## Elements of Geometry |

### From inside the book

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Page xi

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**means**, these proportions will be- come whence A : C :: B : D , A : C :: E : F ; B : D :: E : F , • B : E :: D : F. or IV . Other changes , besides the transposition of terms , may be made among proportionals without destroying the ... Page xii

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**means**in these results , they will become B + A : D + CA : C , B - AD - C :: A : C ; but , by the same change , the proportion gives also A : B :: C : D A : C :: B : D ; and , since the ratios A : C , B : D , are equal , we obtain B + A ... Page 13

... make AK = AI , and join C ' K ; we shall have * This supposition does not exclude the case in which the

... make AK = AI , and join C ' K ; we shall have * This supposition does not exclude the case in which the

**mean**side AC is equal to one of the extremes AB or BC . the triangle C'AK BAI . For , in these two Of Parallel Lines . 13. Page 15

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**means**of the triangle abc , we construct the following triangle a'b'c ' , the sum of the angles a + b ' of this triangle will be equal to the angle a , and will , consequently , be less than any given angle ; it will hence be seen that ... Page 34

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**means**of them , the direct and absolute measure ; for , if we compare the arc , which is used as the measure of an angle , with the fourth part of the circumference , we have the ratio of the given angle to a right angle , which is 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