## Elements of Geometry |

### From inside the book

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**angle**ACE , and there will remain the**angle**ACD equal to its opposite**angle**BCE . It may be demonstrated , in like ...**ACB**, BCD , & c . † These are often called vertical**angles**. THEOREM . 36. Two triangles are equal , when two 6 ... Page 10

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**angle**BAD DAC , and that the**angle**BDA ADC ; therefore these two last are right**angles**. Hence a straight line ...**ACB**( fig . 29 ) , the side AC will be equal to the side AB . For , if these sides are not equal , let AB be the greater ... Page 13

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**angles**is equal to two right**angles**. Demonstration . Let ABC ( fig . 35 ) be the proposed triangle , Fig . 35 in which we suppose * that AB is the greatest side , and BC the least , and that , consequently ,**ACB**is the greatest**angle**... Page 14

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**ACB**, and the**angle**KB'C ' = CAI . = It hence follows , 1. that the**angle**AC'B ' , designated by C ' , is composed of ...**angle**a less than any given term of the decreasing progression A , A , † A , & c . We may therefore suppose this ... Page 32

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**angles ACB**, DCE , are to each other as 7 to 1 ; or , which amounts to the same , that the angle M , which will serve as a common meas- ure , is contained seven times in the**angle ACB**, and four times in the angle DCE . The partial angles ...### 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