## Elements of Geometry and Trigonometry |

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Page 19

1 " triangle GAC is equal to DEF , since , by construction , they have an equal angle in each ,

1 " triangle GAC is equal to DEF , since , by construction , they have an equal angle in each ,

**contained**by equal sides , ( Prop . V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as ... Page 34

If the other magnitude

If the other magnitude

**contain**a certain number of those units , it also may be expressed by the number of its units ... there may perhaps be a smaller unit which will be**contained**an exact number of times in each of the magnitudes . Page 51

In the same circle , or in equal circles , equal angles having their vertices at the centre , intercept equal arcs on the circumference : and conversely , if the arcs intercepted are equal , the angles

In the same circle , or in equal circles , equal angles having their vertices at the centre , intercept equal arcs on the circumference : and conversely , if the arcs intercepted are equal , the angles

**contained**by the radii will also ... Page 52

Suppose , for example , that the angles ACB , DCE , are to each other as 7 is to 4 ; or , which is the same thing , suppose that the angle M , which may serve as a common measure , is

Suppose , for example , that the angles ACB , DCE , are to each other as 7 is to 4 ; or , which is the same thing , suppose that the angle M , which may serve as a common measure , is

**contained**times in the angle ACB , and 4 times in ... Page 60

T Two sides of a triangle , and the angle which they

T Two sides of a triangle , and the angle which they

**contain**, being given , to describe the triangle . E G P H Having drawn the indefinite line DE , at the point D , make the angle EDF equal to the given angle A ; F then take DG - B ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole