Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 pages |
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Page vi
... circle , treats of the most sim- ple properties of the circle , and those of chords , of tangents and of the measure of angles , by the arcs of a circle . These two sections are followed by the resolution of certain problems relating to ...
... circle , treats of the most sim- ple properties of the circle , and those of chords , of tangents and of the measure of angles , by the arcs of a circle . These two sections are followed by the resolution of certain problems relating to ...
Page vii
... circle . Two lemmas are employed as the basis of this measure , which is otherwise demonstrated after the manner of Archimedes . We have then given two methods of approxima- tion for squaring the circle , one of which is that of James ...
... circle . Two lemmas are employed as the basis of this measure , which is otherwise demonstrated after the manner of Archimedes . We have then given two methods of approxima- tion for squaring the circle , one of which is that of James ...
Page 21
... , and are consequently equal ; whence it follows , that the angle AOB BOC , = and that thus the two diagonals of a rhombus cut each other mutually at right angles . ! Fig . 46 . Fig . 47 . SECTION SECOND of the Circle . 21.
... , and are consequently equal ; whence it follows , that the angle AOB BOC , = and that thus the two diagonals of a rhombus cut each other mutually at right angles . ! Fig . 46 . Fig . 47 . SECTION SECOND of the Circle . 21.
Page 22
... circle and the measure of angles . DEFINITIONS . 90. THE circumf rence of a circle is a curved line all the points of which are equally distant from a point within called the centre . The circle is the space terminated by this curved ...
... circle and the measure of angles . DEFINITIONS . 90. THE circumf rence of a circle is a curved line all the points of which are equally distant from a point within called the centre . The circle is the space terminated by this curved ...
Page 23
... circle , when all its sides are tangents to the circumference ; and in this case the circle is said to be inscribed in the polygon . 60 . THEOREM . 98. Every diameter AB ( fig . 49 ) bisects the circle and its cir- Fig . 49 . cumference ...
... circle , when all its sides are tangents to the circumference ; and in this case the circle is said to be inscribed in the polygon . 60 . THEOREM . 98. Every diameter AB ( fig . 49 ) bisects the circle and its cir- Fig . 49 . cumference ...
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Common terms and phrases
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
Popular passages
Page 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 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.
Page 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.
Page 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.
Page 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.
Page 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 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.
Page 203 - In every triangle the sum of the three angles is equal to two right angles.
Page 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Page 141 - If a pyramid is cut by a plane parallel to its base, the...