Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 σελίδες |
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Σελίδα 65
... reduced to num- bers and these numbers multiplied together . 232. Scholium . It may be demonstrated also , that the surface of a triangle is equal to its perimeter multiplied by half of the radius of the inscribed circle . For the ...
... reduced to num- bers and these numbers multiplied together . 232. Scholium . It may be demonstrated also , that the surface of a triangle is equal to its perimeter multiplied by half of the radius of the inscribed circle . For the ...
Σελίδα 67
... reduced to num- bers and these numbers multiplied together . 232. Scholium . It may be demonstrated also , that the surface of a triangle is equal to its perimeter multiplied by half of the radius of the inscribed circle . For the ...
... reduced to num- bers and these numbers multiplied together . 232. Scholium . It may be demonstrated also , that the surface of a triangle is equal to its perimeter multiplied by half of the radius of the inscribed circle . For the ...
Σελίδα 68
... equal to AD , OIX BD = AD × DC . Adding these two results , and observing that BI × BD + OIX BD reduces itself to BO × BD , we obtain BOX BD = AB × BC + AD × DC . If we had taken BP AD , and had drawn 68 Elements of Geometry .
... equal to AD , OIX BD = AD × DC . Adding these two results , and observing that BI × BD + OIX BD reduces itself to BO × BD , we obtain BOX BD = AB × BC + AD × DC . If we had taken BP AD , and had drawn 68 Elements of Geometry .
Σελίδα 75
... reduced to one , may be used to reduce three to two and these two to one , and so of a larger number . Also a similar method may be employed when certain given squares are to be subtracted from others . PROBLEM . 252. To construct a ...
... reduced to one , may be used to reduce three to two and these two to one , and so of a larger number . Also a similar method may be employed when certain given squares are to be subtracted from others . PROBLEM . 252. To construct a ...
Σελίδα 92
... reduces itself to finding the circumference , when the radius is known ; and , for this purpose , it is sufficient to know the ratio of the circumference to the radius or to the diameter . Hitherto we have not been able to obtain this ...
... reduces itself to finding the circumference , when the radius is known ; and , for this purpose , it is sufficient to know the ratio of the circumference to the radius or to the diameter . Hitherto we have not been able to obtain this ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Σελίδα 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.
Σελίδα 203 - In every triangle the sum of the three angles is equal to two right angles.
Σελίδα 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 141 - If a pyramid is cut by a plane parallel to its base, the...