## Elements of Geometry |

### From inside the book

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**intersection**A , is the vertex of the angle ; the lines AB , AC , are its sides . An angle is sometimes denoted simply by the letter at the ver- tex , as A ; sometimes by three letters , as BAC , or CAB , the letter at the vertex always ... Page 7

... ; whence the point D , which must be at the same time in the lines BA and CA , can only be at their

... ; whence the point D , which must be at the same time in the lines BA and CA , can only be at their

**intersection**A ; therefore the two triangles ABC , Fig . 23 . Fig . 24 . Fig . Of Perpendicular and Oblique Lines . 7. Page 28

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**intersection**, and will bisect it . Demonstration . The line AB ( fig . 57 , 58 ) , which joins the points of**intersection**, is a chord common to the two circles ; and , if a perpendicular be erected upon the middle of this chord , it ... Page 29

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**intersection**may take place , the triangle ACD ( fig . 57 , 58 ) must be possible . It is necessary Fig . 57 , then , not only that CD ( fig . 57 ) should be less than AC + AD , Fig . 57 . but also that the greater radius AD ( fig . 58 ) ... Page 84

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**intersections**, the regular circumscribed polygon GHIK & c . , similar to the inscribed polygon . It will be readily perceived , in the first place , that the three points O , B , H , are in a right line , for the right angled triangles ...### 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.