## Elements of Geometry |

### From inside the book

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**triangle**; that of four sides is called a quadrilateral ; that of five sides , a pentagon ; that of six , a hexa- gon , & c . 15. A**triangle**is denominated**equilateral**( fig . 7 ) , when the three sides are equal ,**isosceles**( fig . 8 ) ... Page 9

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**isosceles triangle**, the angles opposite to the equal sides are equal . Demonstration . Let the side AB = AC ( fig . 28 ) , then will Fig . 28 . the angle C be equal to B. Draw the straight line AD from the vertex A to the point D , the ... Page 10

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**isosceles triangle**, the base is that side which is not equal to one of the others . THEOREM . 48. Reciprocally , if two angles of a triangle are equal , the op- posite sides are equal , and the triangle is isosceles . Demonstration ... Page 35

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**triangle**BAC is**isosceles**, and the angle BACABC ; the**triangle**CAD is also**isosceles**, and the angle CAD = ADC ; hence BAC + CAD , or BAD≈ ABD + ADB . But , if the two angles B and D of the**triangle**ABD are together equal to the third ... Page 53

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**triangle**HBC ; consequently the rectangle BDEF , double of the**triangle**ABF , is equivalent to the square AH ...**isosceles**, we have AC = AB + BC = 2AB ; therefore the square described upon the diagonal AC is double of the square ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence