## Elements of Geometry |

### From inside the book

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**respect**to each other , when they have their sides equal , each to each , and placed in the same order ; that is , when , by proceeding round in the same direction , the first in the one is equal to the first in the other , the second ... Page 19

... , CHF , are equal to each other ; the same may be proved with

... , CHF , are equal to each other ; the same may be proved with

**respect**to the four obtuse angles AGE , BGH , GHC , DHF . It may be observed , moreover , that , by adding one of Fig . 39 . Fig . 40 . the four Of Parallel Lines. ... Page 27

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**respect**to the perpendicular CD , two equal oblique lines ; there- fore they are equally distant from the perpendicular ( 52 ) , and ᎯᎠ -- ᎠᏴ . Again , since AD = BD , and CG is a perpendicular erected upon the middle of AB , each ... Page 29

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**respect**to this new tangent , the radius CA would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be less than CA ; therefore this supposed tangent would pass into the circle , and become a ... Page 44

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**respect**to straight lines , that arcs also , which are compared , have not a common meas- ure ; we can then obtain , for the angles , only an approximate ratio in numbers , more or less exact , according to the degree to which the ...### 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