Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 páginas |
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Página 4
... fall upon the point C , the middle of AB . The side GE being thus applied to CA , the side GH will fall upon CD ; for , let us suppose , if it be possible , that it falls upon a line CK , different from CD ; since , by hypo- EGH = HGF ...
... fall upon the point C , the middle of AB . The side GE being thus applied to CA , the side GH will fall upon CD ; for , let us suppose , if it be possible , that it falls upon a line CK , different from CD ; since , by hypo- EGH = HGF ...
Página 7
... fall upon A , and the point E upon B. But , since the angle D is equal to the angle A , when the side DE is placed upon AB , the side DE will take the direction AC ; moreover DF is equal to AC ; therefore the point F will fall upon C ...
... fall upon A , and the point E upon B. But , since the angle D is equal to the angle A , when the side DE is placed upon AB , the side DE will take the direction AC ; moreover DF is equal to AC ; therefore the point F will fall upon C ...
Página 8
... falls without the triangle ABC , on the side BC , or within the triangle . Case 1. Because GC < GI + IC , and AB < AI + IB , there- fore GC + AB < GI + AI + IC + IB , that is , GC + AB < AG + BC . From one 8 Elements of Geometry .
... falls without the triangle ABC , on the side BC , or within the triangle . Case 1. Because GC < GI + IC , and AB < AI + IB , there- fore GC + AB < GI + AI + IC + IB , that is , GC + AB < AG + BC . From one 8 Elements of Geometry .
Página 9
... fall upon the side BC , then Fig . 26 . it is evident that GC , or its equal EF , is less than BC . Case III . If the point G ( fig . 27 ) fall within the triangle Fig . 27 . BAC , then AG + GC < AB + BC ( 41 ) , therefore , taking away ...
... fall upon the side BC , then Fig . 26 . it is evident that GC , or its equal EF , is less than BC . Case III . If the point G ( fig . 27 ) fall within the triangle Fig . 27 . BAC , then AG + GC < AB + BC ( 41 ) , therefore , taking away ...
Página 13
... fall upon AB the perpendicular FG ; the point G will not fall upon A , since the angle FAB is less than a right angle ; still less can it fall upon H in BA produced , for then there would be two perpendiculars KA , KH , let fall from ...
... fall upon AB the perpendicular FG ; the point G will not fall upon A , since the angle FAB is less than a right angle ; still less can it fall upon H in BA produced , for then there would be two perpendiculars KA , KH , let fall from ...
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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...