Elements of Geometry |
From inside the book
Results 1-5 of 22
Page 22
... segment of a circle is the portion comprehended be- tween an arc and its chord . 94. A sector is the part of a ... segments ; but , in speaking of these , the smaller is always to be understood , when the contrary is not expressed . And ...
... segment of a circle is the portion comprehended be- tween an arc and its chord . 94. A sector is the part of a ... segments ; but , in speaking of these , the smaller is always to be understood , when the contrary is not expressed . And ...
Page 33
... segment , are equal ; for they have each for their measure the half of the same arc BOC . 128. Corollary II . Every angle BAD ( fig . 67 ) , inscribed in Fig . 67 . a semicircle , is a right angle ; for it has for its measure the half ...
... segment , are equal ; for they have each for their measure the half of the same arc BOC . 128. Corollary II . Every angle BAD ( fig . 67 ) , inscribed in Fig . 67 . a semicircle , is a right angle ; for it has for its measure the half ...
Page 34
... segment greater than a semicircle , is an acute angle ; for it has for its measure the half of the arc BOC less than a semicir- cumference . And every angle BOC , inscribed in a segment less than a semicircle , is an obtuse angle ; for ...
... segment greater than a semicircle , is an acute angle ; for it has for its measure the half of the arc BOC less than a semicir- cumference . And every angle BOC , inscribed in a segment less than a semicircle , is an obtuse angle ; for ...
Page 40
... segment capable of containing a given angle C , that is a segment such , that each of the angles , which may be inscribed in it , shall be equal to a given angle C. Solution . Produce AB toward D , make at the point B the angle DBE = C ...
... segment capable of containing a given angle C , that is a segment such , that each of the angles , which may be inscribed in it , shall be equal to a given angle C. Solution . Produce AB toward D , make at the point B the angle DBE = C ...
Page 43
... segments , are such as correspond to equal angles at the cen- tre . Thus , the angle A ( fig . 92 ) being equal to the angle Q , the Fig . 92 . arc BC is similar to the arc DE , the sector ABC to the sector ODE , & c . 164. The altitude ...
... segments , are such as correspond to equal angles at the cen- tre . Thus , the angle A ( fig . 92 ) being equal to the angle Q , the Fig . 92 . arc BC is similar to the arc DE , the sector ABC to the sector ODE , & c . 164. The altitude ...
Other editions - View all
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.