Elements of Geometry |
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Page vi
... 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 the construction of figures . The third section , entitled the proportions ...
... 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 the construction of figures . The third section , entitled the proportions ...
Page 22
... chord or subtense of an arc is the straight line FG , which joins its extremities ** . 93. A segment of a circle is the portion comprehended be- tween an arc and its chord . 94. A sector is the part of a circle comprehended between an ...
... chord or subtense of an arc is the straight line FG , which joins its extremities ** . 93. A segment of a circle is the portion comprehended be- tween an arc and its chord . 94. A sector is the part of a circle comprehended between an ...
Page 23
... chord is less than the diameter . Demonstration . If the radii CA , CD ( fig . 49 ) , be drawn from Fig . 49 . the centre to the extremities of the chord AD , we shall have the straight line AD < AC + CD , that is , AD < AB ( 91 ) . 100 ...
... chord is less than the diameter . Demonstration . If the radii CA , CD ( fig . 49 ) , be drawn from Fig . 49 . the centre to the extremities of the chord AD , we shall have the straight line AD < AC + CD , that is , AD < AB ( 91 ) . 100 ...
Page 24
... chords , and conversely , equal chords subtend equal arcs . Demonstration . The radius AC ( fig . 50 ) being equal to the radius EO , and the arc AMD equal to the arc ENG ; the chord AD will be equal to the chord EG . For , the diameter ...
... chords , and conversely , equal chords subtend equal arcs . Demonstration . The radius AC ( fig . 50 ) being equal to the radius EO , and the arc AMD equal to the arc ENG ; the chord AD will be equal to the chord EG . For , the diameter ...
Page 25
... chord would diminish , and the reverse ; thus , the arc AKBD being greater than AKBH , the chord AD of the first is less than the chord AH of the second . THEOREM . 105. The radius CG ( fig . 51 ) , perpendicular to a chord AB , Fig ...
... chord would diminish , and the reverse ; thus , the arc AKBD being greater than AKBH , the chord AD of the first is less than the chord AH of the second . THEOREM . 105. The radius CG ( fig . 51 ) , perpendicular to a chord AB , Fig ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD angles equal base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle intersection isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence
Popular passages
Page 65 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 21 - 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 ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Page 63 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page ii - States entitled an act for the encouragement of learning hy securing the copies of maps, charts and books to the author., and proprietors of such copies during the times therein mentioned, and also to an act entitled an act supplementary to an act, entitled an act for the encouragement of learning by securing the copies of maps, charts and books to the authors and proprietors of such copies during the times therein mentioned and extending the benefits thereof to the arts of designing, engraving and...
Page 80 - 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 164 - 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 24 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 153 - XVII.) ; hence two similar pyramids are to each other as the cubes of their homologous sides.