acute angle would be expressed , by a number comprehended between 0 and 1 , and an obtuse angle by a number between 1 and 2 . But this manner of expressing angles would not be the most convenient in practice . It ...
... unit of measure , the acute angle would be expressed , by a number comprehended between 0 and 1 , and an obtuse angle by a number between 1 and 2 . But this manner of expressing angles would not be the most convenient in practice . It ...
Página 46
... units contained in the base , and the number of linear units contained in the altitude . This measure , however , is not absolute , but relative ; it sup- poses that we estimate , in a similar manner , another rectangle by measuring its ...
... units contained in the base , and the number of linear units contained in the altitude . This measure , however , is not absolute , but relative ; it sup- poses that we estimate , in a similar manner , another rectangle by measuring its ...
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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...