Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 sider |
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Side 18
... known by subtracting the sum of these angles from two right angles . 74. Corollary II . If two angles of one triangle are equal to two angles of another triangle , each to each , the third of the one will be equal to the third of the ...
... known by subtracting the sum of these angles from two right angles . 74. Corollary II . If two angles of one triangle are equal to two angles of another triangle , each to each , the third of the one will be equal to the third of the ...
Side 69
... known . THEOREM . 235. Let P ( fig . 136 ) be a given point within a circle in the Fig . 136 , radius AC , and let there be taken a point Q without the circle in the same radius produced such that CP : CA :: CA : CQ ; if , from any ...
... known . THEOREM . 235. Let P ( fig . 136 ) be a given point within a circle in the Fig . 136 , radius AC , and let there be taken a point Q without the circle in the same radius produced such that CP : CA :: CA : CQ ; if , from any ...
Side 79
... known by a numerical operation , since these two lines are to each other :: √2 : 1 ( 188 ) , but which is rendered clearer by the geomet- rical solution . 261. It is not then possible to find in numbers the exact ratio of the diagonal ...
... known by a numerical operation , since these two lines are to each other :: √2 : 1 ( 188 ) , but which is rendered clearer by the geomet- rical solution . 261. It is not then possible to find in numbers the exact ratio of the diagonal ...
Side 91
... square equal in surface to a circle whose radius is known ; now we have just shown that a circle is equivalent to a rectangle contained by the Fig . 169 . circumference and half of the radius Of the Measure of the Circle . 91.
... square equal in surface to a circle whose radius is known ; now we have just shown that a circle is equivalent to a rectangle contained by the Fig . 169 . circumference and half of the radius Of the Measure of the Circle . 91.
Side 92
... 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 ratio except by approximation ; but the process has been carried ...
... 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 ratio except by approximation ; but the process has been carried ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Side 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.
Side 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.
Side 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.
Side 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.
Side 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Side 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.
Side 203 - In every triangle the sum of the three angles is equal to two right angles.
Side 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Side 141 - If a pyramid is cut by a plane parallel to its base, the...