## Elements of Geometry |

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Page xi

When two proportions have the same antecedents , the consequents may be put into a proportion ; for , if we have A : B :: C : D , A : E :: C : F , by changing the place of the

When two proportions have the same antecedents , the consequents may be put into a proportion ; for , if we have A : B :: C : D , A : E :: C : F , by changing the place of the

**means**, these proportions will become A : C :: B : D , 4 : C ... Page xii

There being a proportion among any magnitudes whatever designated by the letters A : B :: C : D , we have , by the above changes , B + A : A :: D + C : C , B - A : A :: D - C : C. If we change the place of the

There being a proportion among any magnitudes whatever designated by the letters A : B :: C : D , we have , by the above changes , B + A : A :: D + C : C , B - A : A :: D - C : C. If we change the place of the

**means**in these results ... Page 13

... that is , the sum of the ; three angles is the same in the two triangles . To prove this , make AK = AI , and join C K ; we shall have - > > - - * This supposition does not exclude the case in which the

... that is , the sum of the ; three angles is the same in the two triangles . To prove this , 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 ... Page 15

Accordingly , if , by

Accordingly , if , by

**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 ... Page 34

Besides , if the measure of angles by the arcs of a circle be in some degree indirect , it is not the less easy to obtain , by

Besides , if the measure of angles by the arcs of a circle be in some degree indirect , it is not the less easy to obtain , by

**means**of them , the direct and absolute measure ; for , if we compare the arc , which is used as the measure ...### What people are saying - Write a review

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ABC fig ABCD adjacent altitude applied base called centre chord circ circle circumference circumscribed common cone consequently construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces feet figure follows formed four give given greater half hence inclination inscribed intersection isosceles join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM produced proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment similar solid angle Solution sphere spherical square straight line suppose surface taken tangent THEOREM third triangle ABC vertex vertices whence