Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 páginas |
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Página 9
... base BC ; the two triangles ABD , ADC , will have the three sides of the one , equal to the three sides of the other , each to each , namely , AD common to both , ABAC , by hypothesis , and BD DC , by construction ; there- fore ( 43 ) ...
... base BC ; the two triangles ABD , ADC , will have the three sides of the one , equal to the three sides of the other , each to each , namely , AD common to both , ABAC , by hypothesis , and BD DC , by construction ; there- fore ( 43 ) ...
Página 10
... base , is perpendicular to that base , and divides the vertical angle into two equal parts . In a triangle that is not isosceles , any one of its sides may be taken indifferently for a base ; and then its vertex is that of the opposite ...
... base , is perpendicular to that base , and divides the vertical angle into two equal parts . In a triangle that is not isosceles , any one of its sides may be taken indifferently for a base ; and then its vertex is that of the opposite ...
Página 19
... bases the different sides of the polygon , except the two which form the angle BAC . We see , at the same time , that the sum of the angles of all these triangles does not differ from the sum of the angles of the poly- gon ; therefore ...
... bases the different sides of the polygon , except the two which form the angle BAC . We see , at the same time , that the sum of the angles of all these triangles does not differ from the sum of the angles of the poly- gon ; therefore ...
Página 23
... base AB may be common to both , the curved line AEB must fall exactly upon the curved line AFB ; otherwise , there would be points in the one or the other unequally distant from the centre , which is contrary to the definition of a ...
... base AB may be common to both , the curved line AEB must fall exactly upon the curved line AFB ; otherwise , there would be points in the one or the other unequally distant from the centre , which is contrary to the definition of a ...
Página 32
... bases of these sectors . It will be perceived therefore , that the arcs of a circle , which are used as a measure of angles , will also serve as the measure of different sectors of the same circle or of equal circles . THEOREM . 65 ...
... bases of these sectors . It will be perceived therefore , that the arcs of a circle , which are used as a measure of angles , will also serve as the measure of different sectors of the same circle or of equal circles . THEOREM . 65 ...
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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...